An effective method to increase solvability in biochemical systems using S-system

In this paper we propose an effective method to estimate the intrinsic values in an immobilized enzyme system, i.e., Michaelis constant Km and the maximum reaction rate Vm. We combine three techniques: (1) the non-linear least square method for estimating the kinetic values, (2) orthogonal collocation with the Gauss integration method, and (3) Newton–Raphson method (NRM) or S-system method (SSM) as Newton-like method. We build a procedure to combine the first two methods to estimate the unknown kinetic values in a system. We apply this procedure to solve the intrinsic kinetic parameters determination problem in an immobilized enzyme systems following Michaelis–Menten reaction. To demonstrate the effectiveness of the current method, we test their convergence performance in detail. The results show that the basin of attraction in the current method is extremely enlarged compared with that of the S-system alone. We suggest that the current method is one of the most effective ways to solve fairly complicated biochemical reaction systems in general.