T cell activation: Kinetic proofreading, serial engagement and cell adhesion

There is a fundamental difference in complexity between signaling initiated by ligands on the surface of one cell binding to receptors on the surface of another cell and ligands in solution binding to these receptors. The fact that two cells must approach each other and form a number of intercellular bonds of different types, all within the restricted geometry of the intercellular contact region, introduces the possibility of complex spatio-temporal dynamics of surface receptors that is not present otherwise. Mathematical modelling of these dynamics is in its early stages. However, useful tools have emerged. The purpose of this paper is to describe some of these mathematical tools, indicating their strengths and shortcomings, and suggest some directions for future theoretical studies.