Sensing Size through Clustering in Non-Equilibrium Membranes and the Control of Membrane-Bound Enzymatic Reactions

Abstract

The formation of dynamical clusters of proteins is ubiquitous in cellular membranes and is in part regulated by the recycling of membrane components. We show, using stochastic simulations and analytic modeling, that the out-of-equilibrium cluster size distribution of membrane components undergoing continuous recycling is strongly influenced by lateral confinement. This result has significant implications for the clustering of plasma membrane proteins whose mobility is hindered by cytoskeletal “corrals” and for protein clustering in cellular organelles of limited size that generically support material fluxes. We show how the confinement size can be sensed through its effect on the size distribution of clusters of membrane heterogeneities and propose that this could be regulated to control the efficiency of membrane-bound reactions. To illustrate this, we study a chain of enzymatic reactions sensitive to membrane protein clustering. The reaction efficiency is found to be a non-monotonic function of the system size, and can be optimal for sizes comparable to those of cellular organelles.

A Rationale for Mesoscopic Domain Formation in Biomembranes

“…This argument has been completed and confirmed by several theoretical studies in the last decade. They dwell on a variety of theoretical techniques, such as linear stability analysis in the Fourier space [45,56,198,200], or numerical and/or analytical resolutions of stochastic equations belonging to two principal categories:Master Smoluchowski’s coagulation equation [57,196,199,201]. For example, Turner et al [57] studied the coagulation equation normaldcnnormaldt=ζ(n)+∑m=1∞kn,mcn+m−kn,m′cncm+12∑m=1n−1km,n−m′cn−mcm−km,n−mcn, where cn is the area fraction of domains or clusters containing n monomers and the constants kn,m and kn,m′ are scission and fusion rates, respectively.…”

A minimal self-organisation model of the Golgi apparatus

“…The typical compartment’s size is defined as the ratio of the second over the first moments of the size distribution. This corresponds to a size close to half the size of the exponential cut-off (see Appendix 2) beyond which it is unlikely to find a compartment ( Vagne et al, 2015 ).…”

“…One of these laws is the fact that the size distribution for small compartments should follow a power-law. Because of the scission, compartments cannot grow indefinitely and the power-law ends by an exponential cutoff ( Turner et al, 2005 ; Vagne et al, 2015 ). Thus, the size distribution of compartments of size should, on a first approximation, follow this general formulation: where is the cut-off size and is an exponent that has been calculated to be in a similar system ( Turner et al, 2005 ).…”

A rationale for mesoscopic domain formation in biomembranes

“…The "whole cluster recycling" limit corresponds to nv → ∞ and the "monomer recycling" limit to nv = 1. Adapted from [201]. For both figures, see the cited references for more details on the recycling dynamics.…”

“…The on-rates (from the cytosol to the membrane) are also size-dependent. Several models only inject monomers or tiny domains in the membrane [56,57,190,196,199,198,200,201] because they do not assume any pre-order in the exocytosed patches or because they assume direct exchange of monomers from the cytosol to the membrane, e.g., for peripheral proteins. Indeed, Foret argues that the traffic should be modeled differently for peripheral and transmembrane proteins [196], because the former are preferentially exchanged as monomers between the cytosol and the membrane, while the latter preferentially escape and join the membrane by endo-and exocytosis, respectively.…”