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Eydgahi et al. 2012

­­Bayesian estimation of parameter distributions and co-variation in a model of receptor-mediated apoptosis

Hoda Eydgahi, William W. Chen, Dennis Vitkup, John N. Tsitsiklis, and Peter K. Sorger. Molecular Systems Biology 2011; in submission.

Using kinetic models to simulate and analyze biochemical networks requires a principled approach to estimating the parameters that control model dynamics and correspond to forward, reverse and catalytic rate constants. Even for the best-studied pathways literature data yield rather broad estimates of these parameters and parameter estimation does not yield unique values because models are usually nonidentifiable. In this paper we tackle these issues for a previously published ODE-based model of receptor-mediated apoptosis using a Bayesian estimation scheme that returns a joint probability distribution across 78 free parameters. Using this distribution it is possible to make probabilistic predictions about key model features that match experimental data. A remarkable feature of parameter distributions is that they are highly co-variant and ignoring this co-variation, or approximating it by linear regression, generates nonsensical predictions. A clear implication is that parameters cannot be treated as lists of values and variances (as assumed in SBML and MIRIAM) but must instead be represented by complex matrices. Non-linear co-variation means best-fit parameters do not lie at the peak values of marginal parameter distributions and selecting peak values from each marginal distribution individually yields a poor fit to data. We propose that parameters of kinetic models be described by posterior distributions computed using Bayesian estimation. As new experiments are performed it is necessary to update the distributions and thus, the estimation code must also be part of the description of parameters.

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