The first paper introducing the graph theory to enzyme kinetics was published in 1979. 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 by modifying the rules in. In 1985, these graphic rules have been implemented by David Myers and Graham Plamer 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, 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.
Special applications in biology and drug development
These graphic rules can significantly simplify the derivation of enzyme kinetic equations and help mechanism analysis. Later, they have been utilized to investigate the kinetic mechanisms of drugs inhibiting HIV-reverse transcriptase, and inhibition kinetics of processive nucleic acid polymerases and nucleases. In 2008, based on Chou’s graphic rules, John Andraos 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.