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Graph theory in enzymatic kinetics

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The first paper introducing the graph theory to enzyme kinetics was published in 1979.[1] In that paper, three graphical rules based on the graph theory were introduced for deriving the kinetic equations in the steady-state enzyme-catalyzed systems. Shortly afterwards, two more effective graphical rules were proposed [2] by modifying the rules in.[1] In 1985, these graphic rules have been implemented by David Myers and Graham Plamer [3] as microcomputer tools for finding the numeric solutions for extremely complicated enzyme kinetics systems. Using graphic rules to deal with kinetic systems is an elegant approach by combining the graph representation and rigorous mathematical derivation. It bears the following advantages: (1) providing an intuitive picture or illuminative insights; (2) helping grasp the key points from complicated details; (3) greatly simplifying many tedious, laborious, and error-prone calculations; and (4) able to double-check the final results. In 1989, a set of four graphic rules were summarized by Kuo-Chen Chou,[4] where Rules 1-3 are for the steady state enzyme-catalyzed systems, while Rule 4 is for the non-steady state enzyme-catalyzed systems. Subsequently, these graphic rules were extended to deal with the protein folding kinetics as well.[5]

Special applications in biology and drug development

These graphic rules can significantly simplify the derivation of enzyme kinetic equations [6] and help mechanism analysis.[7] Later, they have been utilized to investigate the kinetic mechanisms of drugs inhibiting HIV-reverse transcriptase,[8][9] and inhibition kinetics of processive nucleic acid polymerases and nucleases.[10] In 2008, based on Chou’s graphic rules,[4] John Andraos [11] developed two fast methods for determining product ratios for kinetic schemes leading to multiple products without rate laws. In 2010, the non-steady state graphic rule has been extended to deal with drug metabolism systems.[12]

References

  1. ^ a b Chou, Kuo-Chen; Jiang, Shou-Ping; Liu, Wei-Min; Fee, Chih-Hao (1979). "Graph theory of enzyme kinetics: 1. Steady-state reaction systems". Scientia Sinica. 22 (3): 341–58.
  2. ^ Chou, Kuo-Chen; Forsén, Sture (1980). "Graphical Rules for Enzyme-Catalysed Rate Laws". The Biochemical Journal. 187 (3): 829–35. PMC 1162468. PMID 7188428.
  3. ^ Myers, David; Palmer, Graham (1985). "Microcomputer tools for steady–state enzyme kinetics". Computer Applications in the Biosciences. 1 (2): 105–10. doi:10.1093/bioinformatics/1.2.105. PMID 3880330.
  4. ^ a b Chou, Kuo-Chen (1989). "Graphic Rules in Steady and Non-steady State Enzyme Kinetics". The Journal of Biological Chemistry. 264 (20): 12074–9. PMID 2745429.
  5. ^ Chou, Kuo-Chen (1990). "Applications of graph theory to enzyme kinetics and protein folding kinetics". Biophysical Chemistry. 35 (1): 1–24. doi:10.1016/0301-4622(90)80056-D. PMID 2183882.
  6. ^ Zhou, Guo-Ping; Deng, Mei-Hua (1984). "An extension of Chou's graphic rules for deriving enzyme kinetic equations to systems involving parallel reaction pathways". The Biochemical Journal. 222 (1): 169–76. PMC 1144157. PMID 6477507.
  7. ^ Lin, Sheng-Xiang; Neet, Kenneth E. (1990). "Demonstration of a Slow Conformational Change in Liver Glucokinase by Fluorescence Spectroscopy". The Journal of Biological Chemistry. 265 (17): 9670–5. PMID 2351663.
  8. ^ Althaus, Irene W.; Chou, James J.; Gonzales, Andrea J.; Deibel, Martin R.; Chou, Kuo-Chen; Kezdy, Ferenc J.; Romero, Donna L.; Aristoff, Paul A.; et al. (1993). "Steady-state kinetic studies with the non-nucleoside HIV-1 reverse transcriptase inhibitor U-87201E". The Journal of Biological Chemistry. 268 (9): 6119–24. PMID 7681060.
  9. ^ Althaus, IW; Chou, JJ; Gonzales, AJ; Deibel, MR; Chou, KC; Kezdy, FJ; Romero, DL; Palmer, JR; et al. (1993). "Kinetic studies with the non-nucleoside HIV-1 reverse transcriptase inhibitor U-88204E". Biochemistry. 32 (26): 6548–54. doi:10.1021/bi00077a008. PMID 7687145.
  10. ^ Chou, K.C.; Kezdy, F.J.; Reusser, F. (1994). "Kinetics of Processive Nucleic Acid Polymerases and Nucleases". Analytical Biochemistry. 221 (2): 217–30. doi:10.1006/abio.1994.1405. PMID 7529005.
  11. ^ Andraos, John (2008). "Kinetic plasticity and the determination of product ratios for kinetic schemes leading to multiple products without rate laws — New methods based on directed graphs". Canadian Journal of Chemistry. 86 (4): 342–57. doi:10.1139/V08-020.
  12. ^ Chou, Kuo-Chen (2010). "Graphic Rule for Drug Metabolism Systems". Current Drug Metabolism. 11 (4): 369–78. doi:10.2174/138920010791514261. PMID 20446902.
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