A distribution‐matching method for parameter estimation and model selection in computational biology

Abstract

SUMMARYThe determination of the model parameters is a central challenge in computational modeling of biological systems. Typically, only a fraction of the parameters (such as kinetic rate constants) is experimentally measured, whereas the rest is fitted. The fitting process is usually based on experimental time course measurements of observables, which are used to assign parameter values that minimize some measure of the error between these measurements and the corresponding model prediction. The data, which can come from real‐time polymerase chain reaction (PCR), enzymatic reactions, flow cytometry, etc., tend to be very noisy, but the statistics of the noise can often be inferred by performing calibration procedures. In this paper, we show how the knowledge of the properties of the noise, expressed in terms of its cumulative distribution function, can be used to validate or invalidate the estimates provided by an upstream state observer (a particle filter) and to refine them in case they turn out not to be satisfactory. Furthermore, we show how the same tools can be used to discriminate among alternative models of the same biological process. We demonstrate these ideas on a simple gene expression model, and we show how the proposed method is able to handle estimation problems that cannot be effectively solved by classical techniques such as least‐squares estimation. Copyright © 2012 John Wiley & Sons, Ltd.