Iterative Linear Least Squares Method of Parameter Estimation for Linear-Fractional Models of Molecular Biological Systems

Abstract

Based on statistical thermodynamics principle or Michaelis-Menten kinetics equation, the models for biological systems contain linear fractional functions as reaction rates which are nonlinear in both parameters and states. Generally it is challenging to estimate parameters nonlinear in a model although there have been many traditional nonlinear parameter estimation methods such as Gauss-Newton iteration method and its variants. However, in a linear fractional model both the denominator and numerator are linear in the parameters. Based on this observation, we develop an iterative linear least squares method for estimating parameters in biological system modeled by linear fractional function. The basic idea is to transfer optimizing a nonlinear least squares objective function into iteratively solving a sequence of linear least squares problems. The developed method is applied to a linear fractional function and an auto-regulatory gene network. The simulation results show the superior performance of the proposed method over some existing algorithms.