Center for Control, Dynamical Systems and Computation, University of California at Santa Barbara, Santa Barbara, California, United States of America
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.
Author Summary
Parameter estimation is a key issue in systems biology, as it represents the crucial step to obtaining predictions from computational models of biological systems. This issue is usually addressed by “fitting” the model simulations to the observed experimental data. Such approach does not take the measurement noise into full consideration. We introduce a new method built on the combination of Kalman filtering, statistical tests, and optimization techniques. The filter is well-known in control and estimation theory and has found application in a wide range of fields, such as inertial guidance systems, weather forecasting, and economics. We show how the statistics of the measurement noise can be optimally exploited and directly incorporated into the design of the estimation algorithm in order to achieve more accurate results, and to validate/invalidate the computed estimates. We also show that a significant advantage of our estimator is that it offers a powerful tool for model selection, allowing rejection or acceptance of competing models based on the available noisy measurements. These results are of immediate practical application in computational biology, and while we demonstrate their use for two specific examples, they can in fact be used to study a wide class of biological systems.
Citation: Lillacci G, Khammash M (2010) Parameter Estimation and Model Selection in Computational Biology. PLoS Comput Biol 6(3): e1000696. doi:10.1371/journal.pcbi.1000696
Editor: Anand R. Asthagiri, California Institute of Technology, United States of America
Received: January 22, 2009; Accepted: January 30, 2010; Published: March 5, 2010
Copyright: © 2010 Lillacci, Khammash. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Funding: This material is based upon work supported by the National Science Foundation under Grant NSF-CDI ECCS-0835847, NSF-ECCS-0802008, NIH R01GM049831, and the Institute for Collaborative Biotechnologies through Grant DAAD19-03-D-0004 from the U.S. Army Research office. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
Competing interests: The authors have declared that no competing interests exist.
* E-mail: khammash@engr.ucsb.edu
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