Models of Membrane-Mediated Processes: Cascades and Cycles in Insulin Action

Abstract Living cells are surrounded by a plasma membrane. The plasma membrane not only regulates the passage of metabolites, signaling molecules, and waste products into and out of the cell, but serves as an organizing scaffold for numerous cellular processes. One such important signaling pathway is that of insulin, which regulates many diverse biological functions including glucose metabolism, protein synthesis and apoptosis. While an overarching framework of the insulin signaling pathway has been established, many details still require clarification. This task is made more difficult by the complexity of the network arising from the sheer number of signaling molecules and regulatory mechanisms involved. The techniques of mathematical modeling are an indispensable tool kit for studying emergent properties of signal transduction networks that cannot be elucidated by the study of components in isolation. To illustrate some of these modeling techniques, we present and analyze two models of membrane-mediated processes in the insulin signaling pathway in adipocytes. The first is a biochemical activation cascade (the Hornberg model), and the second a physical translocation cycle (the three-pool model of Akt translocation). In both cases, a hypothesis of model structure, informed by the available experimental data, has been developed. The model structure is formalized as a set of equations, and simulated to explore the parameter space. Several analytic techniques are also presented.