Adomian decomposition method, as a convenience device has been used to solve many functional equations so far. In this manuscript, we consider a system of nonlinear ordinary differential equations, which governs on general reaction in biochemistry as a theoretical problem of concentration kinetics. These system, which is known as Brusselator system has been solved by applying Adomian decomposit...

We wish to generalize van Kampen’s theorem to include nonautonomous master equations. Such a theorem is important in applications, e.g. in ion channel kinetics, where subunit opening and closing rates are subject to external forces (e.g. membrane voltage) and are therefore often unavoidably nonautonomous. There are two issues to consider when moving to the nonautonomous case. The first is that,...

In attempting to develop large-scaled metabolic models using general dynamic modeling methods, a large set of data, such as kinetics mechanisms and parameters, is required. It is difficult to obtain a complete set of rate equations and kinetic parameters. To solve the problem, we have proposed an algorithm which simulates a pathway model including dynamic kinetic parts and flux-based static par...

The Michaelis-Menten (MM) equation is the basic equation of enzyme kinetics; it is also a basic building block of many models of biological systems. We build a stochastic and microscopic model of enzyme kinetics inside a small subcellular compartment. Using both theory and simulations, we show that intrinsic noise induces a breakdown of the MM equation even if steady-state metabolic conditions ...