The Influence of Molecular Reach and Diffusivity on the Efficacy of Membrane-Confined Reactions

Signalling by surface receptors often relies on tethered reactions whereby an enzyme bound to the cytoplasmic tail of a receptor catalyses reactions on substrates within reach. The overall length and stiffness of the receptor tail, the enzyme, and the substrate determine a biophysical parameter termed the molecular reach of the reaction. This parameter determines the probability that the receptor-tethered-enzyme will contact the substrate, in the volume proximal to the membrane, when separated by different distances within the membrane plane. Here, we develop particle-based stochastic reaction-diffusion models to study the interplay between molecular reach and diffusion. We find that increasing the molecular reach can increase reaction efficacy when diffusion is slow, but when diffusion is fast, increasing molecular reach reduces reaction efficacy. This switching is lost if reactions are forced to take place within the 2D plasma membrane instead of the 3D volume proximal to it, or if molecules diffuse in 3D. We show results in the context of immune receptors (PD-1 dephosphorylating CD28), a standard opposing kinase-phosphatase reaction, and a minimal two-particle model. The work highlights the 3D nature of many 2D membrane-confined interactions, illustrating a role for molecular reach in controlling biochemical reactions.