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First-Principle Coarse-Graining Framework for Scale-Free Bell-Like Association and Dissociation Rates in Thermal and Active Systems

Fluctuations of surfaces that harbor reactive molecules interacting across the intervening space strongly influence the reaction kinetics. One such paradigmatic system is the cell membrane, with associated proteins, binding to an interior or an exterior scaffold—for example, the cytoskeleton in the former and the extracellular matrix in the latter case. Given that membrane fluctuations are significant and regulated by the activity of the cell, we hypothesize that these active fluctuations can be tuned to influence ligandreceptor-mediated adhesion. However, a comprehensive model, deriving both binding and unbinding rates from first principles, has not yet been established, and as such, the effect of the membrane activity on the rates remains an open problem. Here, we solve this issue by establishing a systematic coarse graining procedure, providing a cascade of expressions for rates appropriate for the observed timescale, and present a scale-free formulation of rates. In the first step, we introduce a minimal model to recover the so-called Bell-Dembo rates from first principles, where the binding and unbinding rates depend on the instantaneous position of the membrane. We then derive the analytical coarse-grained rates for thermal fluctuations, recovering a result that has previously been successfully used in the literature. Finally, we expand this framework to account for active fluctuations of the membrane. In this step, we develop a mechanical model that convolutes Gauss and Laplace distributed noise. This choice may have universal features and is motivated by our analysis of measurements in two very different cell types, namely, human macrophages and red blood cells. We find that cell activation enables the formation of bonds at much larger separations between the cell and the target. This effect is significantly greater for binding to a surface on the extracellular compared to the intracellular side. We thus show that active fluctuations directly influence protein association and dissociation rates, which may have clear physiological implications that are yet to be explored.

Cell adhesion ; Cell mechanics ; Fluctuation mediated interactionsFluctuations & noiseMembranesNonequilibrium fluctuationsNonequilibrium statistical mechanics ; Protein-ligand interactions ; Protein-membrane interactions

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