A systematic framework for the design of reduced-order models for signal transduction pathways from a control theoretic perspective

Systematic study of cellular signaling pathways facilitates improved understanding of processes including cell proliferation, metabolism and embryonic development. Key cell signaling pathway characteristics, such as transduction, amplification, feedback, and filtering display striking similarities to that of a control system. This leads us to believe that a control theoretic analysis of these pathways could enable a systems level understanding and help identify the role of individual modules in controlling the overall cellular behavior. Towards this end, this paper presents a framework with a step-by-step bottom-up methodology to guide the development of modular reduced-order signaling pathway components that collectively predict key observations and yet are simple. Critical steps of this iterative method include (1) modification of the pathway structure by addition and/or deletion of key nodes and/or arcs, (2) critical evaluation of multiple functional forms for fluxes and (3) estimation of the pathway model parameters. The parameter estimation minimizes the mismatch between the desired behavior and the predicted behavior using a hybrid procedure that involves a genetic algorithm to identify interesting regions in the parameter-space that are further explored using a local optimizer. The utility of this framework has been demonstrated by developing a reduced-order model for the mitogen-activated protein kinase (MAPK) pathway in mouse NIH-3T3 fibroblasts. The reduced-order model, consisting of five ordinary differential equations and 16 parameters, quantitatively predicts the bistable and proportional MAPK responses to the PDGF stimulus at different levels of MAP kinase phosphatase (MKP).