Analytical solution to the simultaneous Michaelis-Menten and second-order kinetics problem

Abstract An analytic solution is presented for the simultaneous substrate elimination problem that combines Michaelis-Menten (MM) consumption with an irreversible second-order kinetics process.The implicit solution involves logarithm and inverse tangent functions and perfectly agrees with the numerical solution of the differential equation. A solution is also presented for the generalized dynamical problem that simultaneously combines MM kinetics with first and second-order processes.Useful exact expressions such as the half-life and the area under the curve are also derived for these problems.