Solution of the Michaelis-Menten equation using the decompositionmethod - Jagadeesh R. Sonnad; Chetan T. Goudar (Mathematical Biosciences and Engineering)
We present a low-order recursive solution to the Michaelis-Menten equationusing the decomposition method. This solution is algebraic in nature andprovides a simpler alternative to numerical approaches such as differentialequation evaluation and root-solving techniques that are currently used tocompute substrate concentration in the Michaelis-Menten equation. A detailedcharacterization of the errors in substrate concentrations computed fromdecomposition, Runge-Kutta, and bisection methods over a wide range of $s_{0}$:$K_{m}$ values was made by comparing them with highly accurate solutionsobtained using the Lambert $W$ function. Our results indicated thatsolutions obtained from the decomposition method were usually more accuratethan those from the corresponding classical Runge-Kutta methods. Moreover,these solutions required significantly fewer computations than theroot-solving method. Specifically, when the stepsize was 0.1% of the totaltime interval, the computed substrate concentrations using the decompositionmethod were characterized by accuracies on the order of 10$^-8$ or better.The algebraic nature of the decomposition solution and its relatively highaccuracy make this approach an attractive candidate for computing substrateconcentration in the Michaelis-Menten equation.