The immunological synapse is a stable intercellular structure that specializes in substance and signal transfer from one immune cell to another. Its formation is regulated in part by the diffusion of adhesion and signaling molecules into, and their binding of countermolecules in the contact area. The stability of immunological synapses allows receptor-ligand interactions to approximate chemical equilibrium despite other dynamic aspects. We have developed a mathematical model that describes the coupled reaction-diffusion process in an established immunological synapse. In this study, we extend a previously described contact area fluorescence recovery after photobleaching (FRAP) experiment to test the validity of the model. The receptor binding activity and lateral mobility of fluorescently labeled, lipid-anchored ligands in the bilayer resulted in their accumulation, as revealed by a much higher fluorescence intensity inside the contact area than outside. After complete photobleaching of the synapse, fluorescence recovery requires ligands to dissociate and rebind, and to diffuse in and out of the contact area. Such a FRAP time course consequently provides information on reaction and diffusion, which can be extracted by fitting the model solution to the data. Surprisingly, reverse rates in the two-dimensional contact area were at least 100-fold slower than in three-dimensional solution. As previously reported in immunological synapses, a significant nonrecoverable fraction of fluorescence was observed with one of two systems studied, suggesting some ligands either dissociated or diffused much more slowly compared with other ligands in the same synapse. The combined theory and experiment thus provides a new method for in situ measurements of kinetic rates, diffusion coefficients, and nonrecoverable fractions of interacting molecules in immunological synapses and other stable cell-bilayer junctions.

Kinetic rates and binding affinity of receptor-ligand interactions are important determinants of cell adhesion. Measurements of these parameters in fluid phase using soluble molecules (i.e., three-dimensionial parameters) do not necessarily correlate with their counterparts measured when both binding partners are respectively anchored to two apposing surfaces (i.e., two-dimensional (2D) parameters). Moreover, 2D affinities measured by different methods can differ by orders of magnitude. Here we describe a coupled diffusion-reaction model for the fluorescence recovery after photobleaching experiment previously used to demonstrate the dynamics of adhesive bonds in the contact area. Applying the mathematical model to the contact area fluorescence recovery after photobleaching experiment enables in situ measurements of 2D kinetic rates of the adhesion molecules and their retarded diffusion in a stable contact area. The mathematical properties of the model are characterized in this article and its experimental validation will be presented in the companion article.