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 ligand-receptor-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.

中文翻译：

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热和有源系统中无标度钟状关联和解离率的第一原理粗粒度框架

包含在中间空间相互作用的反应性分子的表面的波动强烈影响反应动力学。一个这样的典型系统是细胞膜，具有相关的蛋白质，与内部或外部支架结合 - 例如，前者的细胞骨架和后者的细胞外基质。鉴于膜波动是显着的并受细胞活性的调节，我们假设这些活性波动可以调整以影响配体受体介导的粘附。然而，尚未建立一个综合模型，从第一原理推导出结合率和非结合率，因此，膜活性对速率的影响仍然是一个悬而未决的问题。在这里，我们通过建立系统的粗粒度程序来解决这个问题，提供适用于观察到的时间尺度的利率的级联表达式，并提出一个无尺度的利率公式。在第一步中，我们引入了一个最小模型来从第一原理中恢复所谓的 Bell-Dembo 速率，其中结合率和非结合率取决于膜的瞬时位置。然后，我们推导出热波动的分析粗粒度速率，恢复以前在文献中成功使用的结果。最后，我们扩展了这个框架来解释膜的主动波动。在这一步中，我们开发了一个对高斯和拉普拉斯分布噪声进行卷积的机械模型。这种选择可能具有普遍的特征，并且是由我们对两种非常不同的细胞类型（即人类巨噬细胞和红细胞）的测量分析推动的。我们发现细胞活化能够在细胞和目标之间更大的距离处形成键。与细胞内侧相比，这种作用对于结合到细胞外表面的表面来说明显更大。因此，我们表明，主动波动直接影响蛋白质结合和解离率，这可能具有尚待探索的明显生理意义。