Estimating parameters of S-systems by an auxiliary function guided coordinate descent method

The S-system, a set of nonlinear ordinary differential equations and derived from the generalized mass action law, is an effective model to describe various biological systems. Parameters in S-systems have significant biological meanings, yet difficult to be estimated because of the nonlinearity and complexity of the model. Given time series biological data, its parameter estimation turns out to be a nonlinear optimization problem. A novel method, auxiliary function guided coordinate descent, is proposed in this paper to solve the optimization problem by cyclically optimizing every parameter. In each iteration, only one parameter value is updated and it proves that the objective function keeps nonincreasing during the iterations. The updating rules in each iteration is simple and efficient. Based on this idea, two algorithms are developed to estimate the S-systems for two different constraint situations. The performances of algorithms are studied in several simulation examples. The results demonstrate the effectiveness of the proposed method.