Enzyme kinetics - Wikipedia

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<span class="vector-toc-numb">2</span> <span>Enzyme assays</span> </div> </a> <ul id="toc-Enzyme_assays-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Single-substrate_reactions" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Single-substrate_reactions"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Single-substrate reactions</span> </div> </a> <button aria-controls="toc-Single-substrate_reactions-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Single-substrate reactions subsection</span> </button> <ul id="toc-Single-substrate_reactions-sublist" class="vector-toc-list"> <li id="toc-Michaelis–Menten_kinetics" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Michaelis–Menten_kinetics"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Michaelis–Menten kinetics</span> </div> </a> <ul id="toc-Michaelis–Menten_kinetics-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Direct_use_of_the_Michaelis–Menten_equation_for_time_course_kinetic_analysis" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Direct_use_of_the_Michaelis–Menten_equation_for_time_course_kinetic_analysis"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2</span> <span>Direct use of the Michaelis–Menten equation for time course kinetic analysis</span> </div> </a> <ul id="toc-Direct_use_of_the_Michaelis–Menten_equation_for_time_course_kinetic_analysis-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Linear_plots_of_the_Michaelis–Menten_equation" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Linear_plots_of_the_Michaelis–Menten_equation"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.3</span> <span>Linear plots of the Michaelis–Menten equation</span> </div> </a> <ul id="toc-Linear_plots_of_the_Michaelis–Menten_equation-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Practical_significance_of_kinetic_constants" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Practical_significance_of_kinetic_constants"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.4</span> <span>Practical significance of kinetic constants</span> </div> </a> <ul id="toc-Practical_significance_of_kinetic_constants-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Michaelis–Menten_kinetics_with_intermediate" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Michaelis–Menten_kinetics_with_intermediate"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.5</span> <span>Michaelis–Menten kinetics with intermediate</span> </div> </a> <ul id="toc-Michaelis–Menten_kinetics_with_intermediate-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Multi-substrate_reactions" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Multi-substrate_reactions"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Multi-substrate reactions</span> </div> </a> <button aria-controls="toc-Multi-substrate_reactions-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Multi-substrate reactions subsection</span> </button> <ul id="toc-Multi-substrate_reactions-sublist" class="vector-toc-list"> <li id="toc-Ternary-complex_mechanisms" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Ternary-complex_mechanisms"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1</span> <span>Ternary-complex mechanisms</span> </div> </a> <ul id="toc-Ternary-complex_mechanisms-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Ping–pong_mechanisms" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Ping–pong_mechanisms"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2</span> <span>Ping–pong mechanisms</span> </div> </a> <ul id="toc-Ping–pong_mechanisms-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Reversible_catalysis_and_the_Haldane_equation" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Reversible_catalysis_and_the_Haldane_equation"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Reversible catalysis and the Haldane equation</span> </div> </a> <ul id="toc-Reversible_catalysis_and_the_Haldane_equation-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Non-Michaelis–Menten_kinetics" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Non-Michaelis–Menten_kinetics"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Non-Michaelis–Menten kinetics</span> </div> </a> <ul id="toc-Non-Michaelis–Menten_kinetics-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Pre-steady-state_kinetics" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Pre-steady-state_kinetics"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Pre-steady-state kinetics</span> </div> </a> <ul id="toc-Pre-steady-state_kinetics-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Chemical_mechanism" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Chemical_mechanism"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Chemical mechanism</span> </div> </a> <ul id="toc-Chemical_mechanism-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Enzyme_inhibition_and_activation" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Enzyme_inhibition_and_activation"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>Enzyme inhibition and activation</span> </div> </a> <button aria-controls="toc-Enzyme_inhibition_and_activation-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Enzyme inhibition and activation subsection</span> </button> <ul id="toc-Enzyme_inhibition_and_activation-sublist" class="vector-toc-list"> <li id="toc-Reversible_inhibitors" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Reversible_inhibitors"> <div class="vector-toc-text"> <span class="vector-toc-numb">9.1</span> <span>Reversible inhibitors</span> </div> </a> <ul id="toc-Reversible_inhibitors-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Irreversible_inhibitors" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Irreversible_inhibitors"> <div class="vector-toc-text"> <span class="vector-toc-numb">9.2</span> <span>Irreversible inhibitors</span> </div> </a> <ul id="toc-Irreversible_inhibitors-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Philosophical_discourse_on_reversibility_and_irreversibility_of_inhibition" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Philosophical_discourse_on_reversibility_and_irreversibility_of_inhibition"> <div class="vector-toc-text"> <span class="vector-toc-numb">9.3</span> <span>Philosophical discourse on reversibility and irreversibility of inhibition</span> </div> </a> <ul id="toc-Philosophical_discourse_on_reversibility_and_irreversibility_of_inhibition-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Mechanisms_of_catalysis" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Mechanisms_of_catalysis"> <div class="vector-toc-text"> <span class="vector-toc-numb">10</span> <span>Mechanisms of catalysis</span> </div> </a> <ul id="toc-Mechanisms_of_catalysis-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-History" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#History"> <div class="vector-toc-text"> <span class="vector-toc-numb">11</span> <span>History</span> </div> </a> <ul id="toc-History-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Software" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Software"> <div class="vector-toc-text"> <span class="vector-toc-numb">12</span> <span>Software</span> </div> </a> <ul id="toc-Software-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">13</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Footnotes" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Footnotes"> <div class="vector-toc-text"> <span class="vector-toc-numb">14</span> <span>Footnotes</span> </div> </a> <ul id="toc-Footnotes-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">15</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Further_reading" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Further_reading"> <div class="vector-toc-text"> <span class="vector-toc-numb">16</span> <span>Further reading</span> </div> </a> <ul id="toc-Further_reading-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">17</span> <span>External links</span> </div> </a> <ul id="toc-External_links-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Toggle the table of contents</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Enzyme kinetics</span></h1> <div id="p-lang-btn" class="vector-dropdown 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Available in 32 languages" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-32" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">32 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%AD%D8%B1%D9%83%D9%8A%D8%A7%D8%AA_%D8%A7%D9%84%D8%A5%D9%86%D8%B2%D9%8A%D9%85" title="حركيات الإنزيم – Arabic" lang="ar" hreflang="ar" data-title="حركيات الإنزيم" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Cin%C3%A9tica_enzim%C3%A1tica" title="Cinética enzimática – Asturian" lang="ast" hreflang="ast" data-title="Cinética enzimática" data-language-autonym="Asturianu" data-language-local-name="Asturian" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Kinetika_enzima" title="Kinetika enzima – Bosnian" lang="bs" hreflang="bs" data-title="Kinetika enzima" data-language-autonym="Bosanski" data-language-local-name="Bosnian" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Cin%C3%A8tica_enzim%C3%A0tica" title="Cinètica enzimàtica – Catalan" lang="ca" hreflang="ca" data-title="Cinètica enzimàtica" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Enzymatick%C3%A1_kinetika" title="Enzymatická kinetika – Czech" lang="cs" hreflang="cs" data-title="Enzymatická kinetika" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Enzymkinetik" title="Enzymkinetik – Danish" lang="da" hreflang="da" data-title="Enzymkinetik" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Enzymkinetik" title="Enzymkinetik – German" lang="de" hreflang="de" data-title="Enzymkinetik" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Ens%C3%BC%C3%BCmikineetika" title="Ensüümikineetika – Estonian" lang="et" hreflang="et" data-title="Ensüümikineetika" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-es badge-Q17437796 badge-featuredarticle mw-list-item" title="featured article badge"><a href="https://es.wikipedia.org/wiki/Cin%C3%A9tica_enzim%C3%A1tica" title="Cinética enzimática – Spanish" lang="es" hreflang="es" data-title="Cinética enzimática" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Entzimen_zinetika" title="Entzimen zinetika – Basque" lang="eu" hreflang="eu" data-title="Entzimen zinetika" data-language-autonym="Euskara" data-language-local-name="Basque" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%B3%DB%8C%D9%86%D8%AA%DB%8C%DA%A9_%D8%A2%D9%86%D8%B2%DB%8C%D9%85%DB%8C" title="سینتیک آنزیمی – Persian" lang="fa" hreflang="fa" data-title="سینتیک آنزیمی" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Cin%C3%A9tique_enzymatique" title="Cinétique enzymatique – French" lang="fr" hreflang="fr" data-title="Cinétique enzymatique" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Cin%C3%A9tica_encim%C3%A1tica" title="Cinética encimática – Galician" lang="gl" hreflang="gl" data-title="Cinética encimática" data-language-autonym="Galego" data-language-local-name="Galician" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%ED%9A%A8%EC%86%8C_%EB%B0%98%EC%9D%91%EC%86%8D%EB%8F%84%EB%A1%A0" title="효소 반응속도론 – Korean" lang="ko" hreflang="ko" data-title="효소 반응속도론" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%8F%E0%A4%82%E0%A4%9C%E0%A4%BE%E0%A4%87%E0%A4%AE_%E0%A4%95%E0%A5%88%E0%A4%A8%E0%A5%87%E0%A4%9F%E0%A5%80%E0%A4%95%E0%A5%8D%E0%A4%B8" title="एंजाइम कैनेटीक्स – Hindi" lang="hi" hreflang="hi" data-title="एंजाइम कैनेटीक्स" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Kinetika_enzim" title="Kinetika enzim – Indonesian" lang="id" hreflang="id" data-title="Kinetika enzim" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%A7%D7%99%D7%A0%D7%98%D7%99%D7%A7%D7%94_%D7%90%D7%A0%D7%96%D7%99%D7%9E%D7%98%D7%99%D7%AA" title="קינטיקה אנזימטית – Hebrew" lang="he" hreflang="he" data-title="קינטיקה אנזימטית" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-kn mw-list-item"><a href="https://kn.wikipedia.org/wiki/%E0%B2%95%E0%B2%BF%E0%B2%A3%E0%B3%8D%E0%B2%B5_%E0%B2%9A%E0%B2%B2%E0%B2%A8%E0%B2%B6%E0%B2%BE%E0%B2%B8%E0%B3%8D%E0%B2%A4%E0%B3%8D%E0%B2%B0" title="ಕಿಣ್ವ ಚಲನಶಾಸ್ತ್ರ – Kannada" lang="kn" hreflang="kn" data-title="ಕಿಣ್ವ ಚಲನಶಾಸ್ತ್ರ" data-language-autonym="ಕನ್ನಡ" data-language-local-name="Kannada" class="interlanguage-link-target"><span>ಕನ್ನಡ</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Enzimkinetika" title="Enzimkinetika – Hungarian" lang="hu" hreflang="hu" data-title="Enzimkinetika" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Enzymkinetiek" title="Enzymkinetiek – Dutch" lang="nl" hreflang="nl" data-title="Enzymkinetiek" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E9%85%B5%E7%B4%A0%E5%8F%8D%E5%BF%9C%E9%80%9F%E5%BA%A6%E8%AB%96" title="酵素反応速度論 – Japanese" lang="ja" hreflang="ja" data-title="酵素反応速度論" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Wikiprojekt:T%C5%82umaczenie_artyku%C5%82%C3%B3w/Kinetyka_enzymatyczna" title="Wikiprojekt:Tłumaczenie artykułów/Kinetyka enzymatyczna – Polish" lang="pl" hreflang="pl" data-title="Wikiprojekt:Tłumaczenie artykułów/Kinetyka enzymatyczna" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Cin%C3%A9tica_enzim%C3%A1tica" title="Cinética enzimática – Portuguese" lang="pt" hreflang="pt" data-title="Cinética enzimática" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Cinetic%C4%83_enzimatic%C4%83" title="Cinetică enzimatică – Romanian" lang="ro" hreflang="ro" data-title="Cinetică enzimatică" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%A4%D0%B5%D1%80%D0%BC%D0%B5%D0%BD%D1%82%D0%B0%D1%82%D0%B8%D0%B2%D0%BD%D0%B0%D1%8F_%D0%BA%D0%B8%D0%BD%D0%B5%D1%82%D0%B8%D0%BA%D0%B0" title="Ферментативная кинетика – Russian" lang="ru" hreflang="ru" data-title="Ферментативная кинетика" 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id="mw-indicator-featured-star" class="mw-indicator"><div class="mw-parser-output"><span typeof="mw:File"><a href="/wiki/Wikipedia:Featured_articles*" title="This is a featured article. Click here for more information."><img alt="Featured article" src="//upload.wikimedia.org/wikipedia/en/thumb/e/e7/Cscr-featured.svg/20px-Cscr-featured.svg.png" decoding="async" width="20" height="19" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/e/e7/Cscr-featured.svg/30px-Cscr-featured.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/e/e7/Cscr-featured.svg/40px-Cscr-featured.svg.png 2x" data-file-width="466" data-file-height="443" /></a></span></div></div> </div> <div id="siteSub" class="noprint">From Wikipedia, the free encyclopedia</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Study of biochemical reaction rates catalysed by an enzyme</div> <p class="mw-empty-elt"> </p> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:EcDHFR_raytraced.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6d/EcDHFR_raytraced.png/260px-EcDHFR_raytraced.png" decoding="async" width="260" height="347" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6d/EcDHFR_raytraced.png/390px-EcDHFR_raytraced.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6d/EcDHFR_raytraced.png/520px-EcDHFR_raytraced.png 2x" data-file-width="600" data-file-height="800" /></a><figcaption><a href="/wiki/Dihydrofolate_reductase" title="Dihydrofolate reductase">Dihydrofolate reductase</a> from <i><a href="/wiki/Escherichia_coli" title="Escherichia coli">E. coli</a></i> with its two substrates <a href="/wiki/Dihydrofolic_acid" title="Dihydrofolic acid">dihydrofolate</a> (right) and <a href="/wiki/Nicotinamide_adenine_dinucleotide_phosphate" title="Nicotinamide adenine dinucleotide phosphate">NADPH</a> (left), bound in the active site. The protein is shown as a <a href="/wiki/Ribbon_diagram" title="Ribbon diagram">ribbon diagram</a>, with alpha helices in red, beta sheathes in yellow and loops in blue. (<span class="plainlinks"><a href="/wiki/Protein_Data_Bank" title="Protein Data Bank">PDB</a>: <a rel="nofollow" class="external text" href="https://www.rcsb.org/structure/7DFR">7DFR</a></span>)</figcaption></figure> <p><b>Enzyme kinetics</b> is the study of the rates of <a href="/wiki/Enzyme_catalysis" title="Enzyme catalysis">enzyme-catalysed</a> <a href="/wiki/Chemical_reaction" title="Chemical reaction">chemical reactions</a>. In enzyme kinetics, the <a href="/wiki/Reaction_rate" title="Reaction rate">reaction rate</a> is measured and the effects of varying the conditions of the reaction are investigated. Studying an enzyme's <a href="/wiki/Chemical_kinetics" title="Chemical kinetics">kinetics</a> in this way can reveal the catalytic mechanism of this enzyme, its role in <a href="/wiki/Metabolism" title="Metabolism">metabolism</a>, how its activity is controlled, and how a <a href="/wiki/Drug" title="Drug">drug</a> or a modifier (<a href="/wiki/Enzyme_inhibitor" title="Enzyme inhibitor">inhibitor</a> or <a href="/wiki/Enzyme_activator" title="Enzyme activator">activator</a>) might affect the rate. </p><p>An enzyme (E) is a <a href="/wiki/Protein" title="Protein">protein</a> <a href="/wiki/Molecule" title="Molecule">molecule</a> that serves as a biological catalyst to facilitate and accelerate a chemical reaction in the body. It does this through binding of another molecule, its <a href="/wiki/Substrate_(biochemistry)" class="mw-redirect" title="Substrate (biochemistry)">substrate</a> (S), which the enzyme acts upon to form the desired product. The substrate binds to the <a href="/wiki/Active_site" title="Active site">active site</a> of the enzyme to produce an enzyme-substrate complex ES, and is transformed into an enzyme-product complex EP and from there to product P, via a <a href="/wiki/Transition_state" title="Transition state">transition state</a> ES*. The series of steps is known as the <a href="/wiki/Enzyme_catalysis" title="Enzyme catalysis">mechanism</a>: </p> <dl><dd>E + S ⇄ ES ⇄ ES* ⇄ EP ⇄ E + P</dd></dl> <p>This example assumes the simplest case of a reaction with one substrate and one product. Such cases exist: for example, a <a href="/wiki/Mutase" title="Mutase">mutase</a> such as <a href="/wiki/Phosphoglucomutase" title="Phosphoglucomutase">phosphoglucomutase</a> catalyses the transfer of a phosphate group from one position to another, and <a href="/wiki/Isomerase" title="Isomerase">isomerase</a> is a more general term for an enzyme that catalyses any one-substrate one-product reaction, such as <a href="/wiki/Triosephosphateisomerase" class="mw-redirect" title="Triosephosphateisomerase">triosephosphate isomerase</a>. However, such enzymes are not very common, and are heavily outnumbered by enzymes that catalyse two-substrate two-product reactions: these include, for example, the NAD-dependent <a href="/wiki/Dehydrogenase" title="Dehydrogenase">dehydrogenases</a> such as <a href="/wiki/Alcohol_dehydrogenase" title="Alcohol dehydrogenase">alcohol dehydrogenase</a>, which catalyses the oxidation of ethanol by NAD<sup>+</sup>. Reactions with three or four substrates or products are less common, but they exist. There is no necessity for the number of products to be equal to the number of substrates; for example, <a href="/wiki/Glyceraldehyde_3-phosphate_dehydrogenase" title="Glyceraldehyde 3-phosphate dehydrogenase">glyceraldehyde 3-phosphate dehydrogenase</a> has three substrates and two products. </p><p>When enzymes bind multiple substrates, such as <a href="/wiki/Dihydrofolate_reductase" title="Dihydrofolate reductase">dihydrofolate reductase</a> (shown right), enzyme kinetics can also show the sequence in which these substrates bind and the sequence in which products are released. An example of enzymes that bind a single substrate and release multiple products are <a href="/wiki/Protease" title="Protease">proteases</a>, which cleave one protein substrate into two polypeptide products. Others join two substrates together, such as <a href="/wiki/DNA_polymerase" title="DNA polymerase">DNA polymerase</a> linking a <a href="/wiki/Nucleotide" title="Nucleotide">nucleotide</a> to <a href="/wiki/DNA" title="DNA">DNA</a>. Although these mechanisms are often a complex series of steps, there is typically one <i>rate-determining step</i> that determines the overall kinetics. This <a href="/wiki/Rate-determining_step" title="Rate-determining step">rate-determining step</a> may be a chemical reaction or a <a href="/wiki/Conformational_isomerism" title="Conformational isomerism">conformational</a> change of the enzyme or substrates, such as those involved in the release of product(s) from the enzyme. </p><p>Knowledge of the <a href="/wiki/Protein_structure" title="Protein structure">enzyme's structure</a> is helpful in interpreting kinetic data. For example, the structure can suggest how substrates and products bind during catalysis; what changes occur during the reaction; and even the role of particular <a href="/wiki/Amino_acid" title="Amino acid">amino acid</a> residues in the mechanism. Some enzymes change shape significantly during the mechanism; in such cases, it is helpful to determine the enzyme structure with and without bound substrate analogues that do not undergo the enzymatic reaction. </p><p>Not all biological catalysts are protein enzymes: <a href="/wiki/RNA" title="RNA">RNA</a>-based catalysts such as <a href="/wiki/Ribozymes" class="mw-redirect" title="Ribozymes">ribozymes</a> and <a href="/wiki/Ribosomes" class="mw-redirect" title="Ribosomes">ribosomes</a> are essential to many cellular functions, such as <a href="/wiki/Splicing_(genetics)" class="mw-redirect" title="Splicing (genetics)">RNA splicing</a> and <a href="/wiki/Translation_(biology)" title="Translation (biology)">translation</a>. The main difference between ribozymes and enzymes is that RNA catalysts are composed of nucleotides, whereas enzymes are composed of amino acids. Ribozymes also perform a more limited set of reactions, although their <a href="/wiki/Reaction_mechanism" title="Reaction mechanism">reaction mechanisms</a> and kinetics can be analysed and classified by the same methods. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="General_principles">General principles</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Enzyme_kinetics&action=edit&section=1" title="Edit section: General principles"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:KinEnzymo(en).svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/09/KinEnzymo%28en%29.svg/300px-KinEnzymo%28en%29.svg.png" decoding="async" width="300" height="167" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/09/KinEnzymo%28en%29.svg/450px-KinEnzymo%28en%29.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/09/KinEnzymo%28en%29.svg/600px-KinEnzymo%28en%29.svg.png 2x" data-file-width="990" data-file-height="550" /></a><figcaption>As larger amounts of <a href="/wiki/Substrate_(biochemistry)" class="mw-redirect" title="Substrate (biochemistry)">substrate</a> are added to a reaction, the available enzyme <a href="/wiki/Binding_site" title="Binding site">binding sites</a> become filled to the limit of <a href="/wiki/Michaelis-Menten_kinetics" class="mw-redirect" title="Michaelis-Menten kinetics"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V_{\max }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mo movablelimits="true" form="prefix">max</mo> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V_{\max }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ee5a8472bc1a42aac13cd279661c00b5a2d2ec84" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.646ex; height:2.509ex;" alt="{\displaystyle V_{\max }}"></span></a>. Beyond this limit the enzyme is saturated with substrate and the reaction rate ceases to increase.</figcaption></figure> <p>The reaction catalysed by an enzyme uses exactly the same reactants and produces exactly the same products as the uncatalysed reaction. Like other <a href="/wiki/Catalysts" class="mw-redirect" title="Catalysts">catalysts</a>, enzymes do not alter the position of <a href="/wiki/Chemical_equilibrium" title="Chemical equilibrium">equilibrium</a> between substrates and products.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> However, unlike uncatalysed chemical reactions, enzyme-catalysed reactions display saturation kinetics. For a given enzyme concentration and for relatively low substrate concentrations, the reaction rate increases linearly with substrate concentration; the enzyme molecules are largely free to catalyse the reaction, and increasing substrate concentration means an increasing rate at which the enzyme and substrate molecules encounter one another. However, at relatively high substrate concentrations, the reaction rate <a href="/wiki/Asymptote" title="Asymptote">asymptotically</a> approaches the theoretical maximum; the enzyme active sites are almost all occupied by substrates resulting in saturation, and the reaction rate is determined by the intrinsic turnover rate of the enzyme.<sup id="cite_ref-Fromm_H.J._2012_2-0" class="reference"><a href="#cite_note-Fromm_H.J._2012-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> The substrate concentration midway between these two limiting cases is denoted by <i>K</i><sub>M</sub>. Thus, <i>K</i><sub>M</sub> is the substrate concentration at which the reaction velocity is half of the maximum velocity.<sup id="cite_ref-Fromm_H.J._2012_2-1" class="reference"><a href="#cite_note-Fromm_H.J._2012-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p><p>The two important properties of enzyme kinetics are how easily the enzyme can be saturated with a substrate, and the maximum rate it can achieve. Knowing these properties suggests what an enzyme might do in the cell and can show how the enzyme will respond to changes in these conditions. </p> <div class="mw-heading mw-heading2"><h2 id="Enzyme_assays">Enzyme assays</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Enzyme_kinetics&action=edit&section=2" title="Edit section: Enzyme assays"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Enzyme_assay" title="Enzyme assay">Enzyme assay</a></div> <figure class="mw-halign-left" typeof="mw:File/Thumb"><a href="/wiki/File:Enzyme_progress_curve.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/86/Enzyme_progress_curve.svg/250px-Enzyme_progress_curve.svg.png" decoding="async" width="250" height="195" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/86/Enzyme_progress_curve.svg/375px-Enzyme_progress_curve.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/86/Enzyme_progress_curve.svg/500px-Enzyme_progress_curve.svg.png 2x" data-file-width="467" data-file-height="364" /></a><figcaption>Progress curve for an enzyme reaction. The slope in the initial rate period is the <b>initial rate of reaction</b> <i>v</i>. The <a href="/wiki/Michaelis%E2%80%93Menten_kinetics" title="Michaelis–Menten kinetics">Michaelis–Menten equation</a> describes how this slope varies with the concentration of substrate.</figcaption></figure> <p><a href="/wiki/Enzyme_assay" title="Enzyme assay">Enzyme assays</a> are laboratory procedures that measure the rate of enzyme reactions. Since enzymes are not consumed by the reactions they catalyse, enzyme assays usually follow changes in the concentration of either substrates or products to measure the rate of reaction. There are many methods of measurement. <a href="/wiki/Ultraviolet-visible_spectroscopy" class="mw-redirect" title="Ultraviolet-visible spectroscopy">Spectrophotometric</a> assays observe the change in the <a href="/wiki/Absorbance" title="Absorbance">absorbance</a> of light between products and reactants; radiometric assays involve the incorporation or release of <a href="/wiki/Radioactivity" class="mw-redirect" title="Radioactivity">radioactivity</a> to measure the amount of product made over time. Spectrophotometric assays are most convenient since they allow the rate of the reaction to be measured continuously. Although radiometric assays require the removal and counting of samples (i.e., they are discontinuous assays) they are usually extremely sensitive and can measure very low levels of enzyme activity.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> An analogous approach is to use <a href="/wiki/Mass_spectrometry" title="Mass spectrometry">mass spectrometry</a> to monitor the incorporation or release of <a href="/wiki/Stable_isotope" class="mw-redirect" title="Stable isotope">stable isotopes</a> as the substrate is converted into product. Occasionally, an assay fails and approaches are essential to resurrect a failed assay. </p><p>The most sensitive enzyme assays use <a href="/wiki/Laser" title="Laser">lasers</a> focused through a <a href="/wiki/Microscope" title="Microscope">microscope</a> to observe changes in single enzyme molecules as they catalyse their reactions. These measurements either use changes in the <a href="/wiki/Fluorescence" title="Fluorescence">fluorescence</a> of <a href="/wiki/Cofactor_(biochemistry)" title="Cofactor (biochemistry)">cofactors</a> during an enzyme's reaction mechanism, or of <a href="/wiki/Fluorescent_dyes" class="mw-redirect" title="Fluorescent dyes">fluorescent dyes</a> added onto specific sites of the <a href="/wiki/Protein" title="Protein">protein</a> to report movements that occur during catalysis.<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> These studies provide a new view of the kinetics and dynamics of single enzymes, as opposed to traditional enzyme kinetics, which observes the average behaviour of populations of millions of enzyme molecules.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </p><p>An example progress curve for an enzyme assay is shown above. The enzyme produces product at an initial rate that is approximately linear for a short period after the start of the reaction. As the reaction proceeds and substrate is consumed, the rate continuously slows (so long as the substrate is not still at saturating levels). To measure the initial (and maximal) rate, enzyme assays are typically carried out while the reaction has progressed only a few percent towards total completion. The length of the initial rate period depends on the assay conditions and can range from milliseconds to hours. However, equipment for rapidly mixing liquids allows fast kinetic measurements at initial rates of less than one second.<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> These very rapid assays are essential for measuring pre-steady-state kinetics, which are discussed below. </p><p>Most enzyme kinetics studies concentrate on this initial, approximately linear part of enzyme reactions. However, it is also possible to measure the complete reaction curve and fit this data to a non-linear <a href="/wiki/Rate_equation" title="Rate equation">rate equation</a>. This way of measuring enzyme reactions is called progress-curve analysis.<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> This approach is useful as an alternative to <a href="/w/index.php?title=Rapid_kinetics&action=edit&redlink=1" class="new" title="Rapid kinetics (page does not exist)">rapid kinetics</a> when the initial rate is too fast to measure accurately. </p><p>The <a href="/wiki/Standards_for_Reporting_Enzymology_Data" title="Standards for Reporting Enzymology Data">Standards for Reporting Enzymology Data</a> Guidelines provide minimum information required to comprehensively report kinetic and equilibrium data from investigations of enzyme activities including corresponding experimental conditions. The guidelines have been developed to report functional enzyme data with rigor and robustness. </p> <div class="mw-heading mw-heading2"><h2 id="Single-substrate_reactions">Single-substrate reactions</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Enzyme_kinetics&action=edit&section=3" title="Edit section: Single-substrate reactions"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Enzymes with single-substrate mechanisms include <a href="/wiki/Isomerase" title="Isomerase">isomerases</a> such as <a href="/wiki/Triosephosphateisomerase" class="mw-redirect" title="Triosephosphateisomerase">triosephosphateisomerase</a> or <a href="/wiki/Bisphosphoglycerate_mutase" title="Bisphosphoglycerate mutase">bisphosphoglycerate mutase</a>, intramolecular <a href="/wiki/Lyase" title="Lyase">lyases</a> such as <a href="/wiki/Adenylate_cyclase" class="mw-redirect" title="Adenylate cyclase">adenylate cyclase</a> and the <a href="/wiki/Hammerhead_ribozyme" title="Hammerhead ribozyme">hammerhead ribozyme</a>, an RNA lyase.<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> However, some enzymes that only have a single substrate do not fall into this category of mechanisms. <a href="/wiki/Catalase" title="Catalase">Catalase</a> is an example of this, as the enzyme reacts with a first molecule of <a href="/wiki/Hydrogen_peroxide" title="Hydrogen peroxide">hydrogen peroxide</a> substrate, becomes oxidised and is then reduced by a second molecule of substrate. Although a single substrate is involved, the existence of a modified enzyme intermediate means that the mechanism of catalase is actually a ping–pong mechanism, a type of mechanism that is discussed in the <i>Multi-substrate reactions</i> section below. </p> <div class="mw-heading mw-heading3"><h3 id="Michaelis–Menten_kinetics"><span id="Michaelis.E2.80.93Menten_kinetics"></span>Michaelis–Menten kinetics</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Enzyme_kinetics&action=edit&section=4" title="Edit section: Michaelis–Menten kinetics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1237032888/mw-parser-output/.tmulti">.mw-parser-output .tmulti .multiimageinner{display:flex;flex-direction:column}.mw-parser-output .tmulti .trow{display:flex;flex-direction:row;clear:left;flex-wrap:wrap;width:100%;box-sizing:border-box}.mw-parser-output .tmulti .tsingle{margin:1px;float:left}.mw-parser-output .tmulti .theader{clear:both;font-weight:bold;text-align:center;align-self:center;background-color:transparent;width:100%}.mw-parser-output .tmulti .thumbcaption{background-color:transparent}.mw-parser-output .tmulti .text-align-left{text-align:left}.mw-parser-output .tmulti .text-align-right{text-align:right}.mw-parser-output .tmulti .text-align-center{text-align:center}@media all and (max-width:720px){.mw-parser-output .tmulti .thumbinner{width:100%!important;box-sizing:border-box;max-width:none!important;align-items:center}.mw-parser-output .tmulti .trow{justify-content:center}.mw-parser-output .tmulti .tsingle{float:none!important;max-width:100%!important;box-sizing:border-box;text-align:center}.mw-parser-output .tmulti .tsingle .thumbcaption{text-align:left}.mw-parser-output .tmulti .trow>.thumbcaption{text-align:center}}@media screen{html.skin-theme-clientpref-night .mw-parser-output .tmulti .multiimageinner img{background-color:white}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .tmulti .multiimageinner img{background-color:white}}</style><div class="thumb tmulti tright"><div class="thumbinner multiimageinner" style="width:329px;max-width:329px"><div class="trow"><div class="tsingle" style="width:327px;max-width:327px"><div class="thumbimage"><span typeof="mw:File"><a href="/wiki/File:Enzyme_mechanism_2.svg" class="mw-file-description"><img alt="Schematic reaction diagrams for uncatalzyed (Substrate to Product) and catalyzed (Enzyme + Substrate to Enzyme/Substrate complex to Enzyme + Product)" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/69/Enzyme_mechanism_2.svg/325px-Enzyme_mechanism_2.svg.png" decoding="async" width="325" height="102" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/69/Enzyme_mechanism_2.svg/488px-Enzyme_mechanism_2.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/69/Enzyme_mechanism_2.svg/650px-Enzyme_mechanism_2.svg.png 2x" data-file-width="400" data-file-height="125" /></a></span></div><div class="thumbcaption">A chemical reaction mechanism with or without <a href="/wiki/Enzyme_catalysis" title="Enzyme catalysis">enzyme catalysis</a>. The enzyme (E) binds <a href="/wiki/Substrate_(chemistry)" title="Substrate (chemistry)">substrate</a> (S) to produce <a href="/wiki/Product_(chemistry)" title="Product (chemistry)">product</a> (P).</div></div></div><div class="trow"><div class="tsingle" style="width:327px;max-width:327px"><div class="thumbimage"><span typeof="mw:File"><a href="/wiki/File:Michaelis_Menten_curve_2.svg" class="mw-file-description"><img alt="A two dimensional plot of substrate concentration (x axis) vs. reaction rate (y axis). The shape of the curve is hyperbolic. The rate of the reaction is zero at zero concentration of substrate and the rate asymptotically reaches a maximum at high substrate concentration." src="//upload.wikimedia.org/wikipedia/commons/thumb/8/83/Michaelis_Menten_curve_2.svg/325px-Michaelis_Menten_curve_2.svg.png" decoding="async" width="325" height="139" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/83/Michaelis_Menten_curve_2.svg/488px-Michaelis_Menten_curve_2.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/83/Michaelis_Menten_curve_2.svg/650px-Michaelis_Menten_curve_2.svg.png 2x" data-file-width="1200" data-file-height="512" /></a></span></div><div class="thumbcaption"><a href="/wiki/Michaelis%E2%80%93Menten_kinetics" title="Michaelis–Menten kinetics">Saturation curve</a> for an enzyme reaction showing the relation between the substrate concentration and reaction rate.</div></div></div></div></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Michaelis%E2%80%93Menten_kinetics" title="Michaelis–Menten kinetics">Michaelis–Menten kinetics</a></div> <p>As enzyme-catalysed reactions are saturable, their rate of catalysis does not show a linear response to increasing substrate. If the initial rate of the reaction is measured over a range of substrate concentrations (denoted as [S]), the initial reaction rate (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v_{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/60faad24775635f4722ccc438093dbbfe05f34ae" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.182ex; height:2.009ex;" alt="{\displaystyle v_{0}}"></span>) increases as [S] increases, as shown on the right. However, as [S] gets higher, the enzyme becomes saturated with substrate and the initial rate reaches <i>V</i><sub>max</sub>, the enzyme's maximum rate. </p><p>The <a href="/wiki/Michaelis%E2%80%93Menten_kinetics" title="Michaelis–Menten kinetics">Michaelis–Menten kinetic model of a single-substrate reaction</a> is shown on the right. There is an initial <a href="/wiki/Chemical_kinetics" title="Chemical kinetics">bimolecular reaction</a> between the enzyme E and substrate S to form the enzyme–substrate complex ES. The rate of enzymatic reaction increases with the increase of the substrate concentration up to a certain level called V<sub>max</sub>; at V<sub>max</sub>, increase in substrate concentration does not cause any increase in reaction rate as there is no more enzyme (E) available for reacting with substrate (S). Here, the rate of reaction becomes dependent on the ES complex and the reaction becomes a <a href="/wiki/Chemical_kinetics" title="Chemical kinetics">unimolecular reaction</a> with an order of zero. Though the enzymatic mechanism for the <a href="/wiki/Chemical_kinetics" title="Chemical kinetics">unimolecular reaction</a> <small><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\ce {ES ->[k_{cat}] E + P}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtext>ES</mtext> <mrow class="MJX-TeXAtom-REL"> <mover> <mo>→</mo> <mpadded width="+0.611em" lspace="0.278em" voffset=".15em"> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> <mi>a</mi> <mi>t</mi> </mrow> </msub> </mpadded> </mover> </mrow> <mtext>E</mtext> <mo>+</mo> <mtext>P</mtext> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\ce {ES ->[k_{cat}] E + P}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/299f3433b9ca64a864deef13f572a0127a2d14e0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; margin-top: -0.396ex; width:14.282ex; height:4.009ex;" alt="{\displaystyle {\ce {ES ->[k_{cat}] E + P}}}"></span></small> can be quite complex, there is typically one rate-determining enzymatic step that allows this reaction to be modelled as a single catalytic step with an apparent unimolecular rate constant <a href="/wiki/Turnover_number" title="Turnover number"><i>k</i><sub>cat</sub></a>. If the reaction path proceeds over one or several intermediates, <i>k</i><sub>cat</sub> will be a function of several elementary rate constants, whereas in the simplest case of a single elementary reaction (e.g. no intermediates) it will be identical to the elementary unimolecular rate constant <i>k</i><sub>2</sub>. The apparent unimolecular rate constant <i>k</i><sub>cat</sub> is also called <a href="/wiki/Turnover_number" title="Turnover number">turnover number</a>, and denotes the maximum number of enzymatic reactions catalysed per second. </p><p>The <a href="/wiki/Michaelis%E2%80%93Menten_kinetics" title="Michaelis–Menten kinetics">Michaelis–Menten equation</a><sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> describes how the (initial) reaction rate <i>v</i><sub>0</sub> depends on the position of the substrate-binding <a href="/wiki/Chemical_equilibrium" title="Chemical equilibrium">equilibrium</a> and the rate constant <i>k</i><sub>2</sub>. </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v_{0}={\frac {V_{\max }[{\ce {S}}]}{K_{M}+[{\ce {S}}]}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mo movablelimits="true" form="prefix">max</mo> </mrow> </msub> <mo stretchy="false">[</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>S</mtext> </mrow> <mo stretchy="false">]</mo> </mrow> <mrow> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>M</mi> </mrow> </msub> <mo>+</mo> <mo stretchy="false">[</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>S</mtext> </mrow> <mo stretchy="false">]</mo> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v_{0}={\frac {V_{\max }[{\ce {S}}]}{K_{M}+[{\ce {S}}]}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8f2f1d1e9d417b925f380340d6d3581d4006672f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:15.475ex; height:6.509ex;" alt="{\displaystyle v_{0}={\frac {V_{\max }[{\ce {S}}]}{K_{M}+[{\ce {S}}]}}}"></span>    <i>(Michaelis–Menten equation)</i></dd></dl> <p>with the constants </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{aligned}K_{M}\ &{\stackrel {\mathrm {def} }{=}}\ {\frac {k_{2}+k_{-1}}{k_{1}}}\approx K_{D}\\V_{\max }\ &{\stackrel {\mathrm {def} }{=}}\ k_{cat}{\ce {[E]}}_{tot}\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>M</mi> </mrow> </msub> <mtext> </mtext> </mtd> <mtd> <mi></mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-REL"> <mover> <mrow class="MJX-TeXAtom-OP MJX-fixedlimits"> <mo>=</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">f</mi> </mrow> </mrow> </mover> </mrow> </mrow> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msub> </mrow> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mfrac> </mrow> <mo>≈</mo> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>D</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mo movablelimits="true" form="prefix">max</mo> </mrow> </msub> <mtext> </mtext> </mtd> <mtd> <mi></mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-REL"> <mover> <mrow class="MJX-TeXAtom-OP MJX-fixedlimits"> <mo>=</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">f</mi> </mrow> </mrow> </mover> </mrow> </mrow> <mtext> </mtext> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> <mi>a</mi> <mi>t</mi> </mrow> </msub> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">[</mo> <mtext>E</mtext> <mo stretchy="false">]</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> <mi>o</mi> <mi>t</mi> </mrow> </msub> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}K_{M}\ &{\stackrel {\mathrm {def} }{=}}\ {\frac {k_{2}+k_{-1}}{k_{1}}}\approx K_{D}\\V_{\max }\ &{\stackrel {\mathrm {def} }{=}}\ k_{cat}{\ce {[E]}}_{tot}\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1714252e04d803899ef6ad5b75c074d0f9ebc50c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.123ex; margin-bottom: -0.215ex; width:24.965ex; height:9.843ex;" alt="{\displaystyle {\begin{aligned}K_{M}\ &{\stackrel {\mathrm {def} }{=}}\ {\frac {k_{2}+k_{-1}}{k_{1}}}\approx K_{D}\\V_{\max }\ &{\stackrel {\mathrm {def} }{=}}\ k_{cat}{\ce {[E]}}_{tot}\end{aligned}}}"></span></dd></dl> <p>This Michaelis–Menten equation is the basis for most single-substrate enzyme kinetics. Two crucial assumptions underlie this equation (apart from the general assumption about the mechanism only involving no intermediate or product inhibition, and there is no <a href="/wiki/Allosteric_regulation" title="Allosteric regulation">allostericity</a> or <a href="/wiki/Cooperative_binding" title="Cooperative binding">cooperativity</a>). The first assumption is the so-called <a href="/wiki/Steady_state_(chemistry)" title="Steady state (chemistry)">quasi-steady-state assumption</a> (or pseudo-steady-state hypothesis), namely that the concentration of the substrate-bound enzyme (and hence also the unbound enzyme) changes much more slowly than those of the product and substrate and thus the change over time of the complex can be set to zero <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle d{\ce {[ES]}}/{dt}\;{\overset {!}{=}}\;0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">[</mo> <mtext>ES</mtext> <mo stretchy="false">]</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>d</mi> <mi>t</mi> </mrow> <mspace width="thickmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mover> <mo>=</mo> <mo>!</mo> </mover> </mrow> <mspace width="thickmathspace" /> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle d{\ce {[ES]}}/{dt}\;{\overset {!}{=}}\;0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0eea1ce2a30471bd05b46fe979bb4f12e365b4d5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:12.864ex; height:3.843ex;" alt="{\displaystyle d{\ce {[ES]}}/{dt}\;{\overset {!}{=}}\;0}"></span>. The second assumption is that the total enzyme concentration does not change over time, thus <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\ce {[E]}}_{\text{tot}}={\ce {[E]}}+{\ce {[ES]}}\;{\overset {!}{=}}\;{\text{const}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">[</mo> <mtext>E</mtext> <mo stretchy="false">]</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext>tot</mtext> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">[</mo> <mtext>E</mtext> <mo stretchy="false">]</mo> </mrow> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">[</mo> <mtext>ES</mtext> <mo stretchy="false">]</mo> </mrow> </mrow> <mspace width="thickmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mover> <mo>=</mo> <mo>!</mo> </mover> </mrow> <mspace width="thickmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mtext>const</mtext> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\ce {[E]}}_{\text{tot}}={\ce {[E]}}+{\ce {[ES]}}\;{\overset {!}{=}}\;{\text{const}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5c082974766078275f236f456e12426c4ea02fc8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:26.601ex; height:4.009ex;" alt="{\displaystyle {\ce {[E]}}_{\text{tot}}={\ce {[E]}}+{\ce {[ES]}}\;{\overset {!}{=}}\;{\text{const}}}"></span>. </p><p>The Michaelis constant <i>K</i><sub>M</sub> is experimentally defined as the concentration at which the rate of the enzyme reaction is half <i>V</i><sub>max</sub>, which can be verified by substituting [S] = <i>K</i><sub>M</sub> into the Michaelis–Menten equation and can also be seen graphically. If the rate-determining enzymatic step is slow compared to substrate dissociation (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle k_{2}\ll k_{-1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>≪</mo> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle k_{2}\ll k_{-1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1d9d943519e45cd086baea0024f3ef86b905dc95" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:9.424ex; height:2.509ex;" alt="{\displaystyle k_{2}\ll k_{-1}}"></span>), the Michaelis constant <i>K</i><sub>M</sub> is roughly the <a href="/wiki/Dissociation_constant" title="Dissociation constant">dissociation constant</a> <i>K</i><sub>D</sub> of the ES complex. </p><p>If <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\ce {[S]}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">[</mo> <mtext>S</mtext> <mo stretchy="false">]</mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\ce {[S]}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e5909e9989dfe9306325e8dab287928f3c984ee3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:2.586ex; height:2.843ex;" alt="{\displaystyle {\ce {[S]}}}"></span> is small compared to <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle K_{M}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>M</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle K_{M}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/14296e7a6cf6d829e6dd8bbb40421855edc4de67" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.932ex; height:2.509ex;" alt="{\displaystyle K_{M}}"></span> then the term <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle [{\ce {S}}]/(K_{M}+[{\ce {S}}])\approx [{\ce {S}}]/K_{M}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">[</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>S</mtext> </mrow> <mo stretchy="false">]</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mo stretchy="false">(</mo> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>M</mi> </mrow> </msub> <mo>+</mo> <mo stretchy="false">[</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>S</mtext> </mrow> <mo stretchy="false">]</mo> <mo stretchy="false">)</mo> <mo>≈</mo> <mo stretchy="false">[</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>S</mtext> </mrow> <mo stretchy="false">]</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>M</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle [{\ce {S}}]/(K_{M}+[{\ce {S}}])\approx [{\ce {S}}]/K_{M}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1d1befa5e00217f79ed63dc6ba5c6a15d78d5425" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:25.696ex; height:2.843ex;" alt="{\displaystyle [{\ce {S}}]/(K_{M}+[{\ce {S}}])\approx [{\ce {S}}]/K_{M}}"></span> and also very little ES complex is formed, thus <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\ce {[E]_{\rm {tot}}\approx [E]}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msubsup> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">[</mo> <mtext>E</mtext> <mo stretchy="false">]</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mtext>tot</mtext> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mspace width="0pt" height="0pt" depth=".2em" /> </mrow> </msubsup> <mo>≈</mo> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">[</mo> <mtext>E</mtext> <mo stretchy="false">]</mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\ce {[E]_{\rm {tot}}\approx [E]}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f6ccda6e543afca4e4287f635c5f1a4931ca93e1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:11.185ex; height:2.843ex;" alt="{\displaystyle {\ce {[E]_{\rm {tot}}\approx [E]}}}"></span>. Therefore, the rate of product formation is </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v_{0}\approx {\frac {k_{cat}}{K_{M}}}{\ce {[E][S]}}\qquad \qquad {\text{if }}[{\ce {S}}]\ll K_{M}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>≈</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> <mi>a</mi> <mi>t</mi> </mrow> </msub> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>M</mi> </mrow> </msub> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">[</mo> <mtext>E</mtext> <mo stretchy="false">]</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">[</mo> <mtext>S</mtext> <mo stretchy="false">]</mo> </mrow> </mrow> <mspace width="2em" /> <mspace width="2em" /> <mrow class="MJX-TeXAtom-ORD"> <mtext>if </mtext> </mrow> <mo stretchy="false">[</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>S</mtext> </mrow> <mo stretchy="false">]</mo> <mo>≪</mo> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>M</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v_{0}\approx {\frac {k_{cat}}{K_{M}}}{\ce {[E][S]}}\qquad \qquad {\text{if }}[{\ce {S}}]\ll K_{M}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/596b2c4659de250ffbd0b65c085402f9fd16735d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:36.874ex; height:5.676ex;" alt="{\displaystyle v_{0}\approx {\frac {k_{cat}}{K_{M}}}{\ce {[E][S]}}\qquad \qquad {\text{if }}[{\ce {S}}]\ll K_{M}}"></span></dd></dl> <p>Thus the product formation rate depends on the enzyme concentration as well as on the substrate concentration, the equation resembles a bimolecular reaction with a corresponding pseudo-second order rate constant <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle k_{2}/K_{M}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>M</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle k_{2}/K_{M}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5fbb1e6cbe74a78948d774119cead039ca23d146" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.36ex; height:2.843ex;" alt="{\displaystyle k_{2}/K_{M}}"></span>. This constant is a measure of <a href="/wiki/Catalytic_efficiency" class="mw-redirect" title="Catalytic efficiency">catalytic efficiency</a>. The most efficient enzymes reach a <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle k_{2}/K_{M}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>M</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle k_{2}/K_{M}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5fbb1e6cbe74a78948d774119cead039ca23d146" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.36ex; height:2.843ex;" alt="{\displaystyle k_{2}/K_{M}}"></span> in the range of <span class="texhtml">10<sup>8</sup> – 10<sup>10</sup> <a href="/wiki/Molar_concentration" title="Molar concentration">M</a><sup>−1</sup> <a href="/wiki/Second" title="Second">s</a><sup>−1</sup></span>. These enzymes are so efficient they effectively catalyse a reaction each time they encounter a substrate molecule and have thus reached an upper theoretical limit for efficiency (<a href="/wiki/Diffusion_limited_enzyme" class="mw-redirect" title="Diffusion limited enzyme">diffusion limit</a>); and are sometimes referred to as <a href="/wiki/Diffusion_limited_enzyme" class="mw-redirect" title="Diffusion limited enzyme">kinetically perfect enzymes</a>.<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> But most enzymes are far from perfect: the average values of <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle k_{2}/K_{\rm {M}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">M</mi> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle k_{2}/K_{\rm {M}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ad8370899ee9ff7938234bdcffc4bb1fdbe9f704" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.14ex; height:2.843ex;" alt="{\displaystyle k_{2}/K_{\rm {M}}}"></span> and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle k_{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle k_{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c51b4ba57ee596d8435fc4ed76703ca3a2fc444a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.265ex; height:2.509ex;" alt="{\displaystyle k_{2}}"></span> are about <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 10^{5}{\rm {s}}^{-1}{\rm {M}}^{-1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> </mrow> </msup> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">s</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msup> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">M</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 10^{5}{\rm {s}}^{-1}{\rm {M}}^{-1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ef512037b4da4d312f89dc4e35a5ca44cee2a187" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:11.092ex; height:2.676ex;" alt="{\displaystyle 10^{5}{\rm {s}}^{-1}{\rm {M}}^{-1}}"></span> and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 10{\rm {s}}^{-1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>10</mn> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">s</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 10{\rm {s}}^{-1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/34cbb1e27dae0c04fc794a91f2aa001aca7054c1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.574ex; height:2.676ex;" alt="{\displaystyle 10{\rm {s}}^{-1}}"></span>, respectively.<sup id="cite_ref-Bar-Even_2011_12-0" class="reference"><a href="#cite_note-Bar-Even_2011-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Direct_use_of_the_Michaelis–Menten_equation_for_time_course_kinetic_analysis"><span id="Direct_use_of_the_Michaelis.E2.80.93Menten_equation_for_time_course_kinetic_analysis"></span>Direct use of the Michaelis–Menten equation for time course kinetic analysis</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Enzyme_kinetics&action=edit&section=5" title="Edit section: Direct use of the Michaelis–Menten equation for time course kinetic analysis"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Further information: <a href="/wiki/Rate_equation" title="Rate equation">Rate equation</a></div><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Further information: <a href="/wiki/Reaction_Progress_Kinetic_Analysis" class="mw-redirect" title="Reaction Progress Kinetic Analysis">Reaction Progress Kinetic Analysis</a></div> <p>The observed velocities predicted by the Michaelis–Menten equation can be used to directly model the <a href="/wiki/Reaction_progress_kinetic_analysis" title="Reaction progress kinetic analysis">time course disappearance of substrate</a> and the production of product through incorporation of the Michaelis–Menten equation into the equation for first order chemical kinetics. This can only be achieved however if one recognises the problem associated with the use of <a href="/wiki/Euler%27s_number" class="mw-redirect" title="Euler's number">Euler's number</a> in the description of first order chemical kinetics. i.e. <i>e</i><sup>−<i>k</i></sup> is a split constant that introduces a systematic error into calculations and can be rewritten as a single constant which represents the remaining substrate after each time period.<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle [S]=[S]_{0}(1-k)^{t}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">[</mo> <mi>S</mi> <mo stretchy="false">]</mo> <mo>=</mo> <mo stretchy="false">[</mo> <mi>S</mi> <msub> <mo stretchy="false">]</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mn>1</mn> <mo>−</mo> <mi>k</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> </mrow> </msup> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle [S]=[S]_{0}(1-k)^{t}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/93211e467eb88a4ed3ce4b1b8a64f3645c540709" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:17.975ex; height:3.009ex;" alt="{\displaystyle [S]=[S]_{0}(1-k)^{t}\,}"></span></dd></dl> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle [S]=[S]_{0}(1-v/[S]_{0})^{t}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">[</mo> <mi>S</mi> <mo stretchy="false">]</mo> <mo>=</mo> <mo stretchy="false">[</mo> <mi>S</mi> <msub> <mo stretchy="false">]</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mn>1</mn> <mo>−</mo> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mo stretchy="false">[</mo> <mi>S</mi> <msub> <mo stretchy="false">]</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> </mrow> </msup> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle [S]=[S]_{0}(1-v/[S]_{0})^{t}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fc767ed4ec3fb17dbb2b342b438ca22f3a0c5e15" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:22.901ex; height:3.009ex;" alt="{\displaystyle [S]=[S]_{0}(1-v/[S]_{0})^{t}\,}"></span></dd></dl> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle [S]=[S]_{0}(1-(V_{\max }[S]_{0}/(K_{M}+[S]_{0})/[S]_{0}))^{t}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">[</mo> <mi>S</mi> <mo stretchy="false">]</mo> <mo>=</mo> <mo stretchy="false">[</mo> <mi>S</mi> <msub> <mo stretchy="false">]</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mn>1</mn> <mo>−</mo> <mo stretchy="false">(</mo> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mo movablelimits="true" form="prefix">max</mo> </mrow> </msub> <mo stretchy="false">[</mo> <mi>S</mi> <msub> <mo stretchy="false">]</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mo stretchy="false">(</mo> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>M</mi> </mrow> </msub> <mo>+</mo> <mo stretchy="false">[</mo> <mi>S</mi> <msub> <mo stretchy="false">]</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mo stretchy="false">[</mo> <mi>S</mi> <msub> <mo stretchy="false">]</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo stretchy="false">)</mo> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> </mrow> </msup> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle [S]=[S]_{0}(1-(V_{\max }[S]_{0}/(K_{M}+[S]_{0})/[S]_{0}))^{t}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/550cebc162d8baf678f05a64c8435882eba78bfb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:45.668ex; height:3.009ex;" alt="{\displaystyle [S]=[S]_{0}(1-(V_{\max }[S]_{0}/(K_{M}+[S]_{0})/[S]_{0}))^{t}\,}"></span></dd></dl> <p>In 1983 Stuart Beal (and also independently <a href="/wiki/Santiago_Schnell" title="Santiago Schnell">Santiago Schnell</a> and Claudio Mendoza in 1997) derived a closed form solution for the time course kinetics analysis of the Michaelis-Menten mechanism.<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> The solution, <span class="failed-verification-content" style="padding-left:0.1em; padding-right:0.1em; color:var(--color-subtle, #54595d); border:1px solid var(--border-color-subtle, #c8ccd1);">known as the Schnell-Mendoza equation</span><sup class="noprint Inline-Template Template-Fact" style="margin-left:0.1em; white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Verifiability" title="Wikipedia:Verifiability"><span title="The material highlighted is not verifiable using the citation(s) presented. (November 2024)">failed verification</span></a></i>]</sup>, has the form: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {[S]}{K_{M}}}=W\left[F(t)\right]\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo stretchy="false">[</mo> <mi>S</mi> <mo stretchy="false">]</mo> </mrow> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>M</mi> </mrow> </msub> </mfrac> </mrow> <mo>=</mo> <mi>W</mi> <mrow> <mo>[</mo> <mrow> <mi>F</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> <mo>]</mo> </mrow> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {[S]}{K_{M}}}=W\left[F(t)\right]\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bbfb88da686a3b0298417f08709f60c89538b35e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:16.76ex; height:6.009ex;" alt="{\displaystyle {\frac {[S]}{K_{M}}}=W\left[F(t)\right]\,}"></span></dd></dl> <p>where W[ ] is the <a href="/wiki/Lambert_W_function" title="Lambert W function">Lambert-W function</a>.<sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> and where F(t) is </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F(t)={\frac {[S]_{0}}{K_{M}}}\exp \!\left({\frac {[S]_{0}}{K_{M}}}-{\frac {V_{\max }}{K_{M}}}\,t\right)\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>F</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo stretchy="false">[</mo> <mi>S</mi> <msub> <mo stretchy="false">]</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>M</mi> </mrow> </msub> </mfrac> </mrow> <mi>exp</mi> <mspace width="negativethinmathspace" /> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo stretchy="false">[</mo> <mi>S</mi> <msub> <mo stretchy="false">]</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>M</mi> </mrow> </msub> </mfrac> </mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mo movablelimits="true" form="prefix">max</mo> </mrow> </msub> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>M</mi> </mrow> </msub> </mfrac> </mrow> <mspace width="thinmathspace" /> <mi>t</mi> </mrow> <mo>)</mo> </mrow> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F(t)={\frac {[S]_{0}}{K_{M}}}\exp \!\left({\frac {[S]_{0}}{K_{M}}}-{\frac {V_{\max }}{K_{M}}}\,t\right)\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/39737501b38ca63037f8350456c777481706c602" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:34.322ex; height:6.343ex;" alt="{\displaystyle F(t)={\frac {[S]_{0}}{K_{M}}}\exp \!\left({\frac {[S]_{0}}{K_{M}}}-{\frac {V_{\max }}{K_{M}}}\,t\right)\,}"></span></dd></dl> <p>This equation is encompassed by the equation below, obtained by Berberan-Santos,<sup id="cite_ref-18" class="reference"><a href="#cite_note-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> which is also valid when the initial substrate concentration is close to that of enzyme, </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {[S]}{K_{M}}}=W\left[F(t)\right]-{\frac {V_{\max }}{k_{cat}K_{M}}}\ {\frac {W\left[F(t)\right]}{1+W\left[F(t)\right]}}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo stretchy="false">[</mo> <mi>S</mi> <mo stretchy="false">]</mo> </mrow> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>M</mi> </mrow> </msub> </mfrac> </mrow> <mo>=</mo> <mi>W</mi> <mrow> <mo>[</mo> <mrow> <mi>F</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> <mo>]</mo> </mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mo movablelimits="true" form="prefix">max</mo> </mrow> </msub> <mrow> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> <mi>a</mi> <mi>t</mi> </mrow> </msub> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>M</mi> </mrow> </msub> </mrow> </mfrac> </mrow> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>W</mi> <mrow> <mo>[</mo> <mrow> <mi>F</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> <mo>]</mo> </mrow> </mrow> <mrow> <mn>1</mn> <mo>+</mo> <mi>W</mi> <mrow> <mo>[</mo> <mrow> <mi>F</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> <mo>]</mo> </mrow> </mrow> </mfrac> </mrow> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {[S]}{K_{M}}}=W\left[F(t)\right]-{\frac {V_{\max }}{k_{cat}K_{M}}}\ {\frac {W\left[F(t)\right]}{1+W\left[F(t)\right]}}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/036e38cefdac7ce988899ea0d4b89f80c0b6e81d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:41.912ex; height:6.509ex;" alt="{\displaystyle {\frac {[S]}{K_{M}}}=W\left[F(t)\right]-{\frac {V_{\max }}{k_{cat}K_{M}}}\ {\frac {W\left[F(t)\right]}{1+W\left[F(t)\right]}}\,}"></span></dd></dl> <p>where W[ ] is again the <a href="/wiki/Lambert_W_function" title="Lambert W function">Lambert-W function</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Linear_plots_of_the_Michaelis–Menten_equation"><span id="Linear_plots_of_the_Michaelis.E2.80.93Menten_equation"></span>Linear plots of the Michaelis–Menten equation</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Enzyme_kinetics&action=edit&section=6" title="Edit section: Linear plots of the Michaelis–Menten equation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/Lineweaver%E2%80%93Burk_plot" title="Lineweaver–Burk plot">Lineweaver–Burk plot</a>, <a href="/wiki/Eadie%E2%80%93Hofstee_diagram" title="Eadie–Hofstee diagram">Eadie–Hofstee diagram</a>, and <a href="/wiki/Hanes%E2%80%93Woolf_plot" title="Hanes–Woolf plot">Hanes–Woolf plot</a></div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Lineweaver-Burke_plot.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/70/Lineweaver-Burke_plot.svg/350px-Lineweaver-Burke_plot.svg.png" decoding="async" width="350" height="231" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/70/Lineweaver-Burke_plot.svg/525px-Lineweaver-Burke_plot.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/70/Lineweaver-Burke_plot.svg/700px-Lineweaver-Burke_plot.svg.png 2x" data-file-width="420" data-file-height="277" /></a><figcaption>Lineweaver–Burk or double-reciprocal plot of kinetic data, showing the significance of the axis intercepts and gradient.</figcaption></figure> <p>The plot of <i>v</i> versus [S] above is not linear; although initially linear at low [S], it bends over to saturate at high [S]. Before the modern era of <a href="/wiki/Nonlinear_regression" title="Nonlinear regression">nonlinear curve-fitting</a> on computers, this nonlinearity could make it difficult to estimate <i>K</i><sub>M</sub> and <i>V</i><sub>max</sub> accurately. Therefore, several researchers developed linearisations of the Michaelis–Menten equation, such as the <a href="/wiki/Lineweaver%E2%80%93Burk_plot" title="Lineweaver–Burk plot">Lineweaver–Burk plot</a>, the <a href="/wiki/Eadie%E2%80%93Hofstee_diagram" title="Eadie–Hofstee diagram">Eadie–Hofstee diagram</a> and the <a href="/wiki/Hanes%E2%80%93Woolf_plot" title="Hanes–Woolf plot">Hanes–Woolf plot</a>. All of these linear representations can be useful for visualising data, but none should be used to determine kinetic parameters, as computer software is readily available that allows for more accurate determination by <a href="/wiki/Nonlinear_regression" title="Nonlinear regression">nonlinear regression</a> methods.<sup id="cite_ref-19" class="reference"><a href="#cite_note-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> </p><p>The <a href="/wiki/Lineweaver%E2%80%93Burk_plot" title="Lineweaver–Burk plot">Lineweaver–Burk plot</a> or double reciprocal plot is a common way of illustrating kinetic data. This is produced by taking the <a href="/wiki/Multiplicative_inverse" title="Multiplicative inverse">reciprocal</a> of both sides of the Michaelis–Menten equation. As shown on the right, this is a linear form of the Michaelis–Menten equation and produces a straight line with the equation <i>y</i> = m<i>x</i> + c with a <i>y</i>-intercept equivalent to 1/<i>V</i><sub>max</sub> and an <i>x</i>-intercept of the graph representing −1/<i>K</i><sub>M</sub>. </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {1}{v}}={\frac {K_{M}}{V_{\max }[{\mbox{S}}]}}+{\frac {1}{V_{\max }}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>v</mi> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>M</mi> </mrow> </msub> <mrow> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mo movablelimits="true" form="prefix">max</mo> </mrow> </msub> <mo stretchy="false">[</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>S</mtext> </mstyle> </mrow> <mo stretchy="false">]</mo> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mo movablelimits="true" form="prefix">max</mo> </mrow> </msub> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {1}{v}}={\frac {K_{M}}{V_{\max }[{\mbox{S}}]}}+{\frac {1}{V_{\max }}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f67c173c3e3e8c78da7dc5fa15c3b5ff299e4439" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:21.489ex; height:6.009ex;" alt="{\displaystyle {\frac {1}{v}}={\frac {K_{M}}{V_{\max }[{\mbox{S}}]}}+{\frac {1}{V_{\max }}}}"></span></dd></dl> <p>Naturally, no experimental values can be taken at negative 1/[S]; the lower limiting value 1/[S] = 0 (the <i>y</i>-intercept) corresponds to an infinite substrate concentration, where <i>1/v=1/V<sub>max</sub></i> as shown at the right; thus, the <i>x</i>-intercept is an <a href="/wiki/Extrapolation" title="Extrapolation">extrapolation</a> of the experimental data taken at positive concentrations. More generally, the Lineweaver–Burk plot skews the importance of measurements taken at low substrate concentrations and, thus, can yield inaccurate estimates of <i>V</i><sub>max</sub> and <i>K</i><sub>M</sub>.<sup id="cite_ref-Tseng_20-0" class="reference"><a href="#cite_note-Tseng-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> A more accurate linear plotting method is the <a href="/wiki/Eadie%E2%80%93Hofstee_diagram" title="Eadie–Hofstee diagram">Eadie–Hofstee plot</a>. In this case, <i>v</i> is plotted against <i>v</i>/[S]. In the third common linear representation, the <a href="/wiki/Hanes%E2%80%93Woolf_plot" title="Hanes–Woolf plot">Hanes–Woolf plot</a>, [S]/<i>v</i> is plotted against [S]. In general, data normalisation can help diminish the amount of experimental work and can increase the reliability of the output, and is suitable for both graphical and numerical analysis.<sup id="cite_ref-21" class="reference"><a href="#cite_note-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Practical_significance_of_kinetic_constants">Practical significance of kinetic constants</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Enzyme_kinetics&action=edit&section=7" title="Edit section: Practical significance of kinetic constants"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The study of enzyme kinetics is important for two basic reasons. Firstly, it helps explain how enzymes work, and secondly, it helps predict how enzymes behave in living organisms. The kinetic constants defined above, <i>K</i><sub>M</sub> and <i>V</i><sub>max</sub>, are critical to attempts to understand how enzymes work together to control <a href="/wiki/Metabolism" title="Metabolism">metabolism</a>. </p><p>Making these predictions is not trivial, even for simple systems. For example, <a href="/wiki/Oxaloacetate" class="mw-redirect" title="Oxaloacetate">oxaloacetate</a> is formed by <a href="/wiki/Malate_dehydrogenase" title="Malate dehydrogenase">malate dehydrogenase</a> within the <a href="/wiki/Mitochondrion" title="Mitochondrion">mitochondrion</a>. Oxaloacetate can then be consumed by <a href="/wiki/Citrate_synthase" title="Citrate synthase">citrate synthase</a>, <a href="/wiki/Phosphoenolpyruvate_carboxykinase" title="Phosphoenolpyruvate carboxykinase">phosphoenolpyruvate carboxykinase</a> or <a href="/wiki/Aspartate_aminotransferase" class="mw-redirect" title="Aspartate aminotransferase">aspartate aminotransferase</a>, feeding into the <a href="/wiki/Citric_acid_cycle" title="Citric acid cycle">citric acid cycle</a>, <a href="/wiki/Gluconeogenesis" title="Gluconeogenesis">gluconeogenesis</a> or <a href="/wiki/Aspartic_acid" title="Aspartic acid">aspartic acid</a> biosynthesis, respectively. Being able to predict how much oxaloacetate goes into which pathway requires knowledge of the concentration of oxaloacetate as well as the concentration and kinetics of each of these enzymes. This aim of predicting the behaviour of metabolic pathways reaches its most complex expression in the synthesis of huge amounts of kinetic and <a href="/wiki/Gene_expression" title="Gene expression">gene expression</a> data into mathematical models of entire organisms. Alternatively, one useful simplification of the metabolic modelling problem is to ignore the underlying enzyme kinetics and only rely on information about the reaction network's stoichiometry, a technique called <a href="/wiki/Flux_balance_analysis" title="Flux balance analysis">flux balance analysis</a>.<sup id="cite_ref-22" class="reference"><a href="#cite_note-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-23" class="reference"><a href="#cite_note-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Michaelis–Menten_kinetics_with_intermediate"><span id="Michaelis.E2.80.93Menten_kinetics_with_intermediate"></span>Michaelis–Menten kinetics with intermediate</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Enzyme_kinetics&action=edit&section=8" title="Edit section: Michaelis–Menten kinetics with intermediate"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>One could also consider the less simple case </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\ce {{E}+S<=>[k_{1}][k_{-1}]ES->[k_{2}]EI->[k_{3}]{E}+P}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mtext>E</mtext> </mrow> <mo>+</mo> <mtext>S</mtext> <mrow class="MJX-TeXAtom-REL"> <munderover> <mo>⇌</mo> <mpadded width="+0.667em" lspace="0.278em" voffset="-.24em"> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msub> </mpadded> <mpadded width="+0.667em" lspace="0.278em" voffset=".15em"> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mpadded> </munderover> </mrow> <mtext>ES</mtext> <mrow class="MJX-TeXAtom-REL"> <mover> <mo>→</mo> <mpadded width="+0.611em" lspace="0.278em" voffset=".15em"> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mpadded> </mover> </mrow> <mtext>EI</mtext> <mrow class="MJX-TeXAtom-REL"> <mover> <mo>→</mo> <mpadded width="+0.611em" lspace="0.278em" voffset=".15em"> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> </mpadded> </mover> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext>E</mtext> </mrow> <mo>+</mo> <mtext>P</mtext> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\ce {{E}+S<=>[k_{1}][k_{-1}]ES->[k_{2}]EI->[k_{3}]{E}+P}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5cd1904bee27689d5df0933e40a4b01631243041" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.223ex; margin-top: -0.32ex; margin-bottom: -0.615ex; width:30.942ex; height:6.676ex;" alt="{\displaystyle {\ce {{E}+S<=>[k_{1}][k_{-1}]ES->[k_{2}]EI->[k_{3}]{E}+P}}}"></span></dd></dl> <p>where a complex with the enzyme and an intermediate exists and the intermediate is converted into product in a second step. In this case we have a very similar equation<sup id="cite_ref-24" class="reference"><a href="#cite_note-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup> </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v_{0}=k_{cat}{\frac {{\ce {[S] [E]_0}}}{K_{M}^{\prime }+{\ce {[S]}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>=</mo> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> <mi>a</mi> <mi>t</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">[</mo> <mtext>S</mtext> <mo stretchy="false">]</mo> </mrow> <msubsup> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">[</mo> <mtext>E</mtext> <mo stretchy="false">]</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mspace width="0pt" height="0pt" depth=".2em" /> </mrow> </msubsup> </mrow> <mrow> <msubsup> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>M</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-variant" mathvariant="normal">′</mi> </mrow> </msubsup> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">[</mo> <mtext>S</mtext> <mo stretchy="false">]</mo> </mrow> </mrow> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v_{0}=k_{cat}{\frac {{\ce {[S] [E]_0}}}{K_{M}^{\prime }+{\ce {[S]}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d90d4c1b92e79705a9ecf0f8615982c0bc91f4a3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:19.094ex; height:6.843ex;" alt="{\displaystyle v_{0}=k_{cat}{\frac {{\ce {[S] [E]_0}}}{K_{M}^{\prime }+{\ce {[S]}}}}}"></span></dd></dl> <p>but the constants are different </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{aligned}K_{M}^{\prime }\ &{\stackrel {\mathrm {def} }{=}}\ {\frac {k_{3}}{k_{2}+k_{3}}}K_{M}={\frac {k_{3}}{k_{2}+k_{3}}}\cdot {\frac {k_{2}+k_{-1}}{k_{1}}}\\k_{cat}\ &{\stackrel {\mathrm {def} }{=}}\ {\dfrac {k_{3}k_{2}}{k_{2}+k_{3}}}\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <msubsup> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>M</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-variant" mathvariant="normal">′</mi> </mrow> </msubsup> <mtext> </mtext> </mtd> <mtd> <mi></mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-REL"> <mover> <mrow class="MJX-TeXAtom-OP MJX-fixedlimits"> <mo>=</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">f</mi> </mrow> </mrow> </mover> </mrow> </mrow> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <mrow> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> </mrow> </mfrac> </mrow> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>M</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <mrow> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msub> </mrow> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> <mi>a</mi> <mi>t</mi> </mrow> </msub> <mtext> </mtext> </mtd> <mtd> <mi></mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-REL"> <mover> <mrow class="MJX-TeXAtom-OP MJX-fixedlimits"> <mo>=</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">f</mi> </mrow> </mrow> </mover> </mrow> </mrow> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mfrac> <mrow> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> <mrow> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> </mrow> </mfrac> </mstyle> </mrow> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}K_{M}^{\prime }\ &{\stackrel {\mathrm {def} }{=}}\ {\frac {k_{3}}{k_{2}+k_{3}}}K_{M}={\frac {k_{3}}{k_{2}+k_{3}}}\cdot {\frac {k_{2}+k_{-1}}{k_{1}}}\\k_{cat}\ &{\stackrel {\mathrm {def} }{=}}\ {\dfrac {k_{3}k_{2}}{k_{2}+k_{3}}}\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1a408a6b97544b6a8c95d3ec9974976cacee9cba" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -5.338ex; width:42.711ex; height:11.843ex;" alt="{\displaystyle {\begin{aligned}K_{M}^{\prime }\ &{\stackrel {\mathrm {def} }{=}}\ {\frac {k_{3}}{k_{2}+k_{3}}}K_{M}={\frac {k_{3}}{k_{2}+k_{3}}}\cdot {\frac {k_{2}+k_{-1}}{k_{1}}}\\k_{cat}\ &{\stackrel {\mathrm {def} }{=}}\ {\dfrac {k_{3}k_{2}}{k_{2}+k_{3}}}\end{aligned}}}"></span></dd></dl> <p>We see that for the limiting case <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle k_{3}\gg k_{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <mo>≫</mo> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle k_{3}\gg k_{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f482bbb82bd526720c99efea00baa289fdf96187" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.145ex; height:2.509ex;" alt="{\displaystyle k_{3}\gg k_{2}}"></span>, thus when the last step from <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\ce {EI -> E + P}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtext>EI</mtext> <mo stretchy="false">⟶</mo> <mtext>E</mtext> <mo>+</mo> <mtext>P</mtext> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\ce {EI -> E + P}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ce5d8cd4343c44180a57a649236c4fca85a7993f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:13.524ex; height:2.343ex;" alt="{\displaystyle {\ce {EI -> E + P}}}"></span> is much faster than the previous step, we get again the original equation. Mathematically we have then <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle K_{M}^{\prime }\approx K_{M}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>M</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-variant" mathvariant="normal">′</mi> </mrow> </msubsup> <mo>≈</mo> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>M</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle K_{M}^{\prime }\approx K_{M}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/866ad8e62e297abcbd3ec5f95d64ac79e66f71eb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:10.963ex; height:2.843ex;" alt="{\displaystyle K_{M}^{\prime }\approx K_{M}}"></span> and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle k_{cat}\approx k_{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> <mi>a</mi> <mi>t</mi> </mrow> </msub> <mo>≈</mo> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle k_{cat}\approx k_{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3ca27e348f3ae09fc272705a48cdd71d52f72b4e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.983ex; height:2.509ex;" alt="{\displaystyle k_{cat}\approx k_{2}}"></span>. </p> <div class="mw-heading mw-heading2"><h2 id="Multi-substrate_reactions">Multi-substrate reactions</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Enzyme_kinetics&action=edit&section=9" title="Edit section: Multi-substrate reactions"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Multi-substrate reactions follow complex rate equations that describe how the substrates bind and in what sequence. The analysis of these reactions is much simpler if the concentration of substrate A is kept constant and substrate B varied. Under these conditions, the enzyme behaves just like a single-substrate enzyme and a plot of <i>v</i> by [S] gives apparent <i>K</i><sub>M</sub> and <i>V</i><sub>max</sub> constants for substrate B. If a set of these measurements is performed at different fixed concentrations of A, these data can be used to work out what the mechanism of the reaction is. For an enzyme that takes two substrates A and B and turns them into two products P and Q, there are two types of mechanism: ternary complex and ping–pong. </p> <div class="mw-heading mw-heading3"><h3 id="Ternary-complex_mechanisms">Ternary-complex mechanisms</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Enzyme_kinetics&action=edit&section=10" title="Edit section: Ternary-complex mechanisms"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Random_order_ternary_mechanism.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/bc/Random_order_ternary_mechanism.svg/310px-Random_order_ternary_mechanism.svg.png" decoding="async" width="310" height="149" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/bc/Random_order_ternary_mechanism.svg/465px-Random_order_ternary_mechanism.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/bc/Random_order_ternary_mechanism.svg/620px-Random_order_ternary_mechanism.svg.png 2x" data-file-width="450" data-file-height="217" /></a><figcaption>Random-order ternary-complex mechanism for an enzyme reaction. The reaction path is shown as a line and enzyme intermediates containing substrates A and B or products P and Q are written below the line.</figcaption></figure> <p>In these enzymes, both substrates bind to the enzyme at the same time to produce an EAB ternary complex. The order of binding can either be random (in a random mechanism) or substrates have to bind in a particular sequence (in an ordered mechanism). When a set of <i>v</i> by [S] curves (fixed A, varying B) from an enzyme with a ternary-complex mechanism are plotted in a <a href="/wiki/Lineweaver%E2%80%93Burk_plot" title="Lineweaver–Burk plot">Lineweaver–Burk plot</a>, the set of lines produced will intersect. </p><p>Enzymes with ternary-complex mechanisms include <a href="/wiki/Glutathione_S-transferase" title="Glutathione S-transferase">glutathione <i>S</i>-transferase</a>,<sup id="cite_ref-25" class="reference"><a href="#cite_note-25"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Dihydrofolate_reductase" title="Dihydrofolate reductase">dihydrofolate reductase</a><sup id="cite_ref-26" class="reference"><a href="#cite_note-26"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup> and <a href="/wiki/DNA_polymerase" title="DNA polymerase">DNA polymerase</a>.<sup id="cite_ref-27" class="reference"><a href="#cite_note-27"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup> The following links show short animations of the ternary-complex mechanisms of the enzymes dihydrofolate reductase<style data-mw-deduplicate="TemplateStyles:r1041539562">.mw-parser-output .citation{word-wrap:break-word}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}</style><sup class="citation nobold" id="ref_Bnone"><a href="#endnote_Bnone">[β]</a></sup> and DNA polymerase<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1041539562"><sup class="citation nobold" id="ref_Cnone"><a href="#endnote_Cnone">[γ]</a></sup>. </p> <div class="mw-heading mw-heading3"><h3 id="Ping–pong_mechanisms"><span id="Ping.E2.80.93pong_mechanisms"></span>Ping–pong mechanisms</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Enzyme_kinetics&action=edit&section=11" title="Edit section: Ping–pong mechanisms"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="thumb tright" style=""><div class="thumbinner" style="width:412px"><div class="thumbimage noresize" style="width:410px;"> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\ce {\overset {}{E->[{\ce {A \atop \downarrow }}]EA<=>E^{\ast }P->[{\ce {P \atop \uparrow }}]E^{\ast }->[{\ce {B \atop \downarrow }}]E^{\ast }B<=>EQ->[{\ce {Q \atop \uparrow }}]E}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow> <mtext>E</mtext> <mrow class="MJX-TeXAtom-REL"> <mover> <mo>→</mo> <mpadded width="+0.611em" lspace="0.278em" voffset=".15em"> <mrow class="MJX-TeXAtom-ORD"> <mfrac linethickness="0"> <mtext>A</mtext> <mo stretchy="false">↓</mo> </mfrac> </mrow> </mpadded> </mover> </mrow> <mtext>EA</mtext> <mrow class="MJX-TeXAtom-REL"> <mover> <mrow class="MJX-TeXAtom-OP MJX-fixedlimits"> <mrow class="MJX-TeXAtom-ORD"> <mpadded height="0" depth="0"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">↽</mo> </mrow> <mspace width="negativethinmathspace" /> <mspace width="negativethinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> </mrow> </mpadded> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> </mrow> <mspace width="negativethinmathspace" /> <mspace width="negativethinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">⇀</mo> </mrow> </mrow> </mstyle> </mrow> </mover> </mrow> <msup> <mtext>E</mtext> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msup> <mtext>P</mtext> <mrow class="MJX-TeXAtom-REL"> <mover> <mo>→</mo> <mpadded width="+0.611em" lspace="0.278em" voffset=".15em"> <mrow class="MJX-TeXAtom-ORD"> <mfrac linethickness="0"> <mtext>P</mtext> <mo stretchy="false">↑</mo> </mfrac> </mrow> </mpadded> </mover> </mrow> <msup> <mtext>E</mtext> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msup> <mrow class="MJX-TeXAtom-REL"> <mover> <mo>→</mo> <mpadded width="+0.611em" lspace="0.278em" voffset=".15em"> <mrow class="MJX-TeXAtom-ORD"> <mfrac linethickness="0"> <mtext>B</mtext> <mo stretchy="false">↓</mo> </mfrac> </mrow> </mpadded> </mover> </mrow> <msup> <mtext>E</mtext> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msup> <mtext>B</mtext> <mrow class="MJX-TeXAtom-REL"> <mover> <mrow class="MJX-TeXAtom-OP MJX-fixedlimits"> <mrow class="MJX-TeXAtom-ORD"> <mpadded height="0" depth="0"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">↽</mo> </mrow> <mspace width="negativethinmathspace" /> <mspace width="negativethinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> </mrow> </mpadded> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> </mrow> <mspace width="negativethinmathspace" /> <mspace width="negativethinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">⇀</mo> </mrow> </mrow> </mstyle> </mrow> </mover> </mrow> <mtext>EQ</mtext> <mrow class="MJX-TeXAtom-REL"> <mover> <mo>→</mo> <mpadded width="+0.611em" lspace="0.278em" voffset=".15em"> <mrow class="MJX-TeXAtom-ORD"> <mfrac linethickness="0"> <mtext>Q</mtext> <mo stretchy="false">↑</mo> </mfrac> </mrow> </mpadded> </mover> </mrow> <mtext>E</mtext> </mrow> <mrow /> </mover> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\ce {\overset {}{E->[{\ce {A \atop \downarrow }}]EA<=>E^{\ast }P->[{\ce {P \atop \uparrow }}]E^{\ast }->[{\ce {B \atop \downarrow }}]E^{\ast }B<=>EQ->[{\ce {Q \atop \uparrow }}]E}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f9b768dbbd547267c22748f29590cb0a639375de" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:46.896ex; height:6.176ex;" alt="{\displaystyle {\ce {\overset {}{E->[{\ce {A \atop \downarrow }}]EA<=>E^{\ast }P->[{\ce {P \atop \uparrow }}]E^{\ast }->[{\ce {B \atop \downarrow }}]E^{\ast }B<=>EQ->[{\ce {Q \atop \uparrow }}]E}}}}"></span></div><div class="thumbcaption">Ping–pong mechanism for an enzyme reaction. Intermediates contain substrates A and B or products P and Q.</div></div></div> <p>As shown on the right, enzymes with a ping-pong mechanism can exist in two states, E and a chemically modified form of the enzyme E*; this modified enzyme is known as an <a href="/wiki/Reactive_intermediate" title="Reactive intermediate">intermediate</a>. In such mechanisms, substrate A binds, changes the enzyme to E* by, for example, transferring a chemical group to the active site, and is then released. Only after the first substrate is released can substrate B bind and react with the modified enzyme, regenerating the unmodified E form. When a set of <i>v</i> by [S] curves (fixed A, varying B) from an enzyme with a ping–pong mechanism are plotted in a Lineweaver–Burk plot, a set of parallel lines will be produced. This is called a <a href="/wiki/Secondary_plot_(kinetics)" title="Secondary plot (kinetics)">secondary plot</a>. </p><p>Enzymes with ping–pong mechanisms include some <a href="/wiki/Oxidoreductases" class="mw-redirect" title="Oxidoreductases">oxidoreductases</a> such as <a href="/wiki/Peroxidase" title="Peroxidase">thioredoxin peroxidase</a>,<sup id="cite_ref-28" class="reference"><a href="#cite_note-28"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Transferases" class="mw-redirect" title="Transferases">transferases</a> such as acylneuraminate cytidylyltransferase<sup id="cite_ref-29" class="reference"><a href="#cite_note-29"><span class="cite-bracket">[</span>29<span class="cite-bracket">]</span></a></sup> and <a href="/wiki/Serine_protease" title="Serine protease">serine proteases</a> such as <a href="/wiki/Trypsin" title="Trypsin">trypsin</a> and <a href="/wiki/Chymotrypsin" title="Chymotrypsin">chymotrypsin</a>.<sup id="cite_ref-30" class="reference"><a href="#cite_note-30"><span class="cite-bracket">[</span>30<span class="cite-bracket">]</span></a></sup> Serine proteases are a very common and diverse family of enzymes, including <a href="/wiki/Digestion" title="Digestion">digestive</a> enzymes (trypsin, chymotrypsin, and elastase), several enzymes of the <a href="/wiki/Coagulation" title="Coagulation">blood clotting cascade</a> and many others. In these serine proteases, the E* intermediate is an acyl-enzyme species formed by the attack of an active site <a href="/wiki/Serine" title="Serine">serine</a> residue on a <a href="/wiki/Peptide_bond" title="Peptide bond">peptide bond</a> in a protein substrate. A short animation showing the mechanism of chymotrypsin is linked here.<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1041539562"><sup class="citation nobold" id="ref_Dnone"><a href="#endnote_Dnone">[δ]</a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Reversible_catalysis_and_the_Haldane_equation">Reversible catalysis and the Haldane equation</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Enzyme_kinetics&action=edit&section=12" title="Edit section: Reversible catalysis and the Haldane equation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Reversible_Michaelis-Menten_kinetics" class="mw-redirect" title="Reversible Michaelis-Menten kinetics">Reversible Michaelis-Menten kinetics</a></div> <p>External factors may limit the ability of an enzyme to catalyse a reaction in both directions (whereas the nature of a catalyst in itself means that it cannot catalyse just one direction, according to the principle of <a href="/wiki/Microscopic_reversibility" title="Microscopic reversibility">microscopic reversibility</a>). We consider the case of an enzyme that catalyses the reaction in both directions: </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\ce {{E}+{S}<=>[k_{1}][k_{-1}]ES<=>[k_{2}][k_{-2}]{E}+{P}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mtext>E</mtext> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>S</mtext> </mrow> <mrow class="MJX-TeXAtom-REL"> <munderover> <mo>⇌</mo> <mpadded width="+0.667em" lspace="0.278em" voffset="-.24em"> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msub> </mpadded> <mpadded width="+0.667em" lspace="0.278em" voffset=".15em"> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mpadded> </munderover> </mrow> <mtext>ES</mtext> <mrow class="MJX-TeXAtom-REL"> <munderover> <mo>⇌</mo> <mpadded width="+0.667em" lspace="0.278em" voffset="-.24em"> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>2</mn> </mrow> </msub> </mpadded> <mpadded width="+0.667em" lspace="0.278em" voffset=".15em"> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mpadded> </munderover> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext>E</mtext> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\ce {{E}+{S}<=>[k_{1}][k_{-1}]ES<=>[k_{2}][k_{-2}]{E}+{P}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fe362b85b97b0614f6139dd0be2e8389a2c3b63e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.223ex; margin-top: -0.32ex; margin-bottom: -0.615ex; width:25.234ex; height:6.676ex;" alt="{\displaystyle {\ce {{E}+{S}<=>[k_{1}][k_{-1}]ES<=>[k_{2}][k_{-2}]{E}+{P}}}}"></span> </p><p>The steady-state, initial rate of the reaction is <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v_{0}={\frac {d\,[{\rm {P}}]}{dt}}={\frac {(k_{1}k_{2}\,[{\rm {S}}]-k_{-1}k_{-2}[{\rm {P}}])[{\rm {E}}]_{0}}{k_{-1}+k_{2}+k_{1}\,[{\rm {S}}]+k_{-2}\,[{\rm {P}}]}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mspace width="thinmathspace" /> <mo stretchy="false">[</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">P</mi> </mrow> </mrow> <mo stretchy="false">]</mo> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo stretchy="false">(</mo> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mspace width="thinmathspace" /> <mo stretchy="false">[</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">S</mi> </mrow> </mrow> <mo stretchy="false">]</mo> <mo>−</mo> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msub> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>2</mn> </mrow> </msub> <mo stretchy="false">[</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">P</mi> </mrow> </mrow> <mo stretchy="false">]</mo> <mo stretchy="false">)</mo> <mo stretchy="false">[</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">E</mi> </mrow> </mrow> <msub> <mo stretchy="false">]</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> <mrow> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mspace width="thinmathspace" /> <mo stretchy="false">[</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">S</mi> </mrow> </mrow> <mo stretchy="false">]</mo> <mo>+</mo> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>2</mn> </mrow> </msub> <mspace width="thinmathspace" /> <mo stretchy="false">[</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">P</mi> </mrow> </mrow> <mo stretchy="false">]</mo> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v_{0}={\frac {d\,[{\rm {P}}]}{dt}}={\frac {(k_{1}k_{2}\,[{\rm {S}}]-k_{-1}k_{-2}[{\rm {P}}])[{\rm {E}}]_{0}}{k_{-1}+k_{2}+k_{1}\,[{\rm {S}}]+k_{-2}\,[{\rm {P}}]}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/01297c24d81598b7438d064174294408dacc5e60" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:40.908ex; height:6.509ex;" alt="{\displaystyle v_{0}={\frac {d\,[{\rm {P}}]}{dt}}={\frac {(k_{1}k_{2}\,[{\rm {S}}]-k_{-1}k_{-2}[{\rm {P}}])[{\rm {E}}]_{0}}{k_{-1}+k_{2}+k_{1}\,[{\rm {S}}]+k_{-2}\,[{\rm {P}}]}}}"></span> </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v_{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/60faad24775635f4722ccc438093dbbfe05f34ae" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.182ex; height:2.009ex;" alt="{\displaystyle v_{0}}"></span> is positive if the reaction proceed in the forward direction (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S\rightarrow P}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> <mo stretchy="false">→</mo> <mi>P</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S\rightarrow P}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bc699757db699063e802dbc1c9f11f8728894f1f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.859ex; height:2.176ex;" alt="{\displaystyle S\rightarrow P}"></span>) and negative otherwise. </p><p><a href="/wiki/Equilibrium_constant" title="Equilibrium constant">Equilibrium</a> requires that <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>v</mi> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ba3d414a23bf4ecfa36cdd039241efc60a5bd9e0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.389ex; height:2.176ex;" alt="{\displaystyle v=0}"></span>, which occurs when <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {[{\rm {P}}]_{\rm {eq}}}{[{\rm {S}}]_{\rm {eq}}}}={\frac {k_{1}k_{2}}{k_{-1}k_{-2}}}=K_{\rm {eq}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo stretchy="false">[</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">P</mi> </mrow> </mrow> <msub> <mo stretchy="false">]</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">q</mi> </mrow> </mrow> </msub> </mrow> <mrow> <mo stretchy="false">[</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">S</mi> </mrow> </mrow> <msub> <mo stretchy="false">]</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">q</mi> </mrow> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> <mrow> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msub> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>2</mn> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>=</mo> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">q</mi> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {[{\rm {P}}]_{\rm {eq}}}{[{\rm {S}}]_{\rm {eq}}}}={\frac {k_{1}k_{2}}{k_{-1}k_{-2}}}=K_{\rm {eq}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4f0ca30bfb4f852fcc02a12f729bcbd3adc500d6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:23.49ex; height:6.509ex;" alt="{\displaystyle {\frac {[{\rm {P}}]_{\rm {eq}}}{[{\rm {S}}]_{\rm {eq}}}}={\frac {k_{1}k_{2}}{k_{-1}k_{-2}}}=K_{\rm {eq}}}"></span>. This shows that <a href="/wiki/Equilibrium_constant" title="Equilibrium constant">thermodynamics</a> forces a relation between the values of the 4 rate constants. </p><p>The values of the forward and backward <i>maximal</i> rates, obtained for <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle [{\rm {S}}]\rightarrow \infty }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">[</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">S</mi> </mrow> </mrow> <mo stretchy="false">]</mo> <mo stretchy="false">→</mo> <mi mathvariant="normal">∞</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle [{\rm {S}}]\rightarrow \infty }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c3e69387ec816688807461db5902b440a6a65ed0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:8.524ex; height:2.843ex;" alt="{\displaystyle [{\rm {S}}]\rightarrow \infty }"></span>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle [{\rm {P}}]=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">[</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">P</mi> </mrow> </mrow> <mo stretchy="false">]</mo> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle [{\rm {P}}]=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/93c498e9bfae3b2d0f1378c8a1a15031f4002279" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.137ex; height:2.843ex;" alt="{\displaystyle [{\rm {P}}]=0}"></span>, and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle [{\rm {S}}]=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">[</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">S</mi> </mrow> </mrow> <mo stretchy="false">]</mo> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle [{\rm {S}}]=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/53ac89660d3f5c0ad06eac244190defc17cd7a61" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.847ex; height:2.843ex;" alt="{\displaystyle [{\rm {S}}]=0}"></span>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle [{\rm {P}}]\rightarrow \infty }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">[</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">P</mi> </mrow> </mrow> <mo stretchy="false">]</mo> <mo stretchy="false">→</mo> <mi mathvariant="normal">∞</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle [{\rm {P}}]\rightarrow \infty }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/020c2fe953abd3c508b7bd3a6d97bb29225faeeb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:8.814ex; height:2.843ex;" alt="{\displaystyle [{\rm {P}}]\rightarrow \infty }"></span>, respectively, are <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V_{\rm {max}}^{f}=k_{2}{\rm {[E]}}_{tot}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">x</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>f</mi> </mrow> </msubsup> <mo>=</mo> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">[</mo> <mi mathvariant="normal">E</mi> <mo stretchy="false">]</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> <mi>o</mi> <mi>t</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V_{\rm {max}}^{f}=k_{2}{\rm {[E]}}_{tot}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1834ca7ac4c486ffc3e1c89742f31c266797da98" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:15.104ex; height:3.509ex;" alt="{\displaystyle V_{\rm {max}}^{f}=k_{2}{\rm {[E]}}_{tot}}"></span> and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V_{\rm {max}}^{b}=-k_{-1}{\rm {[E]}}_{tot}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">x</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msubsup> <mo>=</mo> <mo>−</mo> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msub> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">[</mo> <mi mathvariant="normal">E</mi> <mo stretchy="false">]</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> <mi>o</mi> <mi>t</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V_{\rm {max}}^{b}=-k_{-1}{\rm {[E]}}_{tot}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a09363446309c8c26702430b70bfec463a3b0134" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:18.19ex; height:3.176ex;" alt="{\displaystyle V_{\rm {max}}^{b}=-k_{-1}{\rm {[E]}}_{tot}}"></span>, respectively. Their ratio is not equal to the equilibrium constant, which implies that <a href="/wiki/Equilibrium_constant" title="Equilibrium constant">thermodynamics</a> does not constrain the ratio of the maximal rates. This explains that enzymes can be much "better catalysts" (<i>in terms of maximal rates</i>) in one particular direction of the reaction.<sup id="cite_ref-31" class="reference"><a href="#cite_note-31"><span class="cite-bracket">[</span>31<span class="cite-bracket">]</span></a></sup> </p><p>On can also derive the two Michaelis constants <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle K_{M}^{S}=(k_{-1}+k_{2})/k_{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>M</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>S</mi> </mrow> </msubsup> <mo>=</mo> <mo stretchy="false">(</mo> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle K_{M}^{S}=(k_{-1}+k_{2})/k_{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f6e2bd31e5b448c7b1565012566755f4f8739681" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:20.918ex; height:3.176ex;" alt="{\displaystyle K_{M}^{S}=(k_{-1}+k_{2})/k_{1}}"></span>and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle K_{M}^{P}=(k_{-1}+k_{2})/k_{-2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>M</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>P</mi> </mrow> </msubsup> <mo>=</mo> <mo stretchy="false">(</mo> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle K_{M}^{P}=(k_{-1}+k_{2})/k_{-2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3f95c1d68a0d6c677873f46790d0d07d8925190d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:22.196ex; height:3.176ex;" alt="{\displaystyle K_{M}^{P}=(k_{-1}+k_{2})/k_{-2}}"></span>. The Haldane equation is the relation <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle K_{\rm {eq}}={\frac {[{\rm {P}}]_{\rm {eq}}}{[{\rm {S}}]_{\rm {eq}}}}={\frac {V_{\rm {max}}^{f}/K_{M}^{S}}{V_{\rm {max}}^{b}/K_{M}^{P}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">q</mi> </mrow> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo stretchy="false">[</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">P</mi> </mrow> </mrow> <msub> <mo stretchy="false">]</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">q</mi> </mrow> </mrow> </msub> </mrow> <mrow> <mo stretchy="false">[</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">S</mi> </mrow> </mrow> <msub> <mo stretchy="false">]</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">q</mi> </mrow> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msubsup> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">x</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>f</mi> </mrow> </msubsup> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <msubsup> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>M</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>S</mi> </mrow> </msubsup> </mrow> <mrow> <msubsup> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">x</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msubsup> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <msubsup> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>M</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>P</mi> </mrow> </msubsup> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle K_{\rm {eq}}={\frac {[{\rm {P}}]_{\rm {eq}}}{[{\rm {S}}]_{\rm {eq}}}}={\frac {V_{\rm {max}}^{f}/K_{M}^{S}}{V_{\rm {max}}^{b}/K_{M}^{P}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/621e1b38683241916244c9e90f5625f14f1f0088" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:26.143ex; height:7.509ex;" alt="{\displaystyle K_{\rm {eq}}={\frac {[{\rm {P}}]_{\rm {eq}}}{[{\rm {S}}]_{\rm {eq}}}}={\frac {V_{\rm {max}}^{f}/K_{M}^{S}}{V_{\rm {max}}^{b}/K_{M}^{P}}}}"></span>. </p><p>Therefore, <a href="/wiki/Equilibrium_constant" title="Equilibrium constant">thermodynamics</a> constrains the ratio between the forward and backward <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V_{\rm {max}}/K_{M}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">x</mi> </mrow> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>M</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V_{\rm {max}}/K_{M}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c86cc6d73f03f4478bfce77ff4c555aeaa61a05d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.741ex; height:2.843ex;" alt="{\displaystyle V_{\rm {max}}/K_{M}}"></span> values, not the ratio of <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V_{\rm {max}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">x</mi> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V_{\rm {max}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fa70ca539750e758de455ff485259924561d1700" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.646ex; height:2.509ex;" alt="{\displaystyle V_{\rm {max}}}"></span>values. </p> <div class="mw-heading mw-heading2"><h2 id="Non-Michaelis–Menten_kinetics"><span id="Non-Michaelis.E2.80.93Menten_kinetics"></span>Non-Michaelis–Menten kinetics</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Enzyme_kinetics&action=edit&section=13" title="Edit section: Non-Michaelis–Menten kinetics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Allosteric_regulation" title="Allosteric regulation">Allosteric regulation</a></div> <figure class="mw-halign-left" typeof="mw:File/Thumb"><a href="/wiki/File:Allosteric_v_by_S_curve.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/44/Allosteric_v_by_S_curve.svg/300px-Allosteric_v_by_S_curve.svg.png" decoding="async" width="300" height="231" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/44/Allosteric_v_by_S_curve.svg/450px-Allosteric_v_by_S_curve.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/44/Allosteric_v_by_S_curve.svg/600px-Allosteric_v_by_S_curve.svg.png 2x" data-file-width="565" data-file-height="435" /></a><figcaption>Saturation curve for an enzyme reaction showing sigmoid kinetics.</figcaption></figure> <p>Many different enzyme systems follow non Michaelis-Menten behavior. A select few examples include kinetics of self-catalytic enzymes, cooperative and allosteric enzymes, interfacial and intracellular enzymes, processive enzymes and so forth. Some enzymes produce a <a href="/wiki/Sigmoid_function" title="Sigmoid function">sigmoid</a> <i>v</i> by [S] plot, which often indicates <a href="/wiki/Cooperative_binding" title="Cooperative binding">cooperative binding</a> of substrate to the active site. This means that the binding of one substrate molecule affects the binding of subsequent substrate molecules. This behavior is most common in <a href="/wiki/Protein_structure" title="Protein structure">multimeric</a> enzymes with several interacting active sites.<sup id="cite_ref-32" class="reference"><a href="#cite_note-32"><span class="cite-bracket">[</span>32<span class="cite-bracket">]</span></a></sup> Here, the mechanism of cooperation is similar to that of <a href="/wiki/Hemoglobin" title="Hemoglobin">hemoglobin</a>, with binding of substrate to one active site altering the affinity of the other active sites for substrate molecules. Positive cooperativity occurs when binding of the first substrate molecule <i>increases</i> the affinity of the other active sites for substrate. Negative cooperativity occurs when binding of the first substrate <i>decreases</i> the affinity of the enzyme for other substrate molecules. </p><p>Allosteric enzymes include mammalian tyrosyl tRNA-synthetase, which shows negative cooperativity,<sup id="cite_ref-33" class="reference"><a href="#cite_note-33"><span class="cite-bracket">[</span>33<span class="cite-bracket">]</span></a></sup> and bacterial <a href="/wiki/Aspartate_transcarbamoylase" class="mw-redirect" title="Aspartate transcarbamoylase">aspartate transcarbamoylase</a><sup id="cite_ref-34" class="reference"><a href="#cite_note-34"><span class="cite-bracket">[</span>34<span class="cite-bracket">]</span></a></sup> and <a href="/wiki/Phosphofructokinase" title="Phosphofructokinase">phosphofructokinase</a>,<sup id="cite_ref-35" class="reference"><a href="#cite_note-35"><span class="cite-bracket">[</span>35<span class="cite-bracket">]</span></a></sup> which show positive cooperativity. </p><p>Cooperativity is surprisingly common and can help regulate the responses of enzymes to changes in the concentrations of their substrates. Positive cooperativity makes enzymes much more sensitive to [S] and their activities can show large changes over a narrow range of substrate concentration. Conversely, negative cooperativity makes enzymes insensitive to small changes in [S]. </p><p>The <a href="/wiki/Hill_equation_(biochemistry)" title="Hill equation (biochemistry)">Hill equation</a><sup id="cite_ref-36" class="reference"><a href="#cite_note-36"><span class="cite-bracket">[</span>36<span class="cite-bracket">]</span></a></sup> is often used to describe the degree of cooperativity quantitatively in non-Michaelis–Menten kinetics. The derived Hill coefficient <i>n</i> measures how much the binding of substrate to one active site affects the binding of substrate to the other active sites. A Hill coefficient of <1 indicates negative cooperativity and a coefficient of >1 indicates positive <a href="/wiki/Cooperativity" title="Cooperativity">cooperativity</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Pre-steady-state_kinetics">Pre-steady-state kinetics</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Enzyme_kinetics&action=edit&section=14" title="Edit section: Pre-steady-state kinetics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Burst_phase.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/ab/Burst_phase.svg/300px-Burst_phase.svg.png" decoding="async" width="300" height="208" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/ab/Burst_phase.svg/450px-Burst_phase.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/ab/Burst_phase.svg/600px-Burst_phase.svg.png 2x" data-file-width="704" data-file-height="487" /></a><figcaption>Pre-steady state progress curve, showing the burst phase of an enzyme reaction.</figcaption></figure> <p>In the first moment after an enzyme is mixed with substrate, no product has been formed and no <a href="/wiki/Reactive_intermediate" title="Reactive intermediate">intermediates</a> exist. The study of the next few milliseconds of the reaction is called pre-steady-state kinetics. Pre-steady-state kinetics is therefore concerned with the formation and consumption of enzyme–substrate intermediates (such as ES or E*) until their <a href="/wiki/Steady_state_(chemistry)" title="Steady state (chemistry)">steady-state concentrations</a> are reached. </p><p>This approach was first applied to the hydrolysis reaction catalysed by <a href="/wiki/Chymotrypsin" title="Chymotrypsin">chymotrypsin</a>.<sup id="cite_ref-37" class="reference"><a href="#cite_note-37"><span class="cite-bracket">[</span>37<span class="cite-bracket">]</span></a></sup> Often, the detection of an intermediate is a vital piece of evidence in investigations of what mechanism an enzyme follows. For example, in the ping–pong mechanisms that are shown above, rapid kinetic measurements can follow the release of product P and measure the formation of the modified enzyme intermediate E*.<sup id="cite_ref-Fersht_38-0" class="reference"><a href="#cite_note-Fersht-38"><span class="cite-bracket">[</span>38<span class="cite-bracket">]</span></a></sup> In the case of chymotrypsin, this intermediate is formed by an attack on the substrate by the <a href="/wiki/Nucleophile" title="Nucleophile">nucleophilic</a> serine in the active site and the formation of the acyl-enzyme intermediate. </p><p>In the figure to the right, the enzyme produces E* rapidly in the first few seconds of the reaction. The rate then slows as steady state is reached. This rapid burst phase of the reaction measures a single turnover of the enzyme. Consequently, the amount of product released in this burst, shown as the intercept on the <i>y</i>-axis of the graph, also gives the amount of functional enzyme which is present in the assay.<sup id="cite_ref-39" class="reference"><a href="#cite_note-39"><span class="cite-bracket">[</span>39<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Chemical_mechanism">Chemical mechanism</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Enzyme_kinetics&action=edit&section=15" title="Edit section: Chemical mechanism"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>An important goal of measuring enzyme kinetics is to determine the chemical mechanism of an enzyme reaction, i.e., the sequence of chemical steps that transform substrate into product. The kinetic approaches discussed above will show at what rates <a href="/wiki/Reactive_intermediate" title="Reactive intermediate">intermediates</a> are formed and inter-converted, but they cannot identify exactly what these intermediates are. </p><p>Kinetic measurements taken under various solution conditions or on slightly modified enzymes or substrates often shed light on this chemical mechanism, as they reveal the rate-determining step or intermediates in the reaction. For example, the breaking of a <a href="/wiki/Covalent_bond" title="Covalent bond">covalent bond</a> to a <a href="/wiki/Hydrogen" title="Hydrogen">hydrogen</a> <a href="/wiki/Atom" title="Atom">atom</a> is a common rate-determining step. Which of the possible hydrogen transfers is rate determining can be shown by measuring the kinetic effects of substituting each hydrogen by <a href="/wiki/Deuterium" title="Deuterium">deuterium</a>, its stable <a href="/wiki/Isotope" title="Isotope">isotope</a>. The rate will change when the critical hydrogen is replaced, due to a primary <a href="/wiki/Kinetic_isotope_effect" title="Kinetic isotope effect">kinetic isotope effect</a>, which occurs because bonds to deuterium are harder to break than bonds to hydrogen.<sup id="cite_ref-40" class="reference"><a href="#cite_note-40"><span class="cite-bracket">[</span>40<span class="cite-bracket">]</span></a></sup> It is also possible to measure similar effects with other isotope substitutions, such as <sup>13</sup>C/<sup>12</sup>C and <sup>18</sup>O/<sup>16</sup>O, but these effects are more subtle.<sup id="cite_ref-41" class="reference"><a href="#cite_note-41"><span class="cite-bracket">[</span>41<span class="cite-bracket">]</span></a></sup> </p><p>Isotopes can also be used to reveal the fate of various parts of the substrate molecules in the final products. For example, it is sometimes difficult to discern the origin of an <a href="/wiki/Oxygen" title="Oxygen">oxygen</a> atom in the final product; since it may have come from water or from part of the substrate. This may be determined by systematically substituting oxygen's stable isotope <sup>18</sup>O into the various molecules that participate in the reaction and checking for the isotope in the product.<sup id="cite_ref-42" class="reference"><a href="#cite_note-42"><span class="cite-bracket">[</span>42<span class="cite-bracket">]</span></a></sup> The chemical mechanism can also be elucidated by examining the kinetics and isotope effects under different pH conditions,<sup id="cite_ref-43" class="reference"><a href="#cite_note-43"><span class="cite-bracket">[</span>43<span class="cite-bracket">]</span></a></sup> by altering the metal ions or other bound <a href="/wiki/Cofactor_(biochemistry)" title="Cofactor (biochemistry)">cofactors</a>,<sup id="cite_ref-44" class="reference"><a href="#cite_note-44"><span class="cite-bracket">[</span>44<span class="cite-bracket">]</span></a></sup> by <a href="/wiki/Site-directed_mutagenesis" title="Site-directed mutagenesis">site-directed mutagenesis</a> of conserved amino acid residues, or by studying the behaviour of the enzyme in the presence of analogues of the substrate(s).<sup id="cite_ref-45" class="reference"><a href="#cite_note-45"><span class="cite-bracket">[</span>45<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Enzyme_inhibition_and_activation">Enzyme inhibition and activation</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Enzyme_kinetics&action=edit&section=16" title="Edit section: Enzyme inhibition and activation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Enzyme_inhibitor" title="Enzyme inhibitor">Enzyme inhibitor</a></div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Reversible_inhibition.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f3/Reversible_inhibition.svg/300px-Reversible_inhibition.svg.png" decoding="async" width="300" height="142" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f3/Reversible_inhibition.svg/450px-Reversible_inhibition.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f3/Reversible_inhibition.svg/600px-Reversible_inhibition.svg.png 2x" data-file-width="761" data-file-height="361" /></a><figcaption>Kinetic scheme for reversible enzyme inhibitors.</figcaption></figure> <p>Enzyme inhibitors are molecules that reduce or abolish enzyme activity, while enzyme activators are molecules that increase the catalytic rate of enzymes. These interactions can be either <i>reversible</i> (i.e., removal of the inhibitor restores enzyme activity) or <i>irreversible</i> (i.e., the inhibitor permanently inactivates the enzyme). </p> <div class="mw-heading mw-heading3"><h3 id="Reversible_inhibitors">Reversible inhibitors</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Enzyme_kinetics&action=edit&section=17" title="Edit section: Reversible inhibitors"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Traditionally reversible enzyme inhibitors have been classified as <a href="/wiki/Competitive_inhibition" title="Competitive inhibition">competitive</a>, <a href="/wiki/Uncompetitive_inhibition" title="Uncompetitive inhibition">uncompetitive</a>, or <a href="/wiki/Non-competitive_inhibition" title="Non-competitive inhibition">non-competitive</a>, according to their effects on <i>K</i><sub>M</sub> and <i>V</i><sub>max</sub>. These different effects result from the inhibitor binding to the enzyme E, to the enzyme–substrate complex ES, or to both, respectively. The division of these classes arises from a problem in their derivation and results in the need to use two different binding constants for one binding event. The binding of an inhibitor and its effect on the enzymatic activity are two distinctly different things, another problem the traditional equations fail to acknowledge. In noncompetitive inhibition the binding of the inhibitor results in 100% inhibition of the enzyme only, and fails to consider the possibility of anything in between.<sup id="cite_ref-46" class="reference"><a href="#cite_note-46"><span class="cite-bracket">[</span>46<span class="cite-bracket">]</span></a></sup> In noncompetitive inhibition, the inhibitor will bind to an enzyme at its allosteric site; therefore, the binding affinity, or inverse of <i>K</i><sub>M</sub>, of the substrate with the enzyme will remain the same. On the other hand, the V<sub>max</sub> will decrease relative to an uninhibited enzyme. On a Lineweaver-Burk plot, the presence of a noncompetitive inhibitor is illustrated by a change in the y-intercept, defined as 1/V<sub>max</sub>. The x-intercept, defined as −1/<i>K</i><sub>M</sub>, will remain the same. In competitive inhibition, the inhibitor will bind to an enzyme at the active site, competing with the substrate. As a result, the <i>K</i><sub>M</sub> will increase and the V<sub>max</sub> will remain the same.<sup id="cite_ref-47" class="reference"><a href="#cite_note-47"><span class="cite-bracket">[</span>47<span class="cite-bracket">]</span></a></sup> The common form of the inhibitory term also obscures the relationship between the inhibitor binding to the enzyme and its relationship to any other binding term be it the Michaelis–Menten equation or a dose response curve associated with ligand receptor binding. To demonstrate the relationship the following rearrangement can be made: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\cfrac {V_{\max }}{1+{\cfrac {[I]}{K_{i}}}}}={\cfrac {V_{\max }}{\cfrac {[I]+K_{i}}{K_{i}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mpadded width="0" height="8.6pt" depth="3pt"> <mrow /> </mpadded> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mo movablelimits="true" form="prefix">max</mo> </mrow> </msub> </mrow> </mstyle> </mrow> <mrow> <mpadded width="0" height="8.6pt" depth="3pt"> <mrow /> </mpadded> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mpadded width="0" height="8.6pt" depth="3pt"> <mrow /> </mpadded> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">[</mo> <mi>I</mi> <mo stretchy="false">]</mo> </mrow> </mstyle> </mrow> <mrow> <mpadded width="0" height="8.6pt" depth="3pt"> <mrow /> </mpadded> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mrow> </mstyle> </mrow> </mfrac> </mrow> </mrow> </mstyle> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mpadded width="0" height="8.6pt" depth="3pt"> <mrow /> </mpadded> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mo movablelimits="true" form="prefix">max</mo> </mrow> </msub> </mrow> </mstyle> </mrow> <mrow> <mpadded width="0" height="8.6pt" depth="3pt"> <mrow /> </mpadded> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mpadded width="0" height="8.6pt" depth="3pt"> <mrow /> </mpadded> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">[</mo> <mi>I</mi> <mo stretchy="false">]</mo> <mo>+</mo> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mrow> </mstyle> </mrow> <mrow> <mpadded width="0" height="8.6pt" depth="3pt"> <mrow /> </mpadded> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mrow> </mstyle> </mrow> </mfrac> </mrow> </mstyle> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\cfrac {V_{\max }}{1+{\cfrac {[I]}{K_{i}}}}}={\cfrac {V_{\max }}{\cfrac {[I]+K_{i}}{K_{i}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1c58cef49731511f5011822f1e92d4da22814891" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -6.671ex; width:21.297ex; height:10.843ex;" alt="{\displaystyle {\cfrac {V_{\max }}{1+{\cfrac {[I]}{K_{i}}}}}={\cfrac {V_{\max }}{\cfrac {[I]+K_{i}}{K_{i}}}}}"></span></dd></dl> <p>Adding zero to the bottom ([I]-[I]) </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\cfrac {V_{\max }}{\cfrac {[I]+K_{i}}{[I]+K_{i}-[I]}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mpadded width="0" height="8.6pt" depth="3pt"> <mrow /> </mpadded> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mo movablelimits="true" form="prefix">max</mo> </mrow> </msub> </mrow> </mstyle> </mrow> <mrow> <mpadded width="0" height="8.6pt" depth="3pt"> <mrow /> </mpadded> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mpadded width="0" height="8.6pt" depth="3pt"> <mrow /> </mpadded> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">[</mo> <mi>I</mi> <mo stretchy="false">]</mo> <mo>+</mo> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mrow> </mstyle> </mrow> <mrow> <mpadded width="0" height="8.6pt" depth="3pt"> <mrow /> </mpadded> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">[</mo> <mi>I</mi> <mo stretchy="false">]</mo> <mo>+</mo> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>−</mo> <mo stretchy="false">[</mo> <mi>I</mi> <mo stretchy="false">]</mo> </mrow> </mstyle> </mrow> </mfrac> </mrow> </mstyle> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\cfrac {V_{\max }}{\cfrac {[I]+K_{i}}{[I]+K_{i}-[I]}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/42e34b0927bf9484b8a664e022d3fd6ba0ad2326" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -6.671ex; width:15.057ex; height:10.843ex;" alt="{\displaystyle {\cfrac {V_{\max }}{\cfrac {[I]+K_{i}}{[I]+K_{i}-[I]}}}}"></span></dd></dl> <p>Dividing by [I]+K<sub>i</sub> </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\cfrac {V_{\max }}{\cfrac {1}{1-{\cfrac {[I]}{[I]+K_{i}}}}}}=V_{\max }-V_{\max }{\cfrac {[I]}{[I]+K_{i}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mpadded width="0" height="8.6pt" depth="3pt"> <mrow /> </mpadded> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mo movablelimits="true" form="prefix">max</mo> </mrow> </msub> </mrow> </mstyle> </mrow> <mrow> <mpadded width="0" height="8.6pt" depth="3pt"> <mrow /> </mpadded> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mpadded width="0" height="8.6pt" depth="3pt"> <mrow /> </mpadded> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </mstyle> </mrow> <mrow> <mpadded width="0" height="8.6pt" depth="3pt"> <mrow /> </mpadded> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mpadded width="0" height="8.6pt" depth="3pt"> <mrow /> </mpadded> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">[</mo> <mi>I</mi> <mo stretchy="false">]</mo> </mrow> </mstyle> </mrow> <mrow> <mpadded width="0" height="8.6pt" depth="3pt"> <mrow /> </mpadded> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">[</mo> <mi>I</mi> <mo stretchy="false">]</mo> <mo>+</mo> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mrow> </mstyle> </mrow> </mfrac> </mrow> </mrow> </mstyle> </mrow> </mfrac> </mrow> </mstyle> </mrow> </mfrac> </mrow> <mo>=</mo> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mo movablelimits="true" form="prefix">max</mo> </mrow> </msub> <mo>−</mo> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mo movablelimits="true" form="prefix">max</mo> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mpadded width="0" height="8.6pt" depth="3pt"> <mrow /> </mpadded> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">[</mo> <mi>I</mi> <mo stretchy="false">]</mo> </mrow> </mstyle> </mrow> <mrow> <mpadded width="0" height="8.6pt" depth="3pt"> <mrow /> </mpadded> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">[</mo> <mi>I</mi> <mo stretchy="false">]</mo> <mo>+</mo> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mrow> </mstyle> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\cfrac {V_{\max }}{\cfrac {1}{1-{\cfrac {[I]}{[I]+K_{i}}}}}}=V_{\max }-V_{\max }{\cfrac {[I]}{[I]+K_{i}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4132fbd61b7474f8e3ef391f82d1d196a2a325ff" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -10.171ex; width:38.736ex; height:14.343ex;" alt="{\displaystyle {\cfrac {V_{\max }}{\cfrac {1}{1-{\cfrac {[I]}{[I]+K_{i}}}}}}=V_{\max }-V_{\max }{\cfrac {[I]}{[I]+K_{i}}}}"></span></dd></dl> <p>This notation demonstrates that similar to the Michaelis–Menten equation, where the rate of reaction depends on the percent of the enzyme population interacting with substrate, the effect of the inhibitor is a result of the percent of the enzyme population interacting with inhibitor. The only problem with this equation in its present form is that it assumes absolute inhibition of the enzyme with inhibitor binding, when in fact there can be a wide range of effects anywhere from 100% inhibition of substrate turn over to just >0%. To account for this the equation can be easily modified to allow for different degrees of inhibition by including a delta <i>V</i><sub>max</sub> term. </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V_{\max }-\Delta V_{\max }{\cfrac {[I]}{[I]+K_{i}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mo movablelimits="true" form="prefix">max</mo> </mrow> </msub> <mo>−</mo> <mi mathvariant="normal">Δ</mi> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mo movablelimits="true" form="prefix">max</mo> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mpadded width="0" height="8.6pt" depth="3pt"> <mrow /> </mpadded> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">[</mo> <mi>I</mi> <mo stretchy="false">]</mo> </mrow> </mstyle> </mrow> <mrow> <mpadded width="0" height="8.6pt" depth="3pt"> <mrow /> </mpadded> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">[</mo> <mi>I</mi> <mo stretchy="false">]</mo> <mo>+</mo> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mrow> </mstyle> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V_{\max }-\Delta V_{\max }{\cfrac {[I]}{[I]+K_{i}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/90f5601fefd8114c165ac3dfb739e0642e62610c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:22.984ex; height:7.176ex;" alt="{\displaystyle V_{\max }-\Delta V_{\max }{\cfrac {[I]}{[I]+K_{i}}}}"></span></dd></dl> <p>or </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V_{\max 1}-(V_{\max 1}-V_{\max 2}){\cfrac {[I]}{[I]+K_{i}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mo movablelimits="true" form="prefix">max</mo> <mn>1</mn> </mrow> </msub> <mo>−</mo> <mo stretchy="false">(</mo> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mo movablelimits="true" form="prefix">max</mo> <mn>1</mn> </mrow> </msub> <mo>−</mo> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mo movablelimits="true" form="prefix">max</mo> <mn>2</mn> </mrow> </msub> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mpadded width="0" height="8.6pt" depth="3pt"> <mrow /> </mpadded> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">[</mo> <mi>I</mi> <mo stretchy="false">]</mo> </mrow> </mstyle> </mrow> <mrow> <mpadded width="0" height="8.6pt" depth="3pt"> <mrow /> </mpadded> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">[</mo> <mi>I</mi> <mo stretchy="false">]</mo> <mo>+</mo> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mrow> </mstyle> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V_{\max 1}-(V_{\max 1}-V_{\max 2}){\cfrac {[I]}{[I]+K_{i}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8c31b5f56aaeed122d1f8a67491c56d272686b6e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:33.971ex; height:7.176ex;" alt="{\displaystyle V_{\max 1}-(V_{\max 1}-V_{\max 2}){\cfrac {[I]}{[I]+K_{i}}}}"></span></dd></dl> <p>This term can then define the residual enzymatic activity present when the inhibitor is interacting with individual enzymes in the population. However the inclusion of this term has the added value of allowing for the possibility of activation if the secondary <i>V</i><sub>max</sub> term turns out to be higher than the initial term. To account for the possibly of activation as well the notation can then be rewritten replacing the inhibitor "I" with a modifier term denoted here as "X". </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V_{\max 1}-(V_{\max 1}-V_{\max 2}){\cfrac {[X]}{[X]+K_{x}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mo movablelimits="true" form="prefix">max</mo> <mn>1</mn> </mrow> </msub> <mo>−</mo> <mo stretchy="false">(</mo> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mo movablelimits="true" form="prefix">max</mo> <mn>1</mn> </mrow> </msub> <mo>−</mo> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mo movablelimits="true" form="prefix">max</mo> <mn>2</mn> </mrow> </msub> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mpadded width="0" height="8.6pt" depth="3pt"> <mrow /> </mpadded> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">[</mo> <mi>X</mi> <mo stretchy="false">]</mo> </mrow> </mstyle> </mrow> <mrow> <mpadded width="0" height="8.6pt" depth="3pt"> <mrow /> </mpadded> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">[</mo> <mi>X</mi> <mo stretchy="false">]</mo> <mo>+</mo> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> </mrow> </mstyle> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V_{\max 1}-(V_{\max 1}-V_{\max 2}){\cfrac {[X]}{[X]+K_{x}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2bb687fca77a00dba879a00fb32b7ca1bc867973" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:35.152ex; height:7.176ex;" alt="{\displaystyle V_{\max 1}-(V_{\max 1}-V_{\max 2}){\cfrac {[X]}{[X]+K_{x}}}}"></span></dd></dl> <p>While this terminology results in a simplified way of dealing with kinetic effects relating to the maximum velocity of the Michaelis–Menten equation, it highlights potential problems with the term used to describe effects relating to the <i>K</i><sub>M</sub>. The <i>K</i><sub>M</sub> relating to the affinity of the enzyme for the substrate should in most cases relate to potential changes in the binding site of the enzyme which would directly result from enzyme inhibitor interactions. As such a term similar to the one proposed above to modulate <i>V</i><sub>max</sub> should be appropriate in most situations:<sup id="cite_ref-48" class="reference"><a href="#cite_note-48"><span class="cite-bracket">[</span>48<span class="cite-bracket">]</span></a></sup> </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle K_{m1}-(K_{m1}-K_{m2}){\cfrac {[X]}{[X]+K_{x}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> <mn>1</mn> </mrow> </msub> <mo>−</mo> <mo stretchy="false">(</mo> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> <mn>1</mn> </mrow> </msub> <mo>−</mo> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> <mn>2</mn> </mrow> </msub> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mpadded width="0" height="8.6pt" depth="3pt"> <mrow /> </mpadded> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">[</mo> <mi>X</mi> <mo stretchy="false">]</mo> </mrow> </mstyle> </mrow> <mrow> <mpadded width="0" height="8.6pt" depth="3pt"> <mrow /> </mpadded> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">[</mo> <mi>X</mi> <mo stretchy="false">]</mo> <mo>+</mo> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> </mrow> </mstyle> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle K_{m1}-(K_{m1}-K_{m2}){\cfrac {[X]}{[X]+K_{x}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/55a298dbb441e88b96a618cc31df3aaebac17d85" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:30.996ex; height:7.176ex;" alt="{\displaystyle K_{m1}-(K_{m1}-K_{m2}){\cfrac {[X]}{[X]+K_{x}}}}"></span></dd></dl> <div class="mw-heading mw-heading3"><h3 id="Irreversible_inhibitors">Irreversible inhibitors</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Enzyme_kinetics&action=edit&section=18" title="Edit section: Irreversible inhibitors"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Enzyme inhibitors can also irreversibly inactivate enzymes, usually by covalently modifying active site residues. These reactions, which may be called suicide substrates, follow <a href="/wiki/Exponential_decay" title="Exponential decay">exponential decay</a> functions and are usually saturable. Below saturation, they follow <a href="/wiki/Reaction_rate" title="Reaction rate">first order</a> kinetics with respect to inhibitor. Irreversible inhibition could be classified into two distinct types. Affinity labelling is a type of irreversible inhibition where a functional group that is highly reactive modifies a catalytically critical residue on the protein of interest to bring about inhibition. Mechanism-based inhibition, on the other hand, involves binding of the inhibitor followed by enzyme mediated alterations that transform the latter into a reactive group that irreversibly modifies the enzyme. </p> <div class="mw-heading mw-heading3"><h3 id="Philosophical_discourse_on_reversibility_and_irreversibility_of_inhibition">Philosophical discourse on reversibility and irreversibility of inhibition</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Enzyme_kinetics&action=edit&section=19" title="Edit section: Philosophical discourse on reversibility and irreversibility of inhibition"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Having discussed reversible inhibition and irreversible inhibition in the above two headings, it would have to be pointed out that the concept of reversibility (or irreversibility) is a purely theoretical construct exclusively dependent on the time-frame of the assay, i.e., a reversible assay involving association and dissociation of the inhibitor molecule in the minute timescales would seem irreversible if an assay assess the outcome in the seconds and vice versa. There is a continuum of inhibitor behaviors spanning reversibility and irreversibility at a given non-arbitrary assay time frame. There are inhibitors that show slow-onset behavior and most of these inhibitors, invariably, also show tight-binding to the protein target of interest. </p> <div class="mw-heading mw-heading2"><h2 id="Mechanisms_of_catalysis">Mechanisms of catalysis</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Enzyme_kinetics&action=edit&section=20" title="Edit section: Mechanisms of catalysis"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Enzyme_catalysis" title="Enzyme catalysis">Enzyme catalysis</a></div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Activation2_updated.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e3/Activation2_updated.svg/300px-Activation2_updated.svg.png" decoding="async" width="300" height="235" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e3/Activation2_updated.svg/450px-Activation2_updated.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e3/Activation2_updated.svg/600px-Activation2_updated.svg.png 2x" data-file-width="504" data-file-height="395" /></a><figcaption>The energy variation as a function of <a href="/wiki/Reaction_coordinate" title="Reaction coordinate">reaction coordinate</a> shows the stabilisation of the transition state by an enzyme.</figcaption></figure> <p>The favoured model for the enzyme–substrate interaction is the induced fit model.<sup id="cite_ref-49" class="reference"><a href="#cite_note-49"><span class="cite-bracket">[</span>49<span class="cite-bracket">]</span></a></sup> This model proposes that the initial interaction between enzyme and substrate is relatively weak, but that these weak interactions rapidly induce <a href="/wiki/Conformational_change" title="Conformational change">conformational changes</a> in the enzyme that strengthen binding. These <a href="/wiki/Tertiary_structure" class="mw-redirect" title="Tertiary structure">conformational</a> changes also bring catalytic residues in the active site close to the chemical bonds in the substrate that will be altered in the reaction.<sup id="cite_ref-50" class="reference"><a href="#cite_note-50"><span class="cite-bracket">[</span>50<span class="cite-bracket">]</span></a></sup> Conformational changes can be measured using <a href="/wiki/Circular_dichroism" title="Circular dichroism">circular dichroism</a> or <a href="/wiki/Dual_polarisation_interferometry" class="mw-redirect" title="Dual polarisation interferometry">dual polarisation interferometry</a>. After binding takes place, one or more mechanisms of catalysis lower the energy of the reaction's <a href="/wiki/Transition_state" title="Transition state">transition state</a> by providing an alternative chemical pathway for the reaction. Mechanisms of catalysis include catalysis by bond strain; by proximity and orientation; by active-site proton donors or acceptors; covalent catalysis and <a href="/wiki/Quantum_tunnelling" title="Quantum tunnelling">quantum tunnelling</a>.<sup id="cite_ref-Fersht_38-1" class="reference"><a href="#cite_note-Fersht-38"><span class="cite-bracket">[</span>38<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-51" class="reference"><a href="#cite_note-51"><span class="cite-bracket">[</span>51<span class="cite-bracket">]</span></a></sup> </p><p>Enzyme kinetics cannot prove which modes of catalysis are used by an enzyme. However, some kinetic data can suggest possibilities to be examined by other techniques. For example, a ping–pong mechanism with burst-phase pre-steady-state kinetics would suggest covalent catalysis might be important in this enzyme's mechanism. Alternatively, the observation of a strong pH effect on <i>V</i><sub>max</sub> but not <i>K</i><sub>M</sub> might indicate that a residue in the active site needs to be in a particular <a href="/wiki/Ionization" title="Ionization">ionisation</a> state for catalysis to occur. </p> <div class="mw-heading mw-heading2"><h2 id="History">History</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Enzyme_kinetics&action=edit&section=21" title="Edit section: History"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In 1902 <a href="/wiki/Victor_Henri" title="Victor Henri">Victor Henri</a> proposed a quantitative theory of enzyme kinetics,<sup id="cite_ref-52" class="reference"><a href="#cite_note-52"><span class="cite-bracket">[</span>52<span class="cite-bracket">]</span></a></sup> but at the time the experimental significance of the <a href="/wiki/PH" title="PH">hydrogen ion concentration</a> was not yet recognized. After <a href="/wiki/S._P._L._S%C3%B8rensen" title="S. P. L. Sørensen">Peter Lauritz Sørensen</a> had defined the logarithmic pH-scale and introduced the concept of <a href="/wiki/Buffer_solution" title="Buffer solution">buffering</a> in 1909<sup id="cite_ref-53" class="reference"><a href="#cite_note-53"><span class="cite-bracket">[</span>53<span class="cite-bracket">]</span></a></sup> the German chemist <a href="/wiki/Leonor_Michaelis" title="Leonor Michaelis">Leonor Michaelis</a> and Dr. <a href="/wiki/Maud_Leonora_Menten" class="mw-redirect" title="Maud Leonora Menten">Maud Leonora Menten</a> (a postdoctoral researcher in Michaelis's lab at the time) repeated Henri's experiments and confirmed his equation, which is now generally referred to as <a href="/wiki/Michaelis-Menten_kinetics" class="mw-redirect" title="Michaelis-Menten kinetics">Michaelis-Menten kinetics</a> (sometimes also <i>Henri-Michaelis-Menten kinetics</i>).<sup id="cite_ref-54" class="reference"><a href="#cite_note-54"><span class="cite-bracket">[</span>54<span class="cite-bracket">]</span></a></sup> Their work was further developed by <a href="/wiki/George_Edward_Briggs" title="George Edward Briggs">G. E. Briggs</a> and <a href="/wiki/J._B._S._Haldane" title="J. B. S. Haldane">J. B. S. Haldane</a>, who derived kinetic equations that are still widely considered today a starting point in modeling enzymatic activity.<sup id="cite_ref-55" class="reference"><a href="#cite_note-55"><span class="cite-bracket">[</span>55<span class="cite-bracket">]</span></a></sup> </p><p>The major contribution of the Henri-Michaelis-Menten approach was to think of enzyme reactions in two stages. In the first, the substrate binds reversibly to the enzyme, forming the enzyme-substrate complex. This is sometimes called the Michaelis complex. The enzyme then catalyzes the chemical step in the reaction and releases the product. The kinetics of many enzymes is adequately described by the simple Michaelis-Menten model, but all enzymes have <a href="/wiki/Protein_dynamics" title="Protein dynamics">internal motions</a> that are not accounted for in the model and can have significant contributions to the overall reaction kinetics. This can be modeled by introducing several Michaelis-Menten pathways that are connected with fluctuating rates,<sup id="cite_ref-OF_2005_56-0" class="reference"><a href="#cite_note-OF_2005-56"><span class="cite-bracket">[</span>56<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-English_2006_57-0" class="reference"><a href="#cite_note-English_2006-57"><span class="cite-bracket">[</span>57<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Lu_1998_58-0" class="reference"><a href="#cite_note-Lu_1998-58"><span class="cite-bracket">[</span>58<span class="cite-bracket">]</span></a></sup> which is a mathematical extension of the basic Michaelis Menten mechanism.<sup id="cite_ref-XX_2006_59-0" class="reference"><a href="#cite_note-XX_2006-59"><span class="cite-bracket">[</span>59<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Software">Software</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Enzyme_kinetics&action=edit&section=22" title="Edit section: Software"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><b>ENZO</b> (Enzyme Kinetics) is a graphical interface tool for building kinetic models of enzyme catalyzed reactions. ENZO automatically generates the corresponding differential equations from a stipulated enzyme reaction scheme. These differential equations are processed by a numerical solver and a regression algorithm which fits the coefficients of differential equations to experimentally observed time course curves. ENZO allows rapid evaluation of rival reaction schemes and can be used for routine tests in enzyme kinetics.<sup id="cite_ref-60" class="reference"><a href="#cite_note-60"><span class="cite-bracket">[</span>60<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Enzyme_kinetics&action=edit&section=23" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Protein_dynamics" title="Protein dynamics">Protein dynamics</a></li> <li><a href="/wiki/Diffusion_limited_enzyme" class="mw-redirect" title="Diffusion limited enzyme">Diffusion limited enzyme</a></li> <li><a href="/wiki/Langmuir_adsorption_model" title="Langmuir adsorption model">Langmuir adsorption model</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Footnotes">Footnotes</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Enzyme_kinetics&action=edit&section=24" title="Edit section: Footnotes"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <dl><dd><b>α.</b> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1041539562"><span class="citation wikicite" id="endnote_Anone"><a href="#ref_Anone"><b><sup>^</sup></b></a></span> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20120616044431/http://cti.itc.virginia.edu/~cmg/Demo/scriptFrame.html">Link: Interactive Michaelis–Menten kinetics tutorial (Java required)</a></dd></dl> <dl><dd><b>β.</b> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1041539562"><span class="citation wikicite" id="endnote_Bnone"><a href="#ref_Bnone"><b><sup>^</sup></b></a></span> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20060820062258/http://chem-faculty.ucsd.edu/kraut/dhfr.html">Link: dihydrofolate reductase mechanism (Gif)</a></dd></dl> <dl><dd><b>γ.</b> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1041539562"><span class="citation wikicite" id="endnote_Cnone"><a href="#ref_Cnone"><b><sup>^</sup></b></a></span> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20060514070741/http://chem-faculty.ucsd.edu/kraut/dNTP.html">Link: DNA polymerase mechanism (Gif)</a></dd></dl> <dl><dd><b>δ.</b> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1041539562"><span class="citation wikicite" id="endnote_Dnone"><a href="#ref_Dnone"><b><sup>^</sup></b></a></span> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20070319235224/http://courses.cm.utexas.edu/jrobertus/ch339k/overheads-2/06_21_chymotrypsin.html">Link: Chymotrypsin mechanism (Flash required)</a></dd></dl> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Enzyme_kinetics&action=edit&section=25" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist reflist-columns references-column-width" style="column-width: 35em;"> <ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFWrightonEbbing1993" class="citation book cs1">Wrighton MS, Ebbing DD (1993). <i>General chemistry</i> (4th ed.). Boston: Houghton Mifflin. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-395-63696-1" title="Special:BookSources/978-0-395-63696-1"><bdi>978-0-395-63696-1</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=General+chemistry&rft.place=Boston&rft.edition=4th&rft.pub=Houghton+Mifflin&rft.date=1993&rft.isbn=978-0-395-63696-1&rft.aulast=Wrighton&rft.aufirst=MS&rft.au=Ebbing%2C+DD&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEnzyme+kinetics" class="Z3988"></span></span> </li> <li id="cite_note-Fromm_H.J._2012-2"><span class="mw-cite-backlink">^ <a href="#cite_ref-Fromm_H.J._2012_2-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Fromm_H.J._2012_2-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text">Fromm H.J., Hargrove M.S. (2012) Enzyme Kinetics. In: Essentials of Biochemistry. Springer, Berlin, Heidelberg</span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDansonEisenthal2002" class="citation book cs1">Danson M, Eisenthal R (2002). <i>Enzyme assays: a practical approach</i>. Oxford [Oxfordshire]: Oxford University Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-19-963820-8" title="Special:BookSources/978-0-19-963820-8"><bdi>978-0-19-963820-8</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Enzyme+assays%3A+a+practical+approach&rft.place=Oxford+%5BOxfordshire%5D&rft.pub=Oxford+University+Press&rft.date=2002&rft.isbn=978-0-19-963820-8&rft.aulast=Danson&rft.aufirst=M&rft.au=Eisenthal%2C+R&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEnzyme+kinetics" class="Z3988"></span></span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFXieLu1999" class="citation journal cs1">Xie XS, Lu HP (June 1999). <a rel="nofollow" class="external text" href="https://doi.org/10.1074%2Fjbc.274.23.15967">"Single-molecule enzymology"</a>. <i>The Journal of Biological Chemistry</i>. <b>274</b> (23): 15967–15970. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1074%2Fjbc.274.23.15967">10.1074/jbc.274.23.15967</a></span>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/10347141">10347141</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=The+Journal+of+Biological+Chemistry&rft.atitle=Single-molecule+enzymology&rft.volume=274&rft.issue=23&rft.pages=15967-15970&rft.date=1999-06&rft_id=info%3Adoi%2F10.1074%2Fjbc.274.23.15967&rft_id=info%3Apmid%2F10347141&rft.aulast=Xie&rft.aufirst=XS&rft.au=Lu%2C+HP&rft_id=https%3A%2F%2Fdoi.org%2F10.1074%252Fjbc.274.23.15967&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEnzyme+kinetics" class="Z3988"></span></span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLu2004" class="citation journal cs1">Lu HP (June 2004). "Single-molecule spectroscopy studies of conformational change dynamics in enzymatic reactions". <i>Current Pharmaceutical Biotechnology</i>. <b>5</b> (3): 261–269. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.2174%2F1389201043376887">10.2174/1389201043376887</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/15180547">15180547</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Current+Pharmaceutical+Biotechnology&rft.atitle=Single-molecule+spectroscopy+studies+of+conformational+change+dynamics+in+enzymatic+reactions&rft.volume=5&rft.issue=3&rft.pages=261-269&rft.date=2004-06&rft_id=info%3Adoi%2F10.2174%2F1389201043376887&rft_id=info%3Apmid%2F15180547&rft.aulast=Lu&rft.aufirst=HP&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEnzyme+kinetics" class="Z3988"></span></span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSchnellDysonWright2004" class="citation journal cs1">Schnell JR, <a href="/wiki/Jane_Dyson" title="Jane Dyson">Dyson HJ</a>, Wright PE (2004). "Structure, dynamics, and catalytic function of dihydrofolate reductase". <i>Annual Review of Biophysics and Biomolecular Structure</i>. <b>33</b>: 119–140. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1146%2Fannurev.biophys.33.110502.133613">10.1146/annurev.biophys.33.110502.133613</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/15139807">15139807</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Annual+Review+of+Biophysics+and+Biomolecular+Structure&rft.atitle=Structure%2C+dynamics%2C+and+catalytic+function+of+dihydrofolate+reductase&rft.volume=33&rft.pages=119-140&rft.date=2004&rft_id=info%3Adoi%2F10.1146%2Fannurev.biophys.33.110502.133613&rft_id=info%3Apmid%2F15139807&rft.aulast=Schnell&rft.aufirst=JR&rft.au=Dyson%2C+HJ&rft.au=Wright%2C+PE&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEnzyme+kinetics" class="Z3988"></span></span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGibson_QH1969" class="citation book cs1">Gibson QH (1969). "[6] Rapid mixing: Stopped flow". <i>Rapid mixing: Stopped flow</i>. Methods in Enzymology. Vol. 16. pp. 187–228. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2FS0076-6879%2869%2916009-7">10.1016/S0076-6879(69)16009-7</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-12-181873-9" title="Special:BookSources/978-0-12-181873-9"><bdi>978-0-12-181873-9</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=%26%2391%3B6%26%2393%3B+Rapid+mixing%3A+Stopped+flow&rft.btitle=Rapid+mixing%3A+Stopped+flow&rft.series=Methods+in+Enzymology&rft.pages=187-228&rft.date=1969&rft_id=info%3Adoi%2F10.1016%2FS0076-6879%2869%2916009-7&rft.isbn=978-0-12-181873-9&rft.au=Gibson+QH&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEnzyme+kinetics" class="Z3988"></span></span> </li> <li id="cite_note-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-8">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDuggleby_RG1995" class="citation book cs1">Duggleby RG (1995). 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Implications for protein architecture, substrate recognition and catalytic function". <i>European Journal of Biochemistry</i>. <b>220</b> (3): 645–661. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1111%2Fj.1432-1033.1994.tb18666.x">10.1111/j.1432-1033.1994.tb18666.x</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/8143720">8143720</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=European+Journal+of+Biochemistry&rft.atitle=X-ray+crystal+structures+of+cytosolic+glutathione+S-transferases.+Implications+for+protein+architecture%2C+substrate+recognition+and+catalytic+function&rft.volume=220&rft.issue=3&rft.pages=645-661&rft.date=1994-03&rft_id=info%3Adoi%2F10.1111%2Fj.1432-1033.1994.tb18666.x&rft_id=info%3Apmid%2F8143720&rft.aulast=Dirr&rft.aufirst=H&rft.au=Reinemer%2C+P&rft.au=Huber%2C+R&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEnzyme+kinetics" class="Z3988"></span></span> </li> <li id="cite_note-26"><span class="mw-cite-backlink"><b><a href="#cite_ref-26">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFStoneMorrison1988" class="citation journal cs1">Stone SR, Morrison JF (July 1988). 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"Single molecule Michaelis-Menten equation beyond quasistatic disorder". <i>Physical Review E</i>. <b>74</b> (3 Pt 1): 030902. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/cond-mat/0604364">cond-mat/0604364</a></span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2006PhRvE..74c0902X">2006PhRvE..74c0902X</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRevE.74.030902">10.1103/PhysRevE.74.030902</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/17025584">17025584</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:41674948">41674948</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physical+Review+E&rft.atitle=Single+molecule+Michaelis-Menten+equation+beyond+quasistatic+disorder&rft.volume=74&rft.issue=3+Pt+1&rft.pages=030902&rft.date=2006-09&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A41674948%23id-name%3DS2CID&rft_id=info%3Abibcode%2F2006PhRvE..74c0902X&rft_id=info%3Aarxiv%2Fcond-mat%2F0604364&rft_id=info%3Apmid%2F17025584&rft_id=info%3Adoi%2F10.1103%2FPhysRevE.74.030902&rft.aulast=Xue&rft.aufirst=X&rft.au=Liu%2C+F&rft.au=Ou-Yang%2C+ZC&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEnzyme+kinetics" class="Z3988"></span></span> </li> <li id="cite_note-60"><span class="mw-cite-backlink"><b><a href="#cite_ref-60">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBevcKoncStojanHodošček2011" class="citation journal cs1">Bevc S, Konc J, Stojan J, Hodošček M, Penca M, Praprotnik M, Janežič D (2011). <a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3139599">"ENZO: a web tool for derivation and evaluation of kinetic models of enzyme catalyzed reactions"</a>. <i>PLOS ONE</i>. <b>6</b> (7): e22265. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2011PLoSO...622265B">2011PLoSO...622265B</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1371%2Fjournal.pone.0022265">10.1371/journal.pone.0022265</a></span>. <a href="/wiki/PMC_(identifier)" class="mw-redirect" title="PMC (identifier)">PMC</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3139599">3139599</a></span>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/21818304">21818304</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=PLOS+ONE&rft.atitle=ENZO%3A+a+web+tool+for+derivation+and+evaluation+of+kinetic+models+of+enzyme+catalyzed+reactions&rft.volume=6&rft.issue=7&rft.pages=e22265&rft.date=2011&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC3139599%23id-name%3DPMC&rft_id=info%3Apmid%2F21818304&rft_id=info%3Adoi%2F10.1371%2Fjournal.pone.0022265&rft_id=info%3Abibcode%2F2011PLoSO...622265B&rft.aulast=Bevc&rft.aufirst=S&rft.au=Konc%2C+J&rft.au=Stojan%2C+J&rft.au=Hodo%C5%A1%C4%8Dek%2C+M&rft.au=Penca%2C+M&rft.au=Praprotnik%2C+M&rft.au=Jane%C5%BEi%C4%8D%2C+D&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC3139599&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEnzyme+kinetics" class="Z3988"></span> <a rel="nofollow" class="external text" href="http://enzo.cmm.ki.si/">ENZO server</a></span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Enzyme_kinetics&action=edit&section=26" title="Edit section: Further reading"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><b>Introductory</b> </p> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCornish-Bowden2012" class="citation book cs1">Cornish-Bowden A (2012). <i>Fundamentals of enzyme kinetics</i> (4th ed.). Weinheim: Wiley-Blackwell. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-527-33074-4" title="Special:BookSources/978-3-527-33074-4"><bdi>978-3-527-33074-4</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Fundamentals+of+enzyme+kinetics&rft.place=Weinheim&rft.edition=4th&rft.pub=Wiley-Blackwell&rft.date=2012&rft.isbn=978-3-527-33074-4&rft.aulast=Cornish-Bowden&rft.aufirst=A&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEnzyme+kinetics" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFStevensPrice1999" class="citation book cs1">Stevens L, Price NC (1999). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/fundamentalsofen0000pric_h0c7"><i>Fundamentals of enzymology: the cell and molecular biology of catalytic proteins</i></a></span>. Oxford [Oxfordshire]: Oxford University Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-19-850229-6" title="Special:BookSources/978-0-19-850229-6"><bdi>978-0-19-850229-6</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Fundamentals+of+enzymology%3A+the+cell+and+molecular+biology+of+catalytic+proteins&rft.place=Oxford+%5BOxfordshire%5D&rft.pub=Oxford+University+Press&rft.date=1999&rft.isbn=978-0-19-850229-6&rft.aulast=Stevens&rft.aufirst=L&rft.au=Price%2C+NC&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Ffundamentalsofen0000pric_h0c7&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEnzyme+kinetics" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBugg2004" class="citation book cs1">Bugg T (2004). <i>Introduction to Enzyme and Coenzyme Chemistry</i>. Cambridge, MA: Blackwell Publishers. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-4051-1452-3" title="Special:BookSources/978-1-4051-1452-3"><bdi>978-1-4051-1452-3</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Introduction+to+Enzyme+and+Coenzyme+Chemistry&rft.place=Cambridge%2C+MA&rft.pub=Blackwell+Publishers&rft.date=2004&rft.isbn=978-1-4051-1452-3&rft.aulast=Bugg&rft.aufirst=T&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEnzyme+kinetics" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSegel1993" class="citation book cs1">Segel IH (1993). <i>Enzyme kinetics: behavior and analysis of rapid equilibrium and steady state enzyme systems</i>. New York: Wiley. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-471-30309-1" title="Special:BookSources/978-0-471-30309-1"><bdi>978-0-471-30309-1</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Enzyme+kinetics%3A+behavior+and+analysis+of+rapid+equilibrium+and+steady+state+enzyme+systems&rft.place=New+York&rft.pub=Wiley&rft.date=1993&rft.isbn=978-0-471-30309-1&rft.aulast=Segel&rft.aufirst=IH&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEnzyme+kinetics" class="Z3988"></span></li></ul> <p><b>Advanced</b> </p> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFFersht1999" class="citation book cs1">Fersht A (1999). <i>Structure and mechanism in protein science: a guide to enzyme catalysis and protein folding</i>. San Francisco: W.H. Freeman. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-7167-3268-6" title="Special:BookSources/978-0-7167-3268-6"><bdi>978-0-7167-3268-6</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Structure+and+mechanism+in+protein+science%3A+a+guide+to+enzyme+catalysis+and+protein+folding&rft.place=San+Francisco&rft.pub=W.H.+Freeman&rft.date=1999&rft.isbn=978-0-7167-3268-6&rft.aulast=Fersht&rft.aufirst=A&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEnzyme+kinetics" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSchnellMaini2004" class="citation journal cs1">Schnell S, Maini PK (2004). "A century of enzyme kinetics: Reliability of the K<sub>M</sub> and v<sub>max</sub> estimates". <i>Comments on Theoretical Biology</i>. <b>8</b> (2–3): 169–87. <a href="/wiki/CiteSeerX_(identifier)" class="mw-redirect" title="CiteSeerX (identifier)">CiteSeerX</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.493.7178">10.1.1.493.7178</a></span>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1080%2F08948550302453">10.1080/08948550302453</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Comments+on+Theoretical+Biology&rft.atitle=A+century+of+enzyme+kinetics%3A+Reliability+of+the+K%3Csub%3EM%3C%2Fsub%3E+and+v%3Csub%3Emax%3C%2Fsub%3E+estimates&rft.volume=8&rft.issue=2%E2%80%933&rft.pages=169-87&rft.date=2004&rft_id=https%3A%2F%2Fciteseerx.ist.psu.edu%2Fviewdoc%2Fsummary%3Fdoi%3D10.1.1.493.7178%23id-name%3DCiteSeerX&rft_id=info%3Adoi%2F10.1080%2F08948550302453&rft.aulast=Schnell&rft.aufirst=S&rft.au=Maini%2C+PK&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEnzyme+kinetics" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWalsh1979" class="citation book cs1">Walsh C (1979). <i>Enzymatic reaction mechanisms</i>. San Francisco: W. H. Freeman. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-7167-0070-8" title="Special:BookSources/978-0-7167-0070-8"><bdi>978-0-7167-0070-8</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Enzymatic+reaction+mechanisms&rft.place=San+Francisco&rft.pub=W.+H.+Freeman&rft.date=1979&rft.isbn=978-0-7167-0070-8&rft.aulast=Walsh&rft.aufirst=C&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEnzyme+kinetics" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFClelandCook2007" class="citation book cs1">Cleland WW, Cook P (2007). <i>Enzyme kinetics and mechanism</i>. New York: Garland Science. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-8153-4140-6" title="Special:BookSources/978-0-8153-4140-6"><bdi>978-0-8153-4140-6</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Enzyme+kinetics+and+mechanism&rft.place=New+York&rft.pub=Garland+Science&rft.date=2007&rft.isbn=978-0-8153-4140-6&rft.aulast=Cleland&rft.aufirst=WW&rft.au=Cook%2C+P&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEnzyme+kinetics" class="Z3988"></span></li></ul> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Enzyme_kinetics&action=edit&section=27" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="http://www.kscience.co.uk/animations/model.swf">Animation of an enzyme assay</a> — Shows effects of manipulating assay conditions</li> <li><a rel="nofollow" class="external text" href="http://www.ebi.ac.uk/thornton-srv/databases/MACiE/">MACiE</a> — A database of enzyme reaction mechanisms</li> <li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20061006064937/http://us.expasy.org/enzyme/">ENZYME</a> — Expasy enzyme nomenclature database</li> <li><a rel="nofollow" class="external text" href="http://enzo.cmm.ki.si/">ENZO</a> — Web application for easy construction and quick testing of kinetic models of enzyme catalyzed reactions.</li> <li><a rel="nofollow" class="external text" href="http://ezcatdb.cbrc.jp/EzCatDB/">ExCatDB</a> — A database of enzyme catalytic mechanisms</li> <li><a rel="nofollow" class="external text" href="http://www.brenda-enzymes.info/">BRENDA</a> — Comprehensive enzyme database, giving substrates, inhibitors and reaction diagrams</li> <li><a rel="nofollow" class="external text" href="http://sabio.h-its.org/">SABIO-RK</a> — A database of reaction kinetics</li> <li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20060820062258/http://chem-faculty.ucsd.edu/kraut/dhfr.html">Joseph Kraut's Research Group, University of California San Diego</a> — Animations of several enzyme reaction mechanisms</li> <li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20060712051732/http://www.chem.qmul.ac.uk/iubmb/kinetics/">Symbolism and Terminology in Enzyme Kinetics</a> — A comprehensive explanation of concepts and terminology in enzyme kinetics</li> <li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20040612065857/http://orion1.paisley.ac.uk/kinetics/contents.html">An introduction to enzyme kinetics</a> — An accessible set of on-line tutorials on enzyme kinetics</li> <li><a rel="nofollow" class="external text" href="http://www.wiley.com/college/pratt/0471393878/student/animations/enzyme_kinetics/index.html">Enzyme kinetics animated tutorial</a> — An animated tutorial with audio</li></ul> <p class="mw-empty-elt"> </p> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl ul,.mw-parser-output .hlist ol dl,.mw-parser-output .hlist ol ol,.mw-parser-output .hlist ol ul,.mw-parser-output .hlist ul dl,.mw-parser-output .hlist ul ol,.mw-parser-output .hlist ul ul{display:inline}.mw-parser-output .hlist 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style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1239400231">.mw-parser-output .navbar{display:inline;font-size:88%;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar a>span,.mw-parser-output .navbar a>abbr{text-decoration:inherit}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output 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title="Enzyme">Enzymes</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Activity</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Active_site" title="Active site">Active site</a></li> <li><a href="/wiki/Binding_site" title="Binding site">Binding site</a></li> <li><a href="/wiki/Catalytic_triad" title="Catalytic triad">Catalytic triad</a></li> <li><a href="/wiki/Oxyanion_hole" title="Oxyanion hole">Oxyanion hole</a></li> <li><a href="/wiki/Enzyme_promiscuity" title="Enzyme promiscuity">Enzyme promiscuity</a></li> <li><a href="/wiki/Diffusion-limited_enzyme" title="Diffusion-limited enzyme">Diffusion-limited enzyme</a></li> <li><a href="/wiki/Cofactor_(biochemistry)" title="Cofactor (biochemistry)">Cofactor</a></li> <li><a href="/wiki/Enzyme_catalysis" title="Enzyme catalysis">Enzyme catalysis</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Regulation</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Allosteric_regulation" title="Allosteric regulation">Allosteric regulation</a></li> <li><a href="/wiki/Cooperativity" title="Cooperativity">Cooperativity</a></li> <li><a href="/wiki/Enzyme_inhibitor" title="Enzyme inhibitor">Enzyme inhibitor</a></li> <li><a href="/wiki/Enzyme_activator" title="Enzyme activator">Enzyme activator</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Classification</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Enzyme_Commission_number" title="Enzyme Commission number">EC number</a></li> <li><a href="/wiki/Protein_superfamily" title="Protein superfamily">Enzyme superfamily</a></li> <li><a href="/wiki/Protein_family" title="Protein family">Enzyme family</a></li> <li><a href="/wiki/List_of_enzymes" title="List of enzymes">List of enzymes</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Kinetics</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a class="mw-selflink selflink">Enzyme kinetics</a></li> <li><a href="/wiki/Eadie%E2%80%93Hofstee_diagram" title="Eadie–Hofstee diagram">Eadie–Hofstee diagram</a></li> <li><a href="/wiki/Hanes%E2%80%93Woolf_plot" title="Hanes–Woolf plot">Hanes–Woolf plot</a></li> <li><a href="/wiki/Lineweaver%E2%80%93Burk_plot" title="Lineweaver–Burk plot">Lineweaver–Burk plot</a></li> <li><a href="/wiki/Michaelis%E2%80%93Menten_kinetics" title="Michaelis–Menten kinetics">Michaelis–Menten kinetics</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Types</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><b>EC1 <a href="/wiki/Oxidoreductase" title="Oxidoreductase">Oxidoreductases</a></b> (<a href="/wiki/List_of_EC_numbers_(EC_1)" title="List of EC numbers (EC 1)">list</a>)</li> <li><b>EC2 <a href="/wiki/Transferase" title="Transferase">Transferases</a></b> (<a href="/wiki/List_of_EC_numbers_(EC_2)" title="List of EC numbers (EC 2)">list</a>)</li> <li><b>EC3 <a href="/wiki/Hydrolase" title="Hydrolase">Hydrolases</a></b> (<a href="/wiki/List_of_EC_numbers_(EC_3)" title="List of EC numbers (EC 3)">list</a>)</li> <li><b>EC4 <a href="/wiki/Lyase" title="Lyase">Lyases</a></b> (<a href="/wiki/List_of_EC_numbers_(EC_4)" title="List of EC numbers (EC 4)">list</a>)</li> <li><b>EC5 <a href="/wiki/Isomerase" title="Isomerase">Isomerases</a></b> (<a href="/wiki/List_of_EC_numbers_(EC_5)" title="List of EC numbers (EC 5)">list</a>)</li> <li><b>EC6 <a href="/wiki/Ligase" title="Ligase">Ligases</a></b> (<a href="/wiki/List_of_EC_numbers_(EC_6)" title="List of EC numbers (EC 6)">list</a>)</li> <li><b>EC7 <a href="/wiki/Translocase" title="Translocase">Translocases</a></b> (<a href="/wiki/List_of_EC_numbers_(EC_7)" title="List of EC numbers (EC 7)">list</a>)</li></ul> </div></td></tr></tbody></table></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Retrieved from "<a dir="ltr" href="https://en.wikipedia.org/w/index.php?title=Enzyme_kinetics&oldid=1259494287">https://en.wikipedia.org/w/index.php?title=Enzyme_kinetics&oldid=1259494287</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Help:Category" title="Help:Category">Categories</a>: <ul><li><a href="/wiki/Category:Enzyme_kinetics" title="Category:Enzyme 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Enzyme kinetics - Wikipedia