Parameter Estimation and Model Selection in Computational Biology

By Gabriele Lillacci, Mustafa Hani Khammash. PLoS Comput. Biol., 2010

340 citations recorded by the source corpus.

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.

Subfields: Genetics, Molecular Biology

View Paper: https://www.semanticscholar.org/paper/9a362ed58bcf80e6191bf963bfb5cc5a48f26719

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Citations in the corpus

Dynamical analysis of a prey–predator model with Beddington–DeAngelis type function response incorporating a prey refuge (2014, methodology): “The parameter estimation [41,42] can be done using one of the many well-established algorithms such as trial-and-error processes, numerical optimization techniques such as conjugate gradient method, trust region methods and genetic algorithms (see [43–45]).”
Efficient Inference of Parsimonious Phenomenological Models of Cellular Dynamics Using S-Systems and Alternating Regression (2014, background): “Instead, one often seeks a priori information to constrain the search space to simpler ad hocmodels of the underlying complex processes [2, 4, 8].”
Automated adaptive inference of phenomenological dynamical models (2015, neutral): “…control methods are well established in statistical inference 26 and in choosing a systems biology model for data from a ﬁnite set of models 27–29 , we believe that they have not been used yet in the context of inferring complex, nonlinear dynamics from an inﬁnite, complete set of all…”
WEAK SINDY FOR PARTIAL DIFFERENTIAL EQUATIONS (2020, background): “In the last 20 years, substantial developments have been made at the interface of applied mathematics and statistics to design data-driven model selection algorithms that are both statistically rigorous and computationally efficient (see [4, 11, 12, 21, 23, 24] for both theory and applications).”