Graph theory in enzymatic kinetics

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The first paper introducing the graph theory in enzyme kinetics was published in 1979.[1] In that paper, three graphical rules based on graph theory were presented for deriving kinetic equations in steady-state enzyme-catalyzed systems. Shortly afterwards, two more effective graphical rules were proposed.[2][1] In 1985, these graphic rules had been implemented by David Myers and Graham Plamer[3] as microcomputer tools for finding numeric solutions for extremely complicated enzyme kinetics systems.

Using graphical rules to deal with kinetic systems is an elegant approach that combines graph representation and rigorous mathematical derivation. It has 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 steady state enzyme-catalyzed systems, while Rule 4 is for non-steady state enzyme-catalyzed systems. Subsequently, these graphic rules were extended to deal with protein folding kinetics as well.[5]

Special applications in biology and drug development

These graphical rules can significantly simplify the derivation of enzyme kinetic equations[6] and help mechanism analysis.[7] They may be utilized to investigate 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 was extended to deal with drug metabolism systems.[12]

References

  1. ↑ 1.0 1.1 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. 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. ↑ 4.0 4.1 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. http://www.jbc.org/cgi/pmidlookup?view=long&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. 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. http://www.jbc.org/cgi/pmidlookup?view=long&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. http://www.jbc.org/cgi/pmidlookup?view=long&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. 

[[Category:Enzyme kine




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