Zeitschrift für Informatik und Systembiologie

Parameter Estimation for Stochastic Models of Biochemical Reactions

Abstract

Christoph Zimmer and Sven Sahle

Parameter estimation is very important for the analysis of models in Systems Biology. Stochastic models are of increasing importance. However parameter estimation of stochastic models is still in the early phase of development and there is need for efficient methods to estimate model parameters from time course data which is intrinsically stochastic, only partially observed and has measurement noise.

In this article a fast and efficient method that is well established in the field of parameter estimation for systems of ordinary differential equations (ODE) is adapted to stochastic models. The focus is on the objective function which is shown to have advantageous properties that make it directly applicable to problems in systems biology. The proposed method can deal with stochastic systems where the behaviour qualitatively differs from the corresponding deterministic description. It works with measurements from a single realization of the stochastic process, and with partially observed processes including measurement errors. The objective function is deterministic, therefore a wide range of optimization methods, from derivative based methods to global optimization to Bayesian techniques can be applied. The computational effort required is comparable to similar methods for parameter estimation in deterministic models. To construct the objective function a multiple shooting procedure is used in which the continuity constraints are relaxed to allow for stochasticity. Unobserved states are treated by enlarging the optimization vector and using resulting values from the forward integration. Test functions are suggested that allow to monitor the validity of the approximations involved in this approach. The quality of the method is evaluated for some example models with a statistic of 50 estimates from 50 stochastic realizations. It is shown that the method performs well compared to established approaches.