Multi-model selection of integrated mechanistic-empirical models describing T-cell response

This paper explores the use of information and computational learning theory for the multi-model comparison of hybrid modeling frameworks describing cellular response to environmental cues. The hybrid framework consists of a mechanistic sub-model (describing early intracellular signaling mechanisms) that is used to inform a downstream empirical sub-model. Since the exclusive consideration of a mechanistic model describing intracellular signaling dynamics is often insufficient to predict downstream cell behaviors, an empirical model is incorporated in the framework to fill the gap. We propose a methodology for the selection of a particular integrated multi-scale mechanistic-empirical model based on the tradeoff between linear correlation and agreement with beliefs about the underlying true process. First, experimental input conditions are used in a mechanistic sub-model to stochastically generate an intermediate signaling dataset; effectively augmenting the input data space. Then the most appropriate mechanistic sub-model is selected from various candidates based on its ability to explain the output response data under the appropriate precision. We develop a methodology using the Pearson´s Product Moment Correlation Coefficient as a metric for comparison. In addition, the distribution of the correlation coefficient is compared against the distribution asserted using beliefs about the underlying process. We apply the approach to a T-Cell immune response problem.