Parameter estimation with interval algebra for JAK/STAT signal transduction pathway

Abstract

Computers have been widely used for simulation of kinetics of biochemical reactions. In the process of modeling the biological system and understanding the dynamical mechanisms, parameter estimation plays a key role. Ordinary differential equation is most often used as the tool for quantitative simulation. Various numerical optimization methods exists, and are applied to the parameter estimation problem, mainly including direct search methods, Newton methods, stochastic methods and deterministic methods. There methods are limited on the number of the parameters, and generally requires numerous times of simulations to get the (local/global) optimum. We propose in this paper a parameter estimation method based on ODE simulation with interval variables and parameters. Genetic algorithm is adopted for optimization, and a stepwise refinement scheme is devised to find the parameter interval with a desired size. The method is tested on a simple model of JAK-STAT pathway, successful estimation is achieved. We also applied the method for a model of JAK-STAT pathway describing the mechanism of MPD, by designing an objective function depending on limited information. The results show satisfactory correspondence to the reported observations from literature.