Alternating weighted least squares parameter estimation for biological S-systems

The S-system, which is a set of nonlinear ordinary differential equations and derived from the generalized mass action law, is a consistent model to describe various biological systems. Parameters in S-systems contain important biological information and yet can not be obtained directly from experiments. Therefore, the parameter estimation methods are a choice to estimate parameters in S-systems. However, the parameter estimation for this model turns out to be a complex nonlinear optimization problem. A novel method, alternating weighted least squares (AWLS), is proposed in this paper to estimate the parameters in S-systems. The fast deterministic AWLS method takes advantage of the special structure of the S-system model and reduces solving the nonlinear optimization problem into alternately solving weighed least squares problems which have analytical solutions. The effectiveness of AWLS is demonstrated by the simulation studies and the results show that the AWLS outperforms the existing alternating regression method.