Complete analysis of the full synaptic patterning model without rapid-equilibration of adhesion kinetics

Establish a complete analysis of the full coupled continuum model of immune synapse patterning that includes explicit time-dependent mass-action dynamics for adhesion molecules, together with membrane elastohydrodynamics, receptor binding kinetics, and actomyosin-driven active stresses, without invoking the rapid-equilibration approximation for adhesion molecule kinetics.

Background

The paper develops a continuum model for pattern formation at the immune synapse that couples membrane height dynamics (elastohydrodynamics), receptor and adhesion kinetics, and active cytoskeletal forces. For computational tractability, the authors simplify adhesion molecule kinetics by assuming they are rapidly equilibrated, making the adhesion density a direct function of the local membrane height.

This simplification retains the activity-mediated instabilities relevant to receptor dynamics, but it removes the full time-dependent coupling between adhesion molecule binding/unbinding, advection by cortical flows, and membrane deformation. The authors therefore identify the comprehensive treatment of the full, non-simplified model—where both receptor and adhesion kinetics evolve according to mass-action dynamics—as an explicit open problem.