Spatiotemporal Modeling of Membrane Receptors

We discuss our approach to the detailed computational modeling of the molecular processes involved in early signaling of membrane-bound receptors, typically exemplified by members of the receptor tyrosine kinase (RTK) family. This includes receptors whose mutations are associated with increased risk of cancers (ErbB2) or are involved in the survival of nascent tumors (Kdr). Current imaging methods can visualize individual molecules in the context of the living cell, allowing the direct observation of molecular movement and transformations. Modeling and simulation are necessary to connect these observations to the cell-level kinetics of signaling and to help reveal connections between molecular properties and cell signaling, under both normal and pathological conditions. We describe the relevant methods and provide a minimal mathematical justification for the reader interested in understanding or applying them. The chapter builds up from the simplest modeling approach to the fully spatial, agent-based simulation that is currently used by our group. This should be useful from a tutorial perspective and also to provide the proper connections between models at different levels of granularity.