Bayesian Learning from Marginal Data in Bionetwork Models

In studies of dynamic molecular networks in systems biology, experimental studies are increasingly exploiting technologies such as flow cytometry to generate data on marginal distributions of a few network nodes at snapshots in time. For example, levels of intracellular expression of a few genes, or cell surface protein markers, can be assayed at a series of interim time points and assumed steady-states under experimentally stimulated growth conditions in small cellular systems. Such marginal data on a small number of cellular markers will typically carry very limited information on the parameters and structure of dynamic network models, though experiments will typically be designed to expose variation in cellular phenotypes that are inherently related to some aspects of model parametrization and structure. Our work address the statistical questions of how to integrate such data with dynamic stochastic models in order to properly quantify the information-- or lack of information-- it carries relative to models assumed. We present a Bayesian computational strategy coupled with a novel approach to summarizing and numerically characterizing biological phenotypes that are represented in terms of the resulting sample distributions of cellular markers. We build on Bayesian simulation methods and mixture modelling to define the approach to linking mechanistic mathematical models of network dynamics to snapshot data, using a toggle switch example integrating simulated and real data as context.

Keywords: biological signatures, dynamic stochastic network models, flow cytometry data, posterior simulation, synthetic gene circuit, systems biology, toggle switch model

We are grateful to the editors and two anonymous referees for constructive comments on the original version of this paper, and to Yu Tanouchi of Duke University for experimental assistance in generating the E. coli toggle switch data. This work was supported in part by the U.S. National Institutes of Health under grants P50-GM081883 and RC1-AI086032, and by the National Science Foundation under grant DMS-1106516. Any opinions, findings and conclusions or recommendations expressed in this work are those of the authors and do not necessarily reflect the views of the NIH and/or NSF.

Computer code (in Matlab) is available freely to any interested users. This includes code to replicate the examples and applications in the paper.