{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,22]],"date-time":"2026-06-22T02:03:13Z","timestamp":1782093793194,"version":"3.54.5"},"reference-count":34,"publisher":"Springer Science and Business Media LLC","issue":"1","content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["BMC Bioinformatics"],"published-print":{"date-parts":[[2009,12]]},"abstract":"<jats:title>Abstract<\/jats:title>\n          <jats:sec>\n            <jats:title>Background<\/jats:title>\n            <jats:p>While the theory of enzyme kinetics is fundamental to analyzing and simulating biochemical systems, the derivation of rate equations for complex mechanisms for enzyme-catalyzed reactions is cumbersome and error prone. Therefore, a number of algorithms and related computer programs have been developed to assist in such derivations. Yet although a number of algorithms, programs, and software packages are reported in the literature, one or more significant limitation is associated with each of these tools. Furthermore, none is freely available for download and use by the community.<\/jats:p>\n          <\/jats:sec>\n          <jats:sec>\n            <jats:title>Results<\/jats:title>\n            <jats:p>We have implemented an algorithm based on the schematic method of King and Altman (KA) that employs the topological theory of linear graphs for systematic generation of valid reaction patterns in a GUI-based stand-alone computer program called <jats:italic>KAPattern<\/jats:italic>. The underlying algorithm allows for the assumption steady-state, rapid equilibrium-binding, and\/or irreversibility for individual steps in catalytic mechanisms. The program can automatically generate MathML and MATLAB output files that users can easily incorporate into simulation programs.<\/jats:p>\n          <\/jats:sec>\n          <jats:sec>\n            <jats:title>Conclusion<\/jats:title>\n            <jats:p>A computer program, called <jats:italic>KAPattern<\/jats:italic>, for generating rate equations for complex enzyme system is a freely available and can be accessed at <jats:ext-link xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"http:\/\/www.biocoda.org\" ext-link-type=\"uri\">http:\/\/www.biocoda.org<\/jats:ext-link>.<\/jats:p>\n          <\/jats:sec>","DOI":"10.1186\/1471-2105-10-238","type":"journal-article","created":{"date-parts":[[2009,8,5]],"date-time":"2009-08-05T06:14:37Z","timestamp":1249452877000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":38,"title":["Generating rate equations for complex enzyme systems by a computer-assisted systematic method"],"prefix":"10.1186","volume":"10","author":[{"given":"Feng","family":"Qi","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ranjan K","family":"Dash","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yu","family":"Han","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Daniel A","family":"Beard","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2009,8,4]]},"reference":[{"key":"2968_CR1","volume-title":"Enzyme Kinetics","author":"IH Segel","year":"1993","unstructured":"Segel IH: Enzyme Kinetics. New York: John Wiley & Sons; 1993."},{"key":"2968_CR2","doi-asserted-by":"publisher","first-page":"e1825","DOI":"10.1371\/journal.pone.0001825","volume":"3","author":"DA Beard","year":"2008","unstructured":"Beard DA, Vinnakota KC, Wu F: Detailed enzyme kinetics in terms of biochemical species: study of citrate synthase. PLoS One 2008, 3: e1825. 10.1371\/journal.pone.0001825","journal-title":"PLoS One"},{"key":"2968_CR3","doi-asserted-by":"publisher","first-page":"1641","DOI":"10.1016\/j.bbapap.2008.07.001","volume":"1784","author":"F Qi","year":"2008","unstructured":"Qi F, Chen XW, Beard DA: Detailed kinetics and regulation of mammalian NAD-linked isocitrate dehydrogenase. Biochim Biophys Acta 2008, 1784: 1641\u20131651.","journal-title":"Biochim Biophys Acta"},{"issue":"4","key":"2968_CR4","doi-asserted-by":"publisher","first-page":"e36","DOI":"10.1371\/journal.pcbi.0010036","volume":"1","author":"DA Beard","year":"2005","unstructured":"Beard DA: A biophysical model of the mitochondrial respiratory system and oxidative phosphorylation. PLoS Comput Biol 2005, 1(4):e36. 10.1371\/journal.pcbi.0010036","journal-title":"PLoS Comput Biol"},{"key":"2968_CR5","doi-asserted-by":"publisher","first-page":"24525","DOI":"10.1074\/jbc.M701024200","volume":"282","author":"F Wu","year":"2007","unstructured":"Wu F, Yang F, Vinnakota KC, Beard DA: Computer modeling of mitochondrial TCA cycle, oxidative phosphorylation, metabolite transport, and electophysiology. J Biol Chem 2007, 282: 24525\u201324537. 10.1074\/jbc.M701024200","journal-title":"J Biol Chem"},{"key":"2968_CR6","doi-asserted-by":"publisher","first-page":"696","DOI":"10.1039\/tf9534900696","volume":"49","author":"J Botts","year":"1953","unstructured":"Botts J, Morales M: Analytical description of the effects of modifiers and of enzyme multivalency upon the steady state catalyzed reaction rate. Trans Faraday Soc 1953, 49: 696\u2013707. 10.1039\/tf9534900696","journal-title":"Trans Faraday Soc"},{"key":"2968_CR7","doi-asserted-by":"publisher","first-page":"54","DOI":"10.1016\/0076-6879(79)63006-9","volume":"63","author":"CY Huang","year":"1979","unstructured":"Huang CY: Derivation of initial velocity and isotope exchange rate equations. Method Enzymo 1979, 63: 54\u201384. full_text","journal-title":"Method Enzymo"},{"key":"2968_CR8","doi-asserted-by":"publisher","first-page":"1375","DOI":"10.1021\/j150544a010","volume":"60","author":"EL King","year":"1956","unstructured":"King EL, Altman C: A schematic method of deriving the rate laws for enzyme catalyzed reactions. J Phys Chem 1956, 60: 1375\u20131378. 10.1021\/j150544a010","journal-title":"J Phys Chem"},{"key":"2968_CR9","doi-asserted-by":"publisher","first-page":"478","DOI":"10.1016\/0304-4165(66)90446-6","volume":"115","author":"MV Volkenstein","year":"1966","unstructured":"Volkenstein MV, Goldsein BN: Allosteric enzyme models and their analysis by the theory of graphs. Biochim Biophys Acta 1966, 115: 478\u2013485.","journal-title":"Biochim Biophys Acta"},{"key":"2968_CR10","doi-asserted-by":"crossref","first-page":"820","DOI":"10.1016\/S0021-9258(19)81739-8","volume":"243","author":"S Cha","year":"1968","unstructured":"Cha S: A simple method for derivation of rate equation for enzyme-catalyzed reactions under the rapid equilibrium assumption or combined assumptions of equilibrium and steady state. J Biol Chem 1968, 243: 820\u2013825.","journal-title":"J Biol Chem"},{"key":"2968_CR11","doi-asserted-by":"publisher","first-page":"692","DOI":"10.1016\/0006-291X(70)90959-9","volume":"40","author":"HJ Fromm","year":"1970","unstructured":"Fromm HJ: A simplified schematic method for deriving steady-state rate equations using a modification of the theory of graphs procedure. Biochem Biophys Res Commun 1970, 40: 692\u2013697. 10.1016\/0006-291X(70)90959-9","journal-title":"Biochem Biophys Res Commun"},{"key":"2968_CR12","doi-asserted-by":"publisher","first-page":"4","DOI":"10.1016\/0005-2744(72)90961-8","volume":"258","author":"BA Orsi","year":"1972","unstructured":"Orsi BA: A simple method for the derivation of the steady-state rate equation for an enzyme mechanism. Biochim Biophys Acta 1972, 258: 4\u20138.","journal-title":"Biochim Biophys Acta"},{"key":"2968_CR13","doi-asserted-by":"publisher","first-page":"161","DOI":"10.1016\/S0022-5193(74)80036-6","volume":"44","author":"S Ainsworth","year":"1974","unstructured":"Ainsworth S: A slide rule for deriving the rate equations of enzyme catalysed reactions with unbranched mechanisms. J Theor Biol 1974, 44: 161\u2013165. 10.1016\/S0022-5193(74)80036-6","journal-title":"J Theor Biol"},{"key":"2968_CR14","doi-asserted-by":"publisher","first-page":"141","DOI":"10.1016\/0022-5193(74)90185-4","volume":"48","author":"S Ainsworth","year":"1974","unstructured":"Ainsworth S: A slide rule for deriving the rate equations of enzyme catalysed reactions with mechanisms involving up to six enzyme containing intermediates. J Theor Biol 1974, 48: 141\u2013147. 10.1016\/0022-5193(74)90185-4","journal-title":"J Theor Biol"},{"key":"2968_CR15","doi-asserted-by":"publisher","first-page":"567","DOI":"10.1042\/bj1550567","volume":"155","author":"KJ Indge","year":"1976","unstructured":"Indge KJ, Childs RE: A new method for deriving steady state rate equations suitable for manual or computer use. Biochem J 1976, 155: 567\u2013570.","journal-title":"Biochem J"},{"key":"2968_CR16","doi-asserted-by":"publisher","first-page":"829","DOI":"10.1042\/bj1870829","volume":"187","author":"KC Chou","year":"1980","unstructured":"Chou KC, Forsen S: Graphical rules for enzyme catalysed rate laws. Biochem J 1980, 187: 829\u2013835.","journal-title":"Biochem J"},{"key":"2968_CR17","doi-asserted-by":"publisher","first-page":"436","DOI":"10.1016\/0022-5193(67)90104-X","volume":"17","author":"M Pring","year":"1967","unstructured":"Pring M: The simulation and analysis by digital computer of biochemical systems in terms of kinetic models. 3. Generator programming. J Theor Biol 1967, 17: 436\u2013440. 10.1016\/0022-5193(67)90104-X","journal-title":"J Theor Biol"},{"key":"2968_CR18","doi-asserted-by":"publisher","first-page":"297","DOI":"10.1016\/0022-5193(68)90130-6","volume":"20","author":"DG Rhoads","year":"1968","unstructured":"Rhoads DG, Pring M: The simulation and analysis by digital computer of biochemical systems in terms of kinetic models. IV. Automatic derivation of enzymic rate laws. J Theor Biol 1968, 20: 297\u2013313. 10.1016\/0022-5193(68)90130-6","journal-title":"J Theor Biol"},{"key":"2968_CR19","doi-asserted-by":"publisher","first-page":"248","DOI":"10.1016\/S0006-3495(72)86084-3","volume":"12","author":"CF Lam","year":"1972","unstructured":"Lam CF, Priest DG: Systematic generation of valid King-Altman patterns. Biophys J 1972, 12: 248\u2013256. 10.1016\/S0006-3495(72)86084-3","journal-title":"Biophys J"},{"key":"2968_CR20","doi-asserted-by":"publisher","first-page":"55","DOI":"10.1042\/bj1650055","volume":"165","author":"A Cornish-Bowden","year":"1977","unstructured":"Cornish-Bowden A: An automatic method for deriving steady-state rate equations. Biochem J 1977, 165: 55\u201359.","journal-title":"Biochem J"},{"key":"2968_CR21","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/0020-7101(76)90002-7","volume":"7","author":"J Kinderlerer","year":"1976","unstructured":"Kinderlerer J, Ainsworth S: A computer program to derive the rate equations of enzyme catalysed reactions with up to ten enzyme containg intermediates in the reaction mechanism. Int J Bio-Med Comput 1976, 7: 1\u201320. 10.1016\/0020-7101(76)90002-7","journal-title":"Int J Bio-Med Comput"},{"key":"2968_CR22","doi-asserted-by":"publisher","first-page":"29","DOI":"10.3109\/10242429709003608","volume":"15","author":"AJJ Straathof","year":"1997","unstructured":"Straathof AJJ, Heijnen JJ: Derivation of enzyme rate equations using symbolic software. Biocatal Biotransformation 1997, 15: 29\u201337. 10.3109\/10242429709003608","journal-title":"Biocatal Biotransformation"},{"key":"2968_CR23","doi-asserted-by":"publisher","first-page":"448","DOI":"10.1006\/bbrc.1999.1679","volume":"265","author":"SJ Fromm","year":"1999","unstructured":"Fromm SJ, Fromm HJ: A two step computer-assisted method for deriving steady-state rate equations. Biochem Biophys Res Commun 1999, 265: 448\u2013452. 10.1006\/bbrc.1999.1679","journal-title":"Biochem Biophys Res Commun"},{"key":"2968_CR24","volume-title":"Computeized Derivation of the Steady State Equations of Enzyme Reactions","author":"R Varon","year":"1995","unstructured":"Varon R, Moreno MG, Sevilla FG, Galea MMR, Canovas FG: Computeized Derivation of the Steady State Equations of Enzyme Reactions. Volume A5. Albacete Spain; 1995."},{"key":"2968_CR25","first-page":"159","volume":"13","author":"R Varon","year":"1997","unstructured":"Varon R, Sevilla FG, Canovas MGFG, Peyro R, Duggleby RG: Computer program the equations describing the steady state of enzyme reactions. Comput Appl Biosci 1997, 13: 159\u2013167.","journal-title":"Comput Appl Biosci"},{"key":"2968_CR26","doi-asserted-by":"publisher","first-page":"837","DOI":"10.1016\/j.amc.2006.02.016","volume":"181","author":"JM Yago","year":"2006","unstructured":"Yago JM, Sevilla FG, del Solo CG, Duggleby RG, Varon R: A windows program for the derivation of steady-state equations in enzyme systems. Appl Math Comput 2006, 181: 837\u2013852. 10.1016\/j.amc.2006.02.016","journal-title":"Appl Math Comput"},{"key":"2968_CR27","volume-title":"Linear Graphs and Electrical Networks","author":"S Seshu","year":"1961","unstructured":"Seshu S, Reed MB: Linear Graphs and Electrical Networks. Reading, Mass.: Addison-Wesley Publishing Company, Inc; 1961."},{"key":"2968_CR28","doi-asserted-by":"publisher","first-page":"836","DOI":"10.1093\/bioinformatics\/btp069","volume":"25","author":"J Vanlier","year":"2009","unstructured":"Vanlier J, Wu F, Qi F, Vinnakota KC, Han Y, Dash RK, Yang F, Beard DA: BISEN: Biochemical Simulation Environment. Bioinformatics 2009, 25: 836\u2013837. 10.1093\/bioinformatics\/btp069","journal-title":"Bioinformatics"},{"key":"2968_CR29","doi-asserted-by":"crossref","first-page":"6270","DOI":"10.1016\/S0021-9258(18)63533-1","volume":"244","author":"JM Hansen","year":"1969","unstructured":"Hansen JM, Dinovo EC, Boyer PD: Initial and equilibrium 18O, 14C, 3H, and 2H exchange rates as probe of the fumarase reaction mechanism. J Biol Chem 1969, 244: 6270\u20136279.","journal-title":"J Biol Chem"},{"key":"2968_CR30","volume-title":"Free energy transduction and biochemical cycle kinetics","author":"TL Hill","year":"2005","unstructured":"Hill TL: Free energy transduction and biochemical cycle kinetics. New York: Dover Publications, Inc; 2005."},{"key":"2968_CR31","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4899-3278-5","volume-title":"Enzyme kinetics: the steady-state approach","author":"PC Engel","year":"1981","unstructured":"Engel PC: Enzyme kinetics: the steady-state approach. London and New York: Chapman and Hall; 1981."},{"key":"2968_CR32","first-page":"1344","volume":"113","author":"MS Maxwell","year":"1966","unstructured":"Maxwell MS, Cline JM: Topological network analysis by algebraic method. Proc IEEE 1966, 113: 1344\u20131347.","journal-title":"Proc IEEE"},{"key":"2968_CR33","doi-asserted-by":"publisher","first-page":"763","DOI":"10.1139\/o62-089","volume":"40","author":"JTF Wong","year":"1962","unstructured":"Wong JTF, Hanes CS: Kinetic formulations for enzymic reactions involving two substrates. Can J Biochem Physiol 1962, 40: 763\u2013804.","journal-title":"Can J Biochem Physiol"},{"key":"2968_CR34","volume-title":"Kinetics of enzyme mechanism","author":"JTF Wong","year":"1975","unstructured":"Wong JTF: Kinetics of enzyme mechanism. London: Academic Press; 1975."}],"container-title":["BMC Bioinformatics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1186\/1471-2105-10-238.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,8,31]],"date-time":"2021-08-31T21:38:34Z","timestamp":1630445914000},"score":1,"resource":{"primary":{"URL":"https:\/\/bmcbioinformatics.biomedcentral.com\/articles\/10.1186\/1471-2105-10-238"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,8,4]]},"references-count":34,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2009,12]]}},"alternative-id":["2968"],"URL":"https:\/\/doi.org\/10.1186\/1471-2105-10-238","relation":{},"ISSN":["1471-2105"],"issn-type":[{"value":"1471-2105","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,8,4]]},"assertion":[{"value":"26 January 2009","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"4 August 2009","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"4 August 2009","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"238"}}