Trapping by clusters of channels, receptors, and transporters: quantitative description

Various membrane functional units such as receptors, transporters, and channels, whose action necessarily involves capturing diffusing molecules, are often organized into multimeric complexes forming clusters on the cell and organelle membranes. These functional units themselves are usually oligomers of several integral proteins, which have their own symmetry. Depending on the symmetry, they form clusters on different packing lattices. Moreover, local membrane inhomogeneities, e.g., the so-called membrane domains, rafts, stalks, etc., lead to different patterns even within the structures on the same packing lattice. Units in the cluster compete for diffusing molecules and screen each other. Here we propose a general approach that allows one to quantify the screening effects. The approach is used to derive simple approximate formulas giving the trapping rates of diffusing molecules by clusters of absorbers on lattices of different packing symmetries. The obtained results describe smooth variation of the trapping rate from the sum of the rates of individual absorbers forming the cluster to the effective collective rate. The latter shows how the trapping efficiency of an individual absorber decreases as the number of absorbers in the cluster increases and/or the inter-absorber distance decreases. Numerical tests demonstrate good agreement between the rates predicted by the theory and obtained from Brownian dynamics simulations for clusters of different shapes and sizes.