Graphic rules in steady and non-steady state enzyme kinetics

Graphic methods, when applied to enzyme kinetics, can provide a visually intuitive relation between calculations and reaction graphs. This will not only greatly raise the efficiency of calculations but also significantly help the analysis of enzyme kinetic mechanisms. In this paper, four graphic rules are presented. Rules 1-3 are established for steady state enzyme-catalyzed reaction systems and Rule 4 is for non-steady state ones. In comparison with conventional graphic methods which can only be applied to steady state systems, the present rules have the following merits. 1) Complicated and tedious calculations can be greatly simplified; for example, in calculating the concentrations of enzyme species for the bi-bi random mechanism, the calculation work can be reduced 8-fold compared with the King-Altman's method. 2) A great deal of wasted labor can be avoided; for example, in calculating the rate of product formation for the same mechanism, the operation of finding and removing the 96 reciprocally canceled terms is no longer needed because they automatically disappear during the derivation. 3) Final results can be easily and safely checked by a formula provided in each of the graphic rules. 4) Non-steady state systems can also be treated by the present graphic method; for example, applying Rule 4, one can directly write out the solution for a non-steady state enzyme-catalyzed system, without the need to follow more difficult and complicated operations to solve differential equations. The mathematical proofs of Rules 1-4 are given in Appendices A-D (in the Miniprint), respectively.