Solution to Michaelis–Menten enzyme kinetic equation via undetermined gauge functions: Resolving the nonlinearity of Lineweaver–Burk plot

A composite approximate solution of Michaelis–Menten enzyme kinetic equation, which could describe both transient and slow dynamics, was obtained by ordinary perturbation methods in terms of undetermined gauge functions up to a first-order level. It was found that the zeroth-order perturbation function itself solved the paradox due to steady-state approximation and predicted well the maximum enzyme-substrate complex ([ES]max) and time tm to attain it. Extensive kinetic simulations using a chemical kinetic simulator proved the validity of these results. A comparison between simulated and predicted results showed that error in the prediction of tm was negligible when perturbation parameter falls in the range of (0<ε≪1). Apart from these, also the effect of transient dynamics on the linearity of Lineweaver–Burk plot (especially near the origin) has been explained.