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

Abstract

Signaling by surface receptors often relies on tethered reactions whereby an enzyme bound to the cytoplasmic tail of a receptor catalyzes 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, whereas for rapidly diffusing receptors, increasing molecular reach reduces reaction efficacy. In contrast, if reactions are forced to take place within the two-dimensional plasma membrane instead of the three-dimensional volume proximal to it or if molecules diffuse in three dimensions, 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 threedimensional nature of many two-dimensional membrane-confined interactions, illustrating a role for molecular reach in controlling biochemical reactions.

Determination of the molecular reach of the protein tyrosine phosphatase SHP-1

“…Our work provides a specific instance where a detailed, molecular-scale model has been successfully deployed and validated with systematically controlled experiments. The model assumes a separation of timescales (16) between the fast motion of the tether as it explores its local probability density cloud (Eq. 2), and a reaction rate proportional to local 3D concentrations (k cat (tethered), which has units of µM −1 s −1 ).…”

“…2), and a reaction rate proportional to local 3D concentrations (k cat (tethered), which has units of µM −1 s −1 ). This experimentally validated model can be coupled to surface diffusion (16) and, in the future, other biophysical phenomena.…”

“…In addition to being activated, these tethered enzymes must reach their substrates, which are often other surface receptors (12,15,16). Therefore, the efficacy of these reactions is controlled not only by the binding affinity to the receptor and the substrate catalytic rate, but also by the molecular reach of the reaction (L in Fig.…”

“…1A). This parameter sets the length scale determining how close receptors must be in order for their tethered-enzymes to catalyse reactions, and serves to confine the enzyme and substrate to small membraneproximal volumes that can increase the local concentration (to approximately σ * = 1/L 3 ) and thus the reaction rates (12,(16)(17)(18). Interestingly, many surface receptors on leukocytes form micro-and nanoclusters that co-localise receptors (5,(19)(20)(21)(22)(23)(24)(25)(26), suggesting that cluster formation may be required for receptors to reach each other.…”

“…The molecular reach of these reactions is presently unknown. There are three molecules that contribute to the reach: the receptor tail, the enzyme, and the substrate (16). Structural studies are challenging due to the presence of unstructured, disorder regions in these molecules.…”