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Here, we investigate their role in the evolution of a chemical reaction system from one self-sustaining composition of molecular species to another and their influence on" /> <meta name="twitter:image" content="https://0.academia-photos.com/5196631/2289628/117660324/s200_tomas.veloz.jpg" /> <meta property="fb:app_id" content="2369844204" /> <meta property="og:type" content="article" /> <meta property="og:url" content="https://www.academia.edu/37878330/Cycles_and_the_Qualitative_Evolution_of_Chemical_Systems" /> <meta property="og:title" content="Cycles and the Qualitative Evolution of Chemical Systems" /> <meta property="og:image" content="http://a.academia-assets.com/images/open-graph-icons/fb-paper.gif" /> <meta property="og:description" content="Cycles are abundant in most kinds of networks, especially in biological ones. Here, we investigate their role in the evolution of a chemical reaction system from one self-sustaining composition of molecular species to another and their influence on" /> <meta property="article:author" content="https://utem-cl.academia.edu/TomasVeloz" /> <meta property="article:author" content="https://independent.academia.edu/BryanReynaert" /> <meta name="description" content="Cycles are abundant in most kinds of networks, especially in biological ones. Here, we investigate their role in the evolution of a chemical reaction system from one self-sustaining composition of molecular species to another and their influence on" /> <meta name="robots" content="noindex" /> <title>Cycles and the Qualitative Evolution of Chemical Systems | Tomas Veloz and Bryan Reynaert - Academia.edu</title> <link rel="canonical" href="https://www.academia.edu/37878330/Cycles_and_the_Qualitative_Evolution_of_Chemical_Systems" /> <script async src="https://www.googletagmanager.com/gtag/js?id=G-5VKX33P2DS"></script> <script> window.dataLayer = window.dataLayer || []; function gtag(){dataLayer.push(arguments);} gtag('js', new Date()); gtag('config', 'G-5VKX33P2DS', { cookie_domain: 'academia.edu', send_page_view: false, }); gtag('event', 'page_view', { 'controller': "single_work", 'action': "show", 'controller_action': 'single_work#show', 'logged_in': 'false', 'edge': 'unknown', // Send nil if there is no A/B test bucket, in case some records get logged // with missing data - that way we can distinguish between the two cases. // ab_test_bucket should be of the form <ab_test_name>:<bucket> 'ab_test_bucket': null, }) </script> <script> var $controller_name = 'single_work'; var $action_name = "show"; var $rails_env = 'production'; var $app_rev = '49879c2402910372f4abc62630a427bbe033d190'; var $domain = 'academia.edu'; var $app_host = "academia.edu"; var $asset_host = "academia-assets.com"; var $start_time = new Date().getTime(); var $recaptcha_key = "6LdxlRMTAAAAADnu_zyLhLg0YF9uACwz78shpjJB"; var $recaptcha_invisible_key = "6Lf3KHUUAAAAACggoMpmGJdQDtiyrjVlvGJ6BbAj"; var $disableClientRecordHit = false; </script> <script> window.require = { config: function() { return function() {} } } </script> <script> window.Aedu = window.Aedu || {}; window.Aedu.hit_data = null; window.Aedu.serverRenderTime = new Date(1732417275000); window.Aedu.timeDifference = new Date().getTime() - 1732417275000; </script> <script type="application/ld+json">{"@context":"https://schema.org","@type":"ScholarlyArticle","abstract":"Cycles are abundant in most kinds of networks, especially in biological ones. Here, we investigate their role in the evolution of a chemical reaction system from one self-sustaining composition of molecular species to another and their influence on the stability of these compositions. While it is accepted that, from a topological standpoint, they enhance network robustness, the consequence of cycles to the dynamics are not well understood. In a former study, we developed a necessary criterion for the existence of a fixed point, which is purely based on topological properties of the network. The structures of interest we identified were a generalization of closed autocatalytic sets, called chemical organizations. Here, we show that the existence of these chemical organizations and therefore steady states is linked to the existence of cycles. Importantly, we provide a criterion for a qualitative transition, namely a transition from one self-sustaining set of molecular species to another via the introduction of a cycle. Because results purely based on topology do not yield sufficient conditions for dynamic properties, e.g. stability, other tools must be employed, such as analysis via ordinary differential equations. Hence, we study a special case, namely a particular type of reflexive autocatalytic network. Applications for this can be found in nature, and we give a detailed account of the mitotic spindle assembly and spindle position checkpoints. From our analysis, we conclude that the positive feedback provided by these networks\u0026amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;#39; cycles ensures the existence of a stable positive fixed point. Additionally, we use a genome-scale network model of the Escherichia coli sugar metabolism to illustrate our findings. In summary, our results suggest that the qualitative evolution of chemical systems requires the addition and elimination of cycles.","author":[{"@context":"https://schema.org","@type":"Person","name":"Tomas Veloz"},{"@context":"https://schema.org","@type":"Person","name":"Bryan Reynaert"}],"contributor":[{"@context":"https://schema.org","@type":"Person","name":"Bryan Reynaert"}],"dateCreated":"2018-11-29","dateModified":"2023-06-22","datePublished":"2012-01-01","headline":"Cycles and the Qualitative Evolution of Chemical Systems","inLanguage":"en","keywords":["Catalysis","Multidisciplinary","Biocatalysis","Escherichia coli","Feedback","PLoS one","Reflex"],"locationCreated":null,"publication":"PLoS ONE","publisher":{"@context":"https://schema.org","@type":"Organization","name":"Public Library of Science 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Here, we investigate their role in the evolution of a chemical reaction system from one self-sustaining composition of molecular species to another and their influence on the stability of these compositions. While it is accepted that, from a topological standpoint, they enhance network robustness, the consequence of cycles to the dynamics are not well understood. In a former study, we developed a necessary criterion for the existence of a fixed point, which is purely based on topological properties of the network. The structures of interest we identified were a generalization of closed autocatalytic sets, called chemical organizations. Here, we show that the existence of these chemical organizations and therefore steady states is linked to the existence of cycles. Importantly, we provide a criterion for a qualitative transition, namely a transition from one self-sustaining set of molecular species to another via the introduction of a cycle. Because results purely based on topology do not yield sufficient conditions for dynamic properties, e.g. stability, other tools must be employed, such as analysis via ordinary differential equations. Hence, we study a special case, namely a particular type of reflexive autocatalytic network. Applications for this can be found in nature, and we give a detailed account of the mitotic spindle assembly and spindle position checkpoints. From our analysis, we conclude that the positive feedback provided by these networks\u0026amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;#39; cycles ensures the existence of a stable positive fixed point. Additionally, we use a genome-scale network model of the Escherichia coli sugar metabolism to illustrate our findings. In summary, our results suggest that the qualitative evolution of chemical systems requires the addition and elimination of cycles.","publisher":"Public Library of Science (PLoS)","publication_date":"2012,,","publication_name":"PLoS ONE"},"document_type":"paper","pre_hit_view_count_baseline":null,"quality":"low","language":"en","title":"Cycles and the Qualitative Evolution of Chemical Systems","broadcastable":false,"draft":null,"has_indexable_attachment":false,"indexable":true}}["work"]; window.loswp.workCoauthors = [5196631,98376611]; window.loswp.locale = "en"; window.loswp.countryCode = "SG"; window.loswp.cwvAbTestBucket = ""; window.loswp.designVariant = "grid"; window.loswp.fullPageMobileSutdModalVariant = "full_page_mobile_sutd_modal"; window.loswp.useOptimizedScribd4genScript = false; window.loswp.appleClientId = 'edu.academia.applesignon';</script><script defer="" src="https://accounts.google.com/gsi/client"></script><div class="loswp-grid--container"><div data-auto_select="false" data-client_id="331998490334-rsn3chp12mbkiqhl6e7lu2q0mlbu0f1b" data-landing_url="https://www.academia.edu/37878330/Cycles_and_the_Qualitative_Evolution_of_Chemical_Systems" data-login_uri="https://www.academia.edu/registrations/google_one_tap" data-moment_callback="onGoogleOneTapEvent" id="g_id_onload"></div><div class="above-fold js-swp-splash-above-fold"><div class="work-card--container js-swp-control-work-card" data-entity-id="37878330"><div class="work-cover--wrapper"><div class="work-cover--container"><div class="work-cover--no-attachment-container js-swp-splash-paper-cover"><div class="work-cover--file-icon-wrapper"><img alt="paper cover icon" src="//a.academia-assets.com/images/single_work_splash/adobe.icon.svg" /></div><div class="work-cover--title js-swp-splash-paper-cover-page-title">Cycles and the Qualitative Evolution of Chemical Systems</div><br /><div style="margin-top: 170px"><button class="work-cover--request-pdf-button js-request-pdf-button"><svg style="width: 14px; 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font-size: 14px;">Abstract</div><div class="work-card--abstract js-swp-splash-abstract">Cycles are abundant in most kinds of networks, especially in biological ones. Here, we investigate their role in the evolution of a chemical reaction system from one self-sustaining composition of molecular species to another and their influence on the stability of these compositions. While it is accepted that, from a topological standpoint, they enhance network robustness, the consequence of cycles to the dynamics are not well understood. In a former study, we developed a necessary criterion for the existence of a fixed point, which is purely based on topological properties of the network. The structures of interest we identified were a generalization of closed autocatalytic sets, called chemical organizations. Here, we show that the existence of these chemical organizations and therefore steady states is linked to the existence of cycles. Importantly, we provide a criterion for a qualitative transition, namely a transition from one self-sustaining set of molecular species to another via the introduction of a cycle. Because results purely based on topology do not yield sufficient conditions for dynamic properties, e.g. stability, other tools must be employed, such as analysis via ordinary differential equations. Hence, we study a special case, namely a particular type of reflexive autocatalytic network. Applications for this can be found in nature, and we give a detailed account of the mitotic spindle assembly and spindle position checkpoints. From our analysis, we conclude that the positive feedback provided by these networks&amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;#39; cycles ensures the existence of a stable positive fixed point. Additionally, we use a genome-scale network model of the Escherichia coli sugar metabolism to illustrate our findings. In summary, our results suggest that the qualitative evolution of chemical systems requires the addition and elimination of cycles.</div></div><div class="request-upload--container"><p class="request-upload--title">Tomas Veloz hasn't uploaded this paper.</p><div class="request-upload--info-text"><svg aria-hidden="true" focusable="false" data-prefix="fas" data-icon="info-circle" class="request-upload--info-icon svg-inline--fa fa-info-circle fa-w-16" role="img" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><path fill="currentColor" d="M256 8C119.043 8 8 119.083 8 256c0 136.997 111.043 248 248 248s248-111.003 248-248C504 119.083 392.957 8 256 8zm0 110c23.196 0 42 18.804 42 42s-18.804 42-42 42-42-18.804-42-42 18.804-42 42-42zm56 254c0 6.627-5.373 12-12 12h-88c-6.627 0-12-5.373-12-12v-24c0-6.627 5.373-12 12-12h12v-64h-12c-6.627 0-12-5.373-12-12v-24c0-6.627 5.373-12 12-12h64c6.627 0 12 5.373 12 12v100h12c6.627 0 12 5.373 12 12v24z"></path></svg><p class="no-margin hide-on-small-mobile">Let Tomas know you want this paper to be uploaded.</p><p class="no-margin hide-above-small-mobile">Ask for this paper to be uploaded.</p></div><button class="work-cover--request-pdf-button small js-request-pdf-button hide-on-desktop"><svg style="width: 14px; 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