Parameter Estimation and Model Selection in Computational Biology

Abstract

A central challenge in computational modeling of biological systems is the determination of the model parameters. Typically, only a fraction of the parameters (such as kinetic rate constants) are experimentally measured, while the rest are often 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 measurements, which can come from immunoblotting assays, fluorescent markers, etc., tend to be very noisy and taken at a limited number of time points. In this work we present a new approach to the problem of parameter selection of biological models. We show how one can use a dynamic recursive estimator, known as extended Kalman filter, to arrive at estimates of the model parameters. The proposed method follows. First, we use a variation of the Kalman filter that is particularly well suited to biological applications to obtain a first guess for the unknown parameters. Secondly, we employ an a posteriori identifiability test to check the reliability of the estimates. Finally, we solve an optimization problem to refine the first guess in case it should not be accurate enough. The final estimates are guaranteed to be statistically consistent with the measurements. Furthermore, we show how the same tools can be used to discriminate among alternate models of the same biological process. We demonstrate these ideas by applying our methods to two examples, namely a model of the heat shock response in E. coli, and a model of a synthetic gene regulation system. The methods presented are quite general and may be applied to a wide class of biological systems where noisy measurements are used for parameter estimation or model selection.

The Virtual Brain Integrates Computational Modeling and Multimodal Neuroimaging

“…In the framework of control theory, the challenge of parameter estimation in complex dynamical systems is approached by the implementation of state observers aiming to provide estimates of the internal states of a system, given measurements of the input and output of the system. Recently, several state observer techniques have been developed and successfully applied to biological systems, and the use of extended and unscented Kalman filtering methods has become a de facto standard of nonlinear state estimation (Lillacci and Khammash, 2010;Quach et al, 2007;Sun et al, 2008;Wang et al, 2009). When parameters are assumed to be constants, they are considered as additional state variables with a rate of change equal to zero.…”

“…In the context of biological systems, this problem has been addressed by an approach that combines extended Kalman filtering with a posteriori calculated measures of accuracy of the estimation process based on a v 2 variance test on measurement noise (Lillacci and Khammash, 2010). The core idea is to examine the reliability of estimates after they have been computed by using additional information gathered from noise statistics from the experiment to ensure that the estimated parameters are consistent with all available empirical data or otherwise defined constraints.…”

“…Moreover, it would also be possible to directly integrate BOLD-derived inequality constraints by using constrained Kalman filtering approaches (Simon and Chia, 2002;Simon and Simon, 2003) or to extend approaches for the slow-fast systems. However, BOLD observations do not need to be integrated directly in the observation model, but can be used it in the line of Lillacci and Khammash (2010) for selection between ambiguous estimates.…”

Modeling environmental disturbances with the chemical master equation

“…antibiotic stress, heat stress, oxidative stress, osmotic stress, nutritional stress, etc. We plan on developing novel system identification procedures, as well as levering existing techniques [23] to build a library of models that characterize the manner in which environmental disturbances impact both synthetic and natural biological processes.…”

On the impact of discreteness and abstractions on modelling noise in gene regulatory networks

“…Each step represents a possible control point, where several biochemical mechanisms play a role (see Alberts et al (2002) for a comprehensive review and Lillacci and Khammash (2010) for an application to model selection). Characterising the contributions of each single control point in the regulation process of gene expression is a complex task.…”