Non-steady-state enzyme reaction dynamics

Michaelis-Menten (MM) enzyme kinetics is and has been widely used since early 20th century. However, the conventional enzyme kinetics is not accurate when the substrate is not in excess or when the steady-state approximation does not hold. The steady-state approximation worsens as the enzyme concentration exceeds its substrate concentration, which is the case in many biological processes. Here, to overcome this issue, we present a novel, quasi-exact solution of the enzyme kinetic equations, which provides the time profiles of the substrate, enzyme-substrate complex, and product concentrations. Our theory provides more accurate results than the previously reported theories for all parameter spaces investigated and yields a new relationship of the enzyme reaction time or the enzyme reaction rate to the substrate and enzyme concentrations. We demonstrate our results for the catalytic reaction of beta-galactosidase.