Alternating Constraint Least Squares Parameter Estimation for S-System Models of Biological Networks

S-system models for biological systems are derived from the generalized mass action law and are typically a group of nonlinear differential equations. Estimation of parameters in these models from experimental measurements is thus a nonlinear problem. In principle, all algorithms for nonlinear optimization can be used to estimate parameters in molecular biological systems, for example, Gauss-Newton iteration method and its variants. However, these methods do not take the special structures of biological system models into account and thus are not efficient. In this paper, we propose an alternating constraint least squares method for estimating parameters in S-system model by taking use of their special structure and the biological meaning of parameters. To investigate its performance, the alternating constraint least squares method is applied to a biological system and is compared with other parameter estimation methods. Simulation results show the good performance of the proposed estimation method.