Unified dimensionless transformation in enzyme kinetics: Application to mathematical analyses of ten biochemical reaction systems

A novel general principle was proposed to transform enzyme kinetic equations into unified dimensionless forms. The principle consists of six steps. The principle was applied to ten complex biochemical reaction systems and their characteristics were mathematically analyzed. The approach has six merits.: (i) the number of parameters is reduced, (ii) the rate expressions and their progress curves become much simpler, easily understood and are analyzed globally by the newly defined dimensionless time, T, (iii) the relative magnitude of kinetic constants and of the maximum velocity involved in the rate equations are straightforwardly estimated by three type m values, (iv) mass balance and stoichiometric relationship of the dimensionless rate expressions are exactly the same format as of the actual rate expressions, (v) 2D or 3D plots of the unified dimensionless equations can be depicted without inputs of the actual experimental data of the variables and kinetic constants, and (vi) the newly defined dimensionless inactivation constant, Kiact, is useful to estimate the effect of the enzyme inactivation on the batch reactions. The principle is beneficial for the mathematical analyses of complex biochemical reactions involving two or more kinds of enzymes, for those involving two or more substrates or for those involving both.