Hydrodynamics of transient cell-cell contact: The role of membrane permeability and active protrusion length

Abstract In many biological settings, two or more cells come into physical contact to form a cell-cell interface. In some cases, the cell-cell contact must be transient, forming on timescales of seconds. One example is offered by the T cell, an immune cell which must attach to the surface of other cells in order to decipher information about disease. The aspect ratio of these interfaces (tens of nanometers thick and tens of micrometers in diameter) puts them into the thin-layer limit, or “lubrication limit”, of fluid dynamics. A key question is how the receptors and ligands on opposing cells come into contact. What are the relative roles of thermal undulations of the plasma membrane and deterministic forces from active filopodia? We use a computational fluid dynamics algorithm capable of simulating 10-nanometer-scale fluid-structure interactions with thermal fluctuations up to seconds-and microns-scales. We use this to simulate two opposing membranes, variously including thermal fluctuations, active forces, and membrane permeability. In some regimes dominated by thermal fluctuations, proximity is a rare event, which we capture by computing mean first-passage times using a Weighted Ensemble rare-event computational method. Our results demonstrate that the time-to-contact increases for smaller cell-cell distances (where the thin-layer effect is strongest), leading to an optimal initial cell-cell separation for fastest receptor-ligand binding. We reproduce a previous experimental observation that fluctuation spatial scales are largely unaffected, but timescales are dramatically slowed, by the thin-layer effect. We also find that membrane permeability would need to be above physiological levels to abrogate the thin-layer effect. Author summary The elastohydrodynamics of water in and around cells is playing an increasingly recognized role in biology. In this work, we investigate the flow of extracellular fluid in between cells during the formation of a cell-cell contact, to determine whether its necessary evacuation as the cells approach is a rate-limiting step before molecules on either cell can interact. To overcome the computational challenges associated with simulating fluid in this mechanically soft, stochastic and high-aspect-ratio environment, we extend a computational framework where the cell plasma membranes are treated as immersed boundaries in the fluid, and combine this with computational methods for simulating stochastic rare events in which an ensemble of simulations are given weights according to their probability. We find that the internal dynamics of the membranes has speeds in approximately microseconds, but that as the cells approach, a new slow timescale of approximately milliseconds is introduced. Thermal undulations nor typical amounts of membrane permeability can overcome the timescale, but active forces, e.g., from the cytoskeleton, can. Our results suggest an explanation for differences in molecular interactions in live cells compared to in vitro reconstitution experiments.

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