{"corpus_id":244955207,"paper_sha":"00ebc4a7d65f11c7a54ca1038ff31a21d2afc3a8","doi":"10.1101/2021.12.05.471285","arxiv_id":null,"pmid":36165810,"pmcid":null,"mag_id":null,"dblp_id":null,"acl_id":null,"title":"Mathematical expressions describing enzyme velocity and inhibition at high enzyme concentration","year":2021,"publication_date":"2021-12-06","venue":"bioRxiv","journal":{"name":"Biological Chemistry","pages":"15 - 27","volume":"404"},"journal_issn":null,"journal_title":null,"publication_types":["JournalArticle"],"pubmed_pub_types":["Journal Article"],"s2_fields_of_study":["Biology","Mathematics","Chemistry","Medicine"],"reference_count":27,"citation_count":1,"influential_citation_count":0,"is_open_access":false,"arxiv_categories":null,"arxiv_license":null,"arxiv_journal_ref":null,"mesh_headings":[{"d":"Kinetics","mj":true,"ui":"D007700"},{"d":"Catalysis","mj":false,"ui":"D002384"}],"chemicals":null,"comments_corrections":null,"source_flags":5,"s2_open_access_pdf_url":null,"s2_open_access_landing_url":null,"s2_open_access_license":null,"s2_open_access_status":null,"pmc_open_access_pdf_url":null,"pmc_open_access_landing_url":null,"pmc_open_access_license":null,"pmc_open_access_status":null,"unpaywall_open_access_pdf_url":null,"unpaywall_open_access_landing_url":null,"unpaywall_open_access_license":null,"unpaywall_open_access_status":null,"abstract":"Abstract Enzyme behaviour is characterised in the laboratory using diluted solutions of enzyme. However, in vivo processes usually occur at [S T ] ≈ [E T ] ≈ K m . Furthermore, the study of enzyme action involves characterisation of inhibitors and their mechanisms. However, to date, there have been no reports proposing mathematical expressions that can be used to describe enzyme activity at high enzyme concentration apart from the simplest single substrate, irreversible case. Using a continued fraction approach, equations can be easily derived for the most common cases in monosubstrate reactions, such as irreversible or reversible reactions and effector (inhibitor or activator) kinetic interactions. These expressions are an extension of the classical Michaelis-Menten equations. A first analysis using these expressions permits to deduce some differences at high versus low enzyme concentration, such as the greater effectiveness of allosteric inhibitors compared to catalytic ones. Also, they can be used to understand catalyst saturation in a reaction. Although they can be linearised, these equations also show differences that need to be taken into account. For example, the different meaning of line intersection points in Dixon plots. All in all, these expressions may be useful tools for modelling in vivo and biotechnological processes.","claims":[{"public_id":"cl_70ed55d79d0bffb87c952ec45f50fbdb","status":"active","text":"A continued-fraction approach yields mathematical expressions for common monosubstrate reactions at high enzyme concentration, including irreversible, reversible, and effector kinetic interactions.","confidence":0.96,"contributors":[{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous (12632b8b5f)","roles":["extraction"],"url":"https://sah.borca.ai/u/12632b8b5f"}],"url":"https://sah.borca.ai/claims/cl_70ed55d79d0bffb87c952ec45f50fbdb"},{"public_id":"cl_6fac9bc1aff1b0bf90517ff157fd8729","status":"active","text":"At high enzyme concentration, allosteric inhibitors are more effective than catalytic inhibitors, and the expressions can be used to understand catalyst saturation.","confidence":0.89,"contributors":[{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous (12632b8b5f)","roles":["extraction"],"url":"https://sah.borca.ai/u/12632b8b5f"}],"url":"https://sah.borca.ai/claims/cl_6fac9bc1aff1b0bf90517ff157fd8729"},{"public_id":"cl_770d566726dcf7f8ff13358500664bc1","status":"active","text":"Linearization of the equations changes the interpretation of Dixon plot line intersection points.","confidence":0.82,"contributors":[{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous (12632b8b5f)","roles":["extraction"],"url":"https://sah.borca.ai/u/12632b8b5f"}],"url":"https://sah.borca.ai/claims/cl_770d566726dcf7f8ff13358500664bc1"},{"public_id":"cl_f16e941e03c414fda2f3731d7fbf5e1d","status":"active","text":"The derived expressions extend the classical Michaelis-Menten equations.","confidence":0.93,"contributors":[{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous (12632b8b5f)","roles":["extraction"],"url":"https://sah.borca.ai/u/12632b8b5f"}],"url":"https://sah.borca.ai/claims/cl_f16e941e03c414fda2f3731d7fbf5e1d"},{"public_id":"cl_be4e00550fc04a3801fbd76ab8e12801","status":"active","text":"The expressions may be useful for modelling in vivo and biotechnological processes.","confidence":0.75,"contributors":[{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous (12632b8b5f)","roles":["extraction"],"url":"https://sah.borca.ai/u/12632b8b5f"}],"url":"https://sah.borca.ai/claims/cl_be4e00550fc04a3801fbd76ab8e12801"}],"concepts":[{"public_id":"co_0d02b56df31be90e16964b9642a812ff","status":"active","name":"effector kinetic interactions","description":"Kinetic effects produced by effectors such as inhibitors or activators on enzyme reactions.","types":["mechanism"],"aliases":["kinetic interactions"],"contributors":[{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous (12632b8b5f)","roles":["extraction"],"url":"https://sah.borca.ai/u/12632b8b5f"}],"url":"https://sah.borca.ai/concepts/co_0d02b56df31be90e16964b9642a812ff"},{"public_id":"co_29eaf7d30f388bf7bd2146a22c7e00de","status":"active","name":"biotechnological processes","description":"Processes used in biotechnology for production, transformation, or analysis of biological systems.","types":["process"],"aliases":[],"contributors":[{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous (12632b8b5f)","roles":["extraction"],"url":"https://sah.borca.ai/u/12632b8b5f"}],"url":"https://sah.borca.ai/concepts/co_29eaf7d30f388bf7bd2146a22c7e00de"},{"public_id":"co_357bc98a8f31ec444c9a86208071756c","status":"active","name":"linearized equations","description":"Equations transformed into linear form for analytical or graphical interpretation.","types":["mathematical form"],"aliases":["linearisation"],"contributors":[{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous (12632b8b5f)","roles":["extraction"],"url":"https://sah.borca.ai/u/12632b8b5f"}],"url":"https://sah.borca.ai/concepts/co_357bc98a8f31ec444c9a86208071756c"},{"public_id":"co_42483b651e877e4c81491528e96d740b","status":"active","name":"in vivo processes","description":"Biological processes occurring within living organisms.","types":["process"],"aliases":[],"contributors":[{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous (12632b8b5f)","roles":["extraction"],"url":"https://sah.borca.ai/u/12632b8b5f"}],"url":"https://sah.borca.ai/concepts/co_42483b651e877e4c81491528e96d740b"},{"public_id":"co_5c2276b76905315616593cd779cd0b7c","status":"active","name":"classical Michaelis-Menten equations","description":"Standard equations used to describe enzyme kinetics under classical assumptions.","types":["equation"],"aliases":["Michaelis-Menten equations"],"contributors":[{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous (12632b8b5f)","roles":["extraction"],"url":"https://sah.borca.ai/u/12632b8b5f"}],"url":"https://sah.borca.ai/concepts/co_5c2276b76905315616593cd779cd0b7c"},{"public_id":"co_630a8f4a8b1000980b62ffea0085fd0f","status":"active","name":"catalyst saturation","description":"A state in which increasing substrate or enzyme availability no longer increases reaction rate proportionally.","types":["phenomenon"],"aliases":["enzyme saturation"],"contributors":[{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous (12632b8b5f)","roles":["extraction"],"url":"https://sah.borca.ai/u/12632b8b5f"}],"url":"https://sah.borca.ai/concepts/co_630a8f4a8b1000980b62ffea0085fd0f"},{"public_id":"co_68170c1447b0c1514b14dae01272239c","status":"active","name":"catalytic inhibitors","description":"Inhibitors that interfere with the catalytic process of an enzyme.","types":["inhibitor"],"aliases":[],"contributors":[{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous (12632b8b5f)","roles":["extraction"],"url":"https://sah.borca.ai/u/12632b8b5f"}],"url":"https://sah.borca.ai/concepts/co_68170c1447b0c1514b14dae01272239c"},{"public_id":"co_8ae99f3b22b56737dbbe2c3cb9dfd4fe","status":"active","name":"mathematical expressions describing enzyme velocity and inhibition at high enzyme concentration","description":"Closed-form enzyme-kinetic expressions intended to model velocity and inhibition when enzyme concentration is high.","types":["model"],"aliases":["expressions describing enzyme velocity and inhibition at high enzyme concentration"],"contributors":[{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous (12632b8b5f)","roles":["extraction"],"url":"https://sah.borca.ai/u/12632b8b5f"}],"url":"https://sah.borca.ai/concepts/co_8ae99f3b22b56737dbbe2c3cb9dfd4fe"},{"public_id":"co_b13625d7cea1c20b394d2479b6e8b483","status":"active","name":"allosteric inhibitors","description":"Inhibitors that bind at a site distinct from the active site and alter enzyme activity.","types":["inhibitor"],"aliases":[],"contributors":[{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous (12632b8b5f)","roles":["extraction"],"url":"https://sah.borca.ai/u/12632b8b5f"}],"url":"https://sah.borca.ai/concepts/co_b13625d7cea1c20b394d2479b6e8b483"},{"public_id":"co_b6607ee288fef2eec7e2cec000a00795","status":"active","name":"Dixon plots","description":"Plots used in enzyme inhibition analysis to visualize relationships between inverse reaction rate and inhibitor concentration.","types":["analysis plot"],"aliases":[],"contributors":[{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous (12632b8b5f)","roles":["extraction"],"url":"https://sah.borca.ai/u/12632b8b5f"}],"url":"https://sah.borca.ai/concepts/co_b6607ee288fef2eec7e2cec000a00795"},{"public_id":"co_dd664ae10c1197eee1569df8e4d987c6","status":"active","name":"continued fraction approach","description":"A mathematical derivation strategy that represents expressions as continued fractions.","types":["method"],"aliases":["continued-fraction approach"],"contributors":[{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous (12632b8b5f)","roles":["extraction"],"url":"https://sah.borca.ai/u/12632b8b5f"}],"url":"https://sah.borca.ai/concepts/co_dd664ae10c1197eee1569df8e4d987c6"},{"public_id":"co_f76050de38eb7a739734ea26d356c193","status":"active","name":"monosubstrate reactions","description":"Enzymatic reactions involving a single substrate.","types":["reaction class"],"aliases":["single-substrate reactions"],"contributors":[{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous (12632b8b5f)","roles":["extraction"],"url":"https://sah.borca.ai/u/12632b8b5f"}],"url":"https://sah.borca.ai/concepts/co_f76050de38eb7a739734ea26d356c193"}],"external_ids":{"DOI":"10.1101/2021.12.05.471285","ArXiv":null,"PubMed":36165810,"PubMedCentral":null,"MAG":null,"DBLP":null,"ACL":null},"open_access":{"is_open_access":false,"pdf_url":null,"landing_url":"https://sah.borca.ai/papers/244955207","source":null,"pdf_url_source":null,"license":null,"reason":"pdf_url_not_indexed"},"reference_availability":{"status":"available","references_indexed":true,"full_text_available":false,"full_text_source":null,"count_basis":"semantic_scholar_metadata","extraction_status":"not_applicable","reason":null},"source":{"provider":"episteme2","base_corpus":"semantic_scholar_dump","freshness_mode":"unknown","basis":["semantic_scholar_metadata","postgres_metadata"],"limits":["paper metadata is based on indexed upstream scholarly datasets","claims and concepts are available only for extracted papers","absence of claims or concepts means no extracted graph data is available in this response"],"status":"available","degraded":false,"degraded_reasons":[],"diagnostics":{"status":"available","degraded":false,"degraded_reasons":[],"metadata_status":"available","graph_status":"available","abstract_status":"available"},"source_flags":5},"paper_id":638994,"paper_uid":"ce8c4eaf-1de6-4097-994e-b52f17f91be0","canonical_identity":{"paper_id":638994,"paper_uid":"ce8c4eaf-1de6-4097-994e-b52f17f91be0","identity_status":"available","lookup_basis":"semantic_scholar_external_id","compatibility_path":"corpus_id"},"url":"https://sah.borca.ai/papers/244955207"}