Mathematical Modeling of Synaptic Patterns

During antigen recognition by T cells, a specific spatial structure is formed at the contact face to an antigen-presenting cell (APC), called an immunological synapse (IS). The IS supports bidirectional signaling and release of effector molecules and is widely studied both biologically and numerically, in order to understand the process of T cell activation and signaling. This specialized structure harbors a central area (central supramolecular activation cluster, cSMAC) populated by T cell receptor-peptide-major histocompatibility complex (TCR-pMHC ) interactions, hedged by a peripheral ring (peripheral supramolecular activation cluster, pSMAC) of integrin lymphocyte function associated-1 interactions with its immunoglobulin superfamily ligand intercellular adhesion molecule-1 (LFA-1-ICAM-1). These two regions form the "bull's eye" pattern characteristic of the mature IS.In theoretical studies, different modeling architectures, including partial differential equations (PDE) and agent-based models , have been developed with the purpose to answer mechanistic questions about the IS dynamics. In this chapter, we explain possible physiological mechanisms that lead to the formation of ISs and technical issues that may occur in the course of development of agent-based models.