An Algorithmic Approach for Constraining Stochastic Models with Multiple Data Sets

Brock Sherlock

University of New South Wales

"An Algorithmic Approach for Constraining Stochastic Models with Multiple Data Sets"

Mean-field models of protein translocation in mammalian cell metabolism in response to insulin have previously been used to identify dominant processes at the macroscopic scale (J. Biol. Chem., 289(25): 17280-17298). These mean field models do not take the stochasticity and variance of the data fully into account, however. These models also do not provide explanatory mechanisms for the response to the insulin signal. We have developed a candidate stochastic queuing network model that may provide further insight into mechanisms at the molecular scale for glucose transporter translocation in insulin regulated metabolism. To test the efficacy of the model as an explanation of the biological mechanisms, an assessment of the ability of the model to represent all the different observations needs to be quantified. For each particular experimental protocol the data set consists of small numbers of repeated samples at discrete time points of the system under that experimental condition. The stochastic model then aims to describe all the different time evolving distributions corresponding to the different experimental protocols. Not only do the distributions of the data and model need to be compared at each time point in the data set for each protocol, but also a comparison needs to be made across time as each of the distributions evolve. Additionally, the correspondence of the stochastic model and observations across the different experimental protocols needs to be quantified. In systems where data is sparse, robustness can be given to inference when independent data sets from multiple sources are combined, given that the model parameters constrained by the different protocols overlap. In this investigation, different distance measures and comparators of evolving distributions are explored for the candidate model of glucose transporter translocation with a view to building a practical algorithm for inference of stochastic models with multiple stochastic data sets from different experimental protocols. The efficacy and implications of different approaches and for the candidate model is discussed.
Additional authors: Marko Boon (Department of Mathematics and Computer Science, Eindhoven University of Technology); Maria Vlasiou (Faculty of Electrical Engineering, Mathematics and Computer Science, University of Twente); Adelle Coster (University of New South Wales)

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