  Biological cells can exchange messages through soluble molecules or
membrane-bound receptors. In particular in the latter case, the interaction is
usually located in specific regions of the interacting cells and may depend on
or induce local morphological features or reorganizations of the
membrane-associated or membrane-proximal biochemistry. Examples are
interactions among cells that probe their environment and the surfaces of
neighboring cells with dendrite-like protrusions. Previously, we introduced an
algorithm capable of creating spatially-resolved, stochastic particle-based
computational models of cellular biochemistry. However, its applicability was
limited to the case of soluble ligands. Here, building on this earlier
approach, we introduce a simulation method that accounts for the unique
features that distinguish the sites of cell-cell contact from other regions of
the cell membrane. Employing a smooth, grid-free computational representation
of the contact sites, we extend the applicability of Green's function-based
stochastic simulation algorithms to study intermembrane bimolecular
interactions between particles on adjacent curved surfaces. We demonstrate the
utility of this computational approach by exploring the effects of contact
geometry and local biochemistry for the early phase of T-cell receptor
activation.
