Stochastic single-molecule dynamics of synaptic membrane protein domains

Abstract

-Motivated by single-molecule experiments on synaptic membrane protein domains, we use a stochastic lattice model to study protein reaction and diffusion processes in crowded membranes. We find that the stochastic reaction-diffusion dynamics of synaptic proteins provide a simple physical mechanism for collective fluctuations in synaptic domains, the molecular turnover observed at synaptic domains, key features of the single-molecule trajectories observed for synaptic proteins, and spatially inhomogeneous protein lifetimes at the cell membrane. Our results suggest that central aspects of the single-molecule and collective dynamics observed for membrane protein domains can be understood in terms of stochastic reaction-diffusion processes at the cell membrane.

Stochastic lattice model of synaptic membrane protein domains

“…We focus here on the most straightforward scenario of a 1D system of length L with K patches of size a = L/K. The 2D formulation of our model [36,37] shows [62] similar stochastic dynamics of synaptic domains as the 1D formulation we consider here. We denote the hopping rates of receptors and scaffolds at lattice site i by D r i /τ r and D s i /τ s , where D r i (t) and D s i (t) model spatiotemporal variations in the receptor and scaffold hopping rates.…”

“…Synaptic membrane domains are crowded with molecules [3,15], which is expected [4,6,16,17,43] to affect diffusion and reaction processes at synaptic domains. To account for molecular crowding in our model, we impose [36,37,62] the constraint that the rates of all reaction and diffusion processes that increase the receptor or scaffold number at a lattice site i are ∝ (1 − N r i − N s i ), where N r i /ǫ r and N s i /ǫ s are the occupation numbers of receptors and scaffolds at site i with the normalization constants ǫ r and ǫ s so that, at each site, the number of receptors and scaffolds cannot increase beyond 1/ǫ r and 1/ǫ s , respectively. As a result, we have 0 N r i + N s i 1 for all i. Analogous phenomenological models of crowding have been employed previously in a variety of different contexts [47,54,60,61,72].…”

“…(1) where P (N, t) is the probability that the system is in state N at time t and W (N; m) is the transition rate from state N to state N + m. Unless indicated otherwise, we use here [36,37,62] random initial conditions of N satisfying 0 ≤ N r i + N s i ≤ 1 for all i with periodic boundary conditions. [36,37,62] considered in this article. To model molecular crowding, the rates of all reaction and diffusion processes increasing the molecule number at a given lattice site i, delineated by vertical ticks, are taken to be ∝ (1 − N r i − N s i ).…”

“…in our reaction-diffusion model of synaptic domains [36,37,62], where W react and W diff denote contributions to W due to receptor and scaffold reaction and diffusion processes at the cell membrane. For the receptor and scaffold diffusion processes we have…”

“…In the present article we build on this previous work [62] to provide a detailed discussion of the stochastic lattice model of receptor-scaffold reaction-diffusion dynamics at synaptic domains [36,37,62] and its relation to the corresponding mean-field model. We show [62] that molecular noise can yield substantial deviations from mean-field results for the receptor-scaffold reaction-diffusion dynamics at synaptic domains, and that stochastic lattice models can be employed successfully to provide quantitative insights into the single-molecule and collective dynamics of membrane protein domains [12,[39][40][41][42].…”