Revising Berg-Purcell for finite receptor kinetics
Revising Berg-Purcell for finite receptor kinetics
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DOI：
10.1016/j.bpj.2021.03.021
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发表时间：
2021-06-01
影响因子：
3.4
通讯作者：
Lawley, Sean D.
中科院分区：
文献类型：
--
作者：
Handy, Gregory;Lawley, Sean D.
从营养摄取到化学接受再到突触传递，细胞生物学中的许多系统都依赖于分子的扩散和与膜受体的结合。这类系统的数学分析常常忽略了受体以有限的动力学速率处理分子的事实。一个关键的例子是Berg和Purcell关于细胞表面受体捕获细胞外分子的速率的著名公式。事实上，这个有影响的结果只有在受体通过细胞壁转运分子的速度比分子到达受体的速度快得多的情况下才有效。从数学的角度来看，忽略受体动力学是方便的，因为它使扩散分子独立。相比之下，包括受体动力学引入了扩散分子之间的相关性，因为，例如，结合的受体可能暂时被阻止与其他分子结合。在这项工作中，我们提出了一个以有限的动力学速率耦合体扩散到表面受体的建模框架。该框架利用边界均匀化将扩散方程与边界上的非线性常微分方程耦合起来。我们使用这个框架推导出细胞摄取速率的明确公式，并表明Berg和Purcell的分析在一些典型的生物物理场景中显著高估了摄取。我们通过一个多粒子随机系统的数值模拟来证实我们的分析。
From nutrient uptake to chemoreception to synaptic transmission, many systems in cell biology depend on molecules diffusing and binding to membrane receptors. Mathematical analysis of such systems often neglects the fact that receptors process molecules at finite kinetic rates. A key example is the celebrated formula of Berg and Purcell for the rate that cell surface receptors capture extracellular molecules. Indeed, this influential result is only valid if receptors transport molecules through the cell wall at a rate much faster than molecules arrive at receptors. From a mathematical perspective, ignoring receptor kinetics is convenient because it makes the diffusing molecules independent. In contrast, including receptor kinetics introduces correlations between the diffusing molecules because, for example, bound receptors may be temporarily blocked from binding additional molecules. In this work, we present a modeling framework for coupling bulk diffusion to surface receptors with finite kinetic rates. The framework uses boundary homogenization to couple the diffusion equation to nonlinear ordinary differential equations on the boundary. We use this framework to derive an explicit formula for the cellular uptake rate and show that the analysis of Berg and Purcell significantly overestimates uptake in some typical biophysical scenarios. We confirm our analysis by numerical simulations of a many-particle stochastic system.