Parameter Inference for Nonlinear Pathway Models via Adaptive Markov Chain Monte Carlo

Parameter Inference for Nonlinear Pathway Models via Adaptive Markov Chain Monte Carlo

Patrick Muchmore, University of Southern California

INTRODUCTION: Systems of differential equations are often appropriate for modeling time dependent metabolic processes, as they enable biological systems to be described using established principles from physics and chemistry. One well studied example is the frequently sampled intravenous glucose test (FSIGT), which consists of a glucose injection at time 0 followed by ~20 glucose and insulin measurements over the subsequent ~4 hours. This process can be well characterized by Bergman’s “minimal-model”, which consists of 3 coupled differential equations describing the time course of glucose, insulin, and their interaction over the follow-up period. However, the nonlinear nature of these systems makes it difficult to relate them to observed phenomena.  AIMS: Estimate the (physiologically relevant) differential equation parameters that are most likely to have given rise to the observed time series measurements.  METHODS: The model is fit under the assumption that glucose measurements are subject to mean zero normal errors with error variance proportional to the true value. While optimization can be used for point estimation, Bayesian techniques enable further parameter inferences. Using an adaptive Markov chain Monte Carlo (MCMC) inference routine we calculate both estimates for each parameter and credible intervals characterizing the estimates’ uncertainty.  CONCLUSIONS: Because the model is characterized by a system of equations derived from first principles, it reflects domain expert beliefs regarding the mechanisms at work (in contrast to purely statistical curve fitting). The adaptive MCMC scheme enables efficient estimation of the parameter values most consistent with the observed data, while simultaneously characterizing the associated uncertainty.

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