Modeling of nonlinear biological phenomena modeled by S-systems using Bayesian method

A biological dynamic pathway is usually modeled as a nonlinear system described by a set of nonlinear ODEs. A main challenge in modeling of biological systems is the estimation of the model parameters. In these cases, estimating these variables or parameters from other easily obtained measurements can be extremely useful. This paper addresses states and parameters estimation of biological phenomena modeled by S-systems using Bayesian approach. Nonlinear states and parameters estimation is a major issue in biology systems, since it represents a key step for achieving quantitative and qualitative information from dynamical and structured models of biology systems. Thus, we propose to use Particle Filtering (PF) to estimate nonlinear states and model parameters of the Cad System in E. coli (CSEC) in biology. For most nonlinear systems and non-Gaussian noise observations, closed-form analytic expression of the posterior distribution of the state is untractable. To overcome this drawback, a non-parametric particle filtering has recently gained popularity. Simulation analysis demonstrates that the Bayesian algorithm can well estimate the unknown model parameters under the disturbs of the noise, and it provides an efficient accuracies for the states estimation. Evaluation of the methods was performed by using Root Mean Square Error (RMSE).