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. In this work 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 for slowly diffusing receptors, while for rapidly diffusing receptors increasing molecular reach reduces reaction efficacy. In contrast, 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, increasing molecular reach increases reaction efficacy for all diffusivities. We show results in the context of immune checkpoint receptors (PD-1 dephosphorylating CD28), a standard opposing kinase-phosphatase reaction, and a minimal two-particle model. The work highlights the importance of the 3D nature of many 2D membrane-confined interactions, illustrating a role for molecular reach in controlling biochemical reactions.