扩散限制反应速率的浓度依赖性及其结果
Concentration dependence of diffusion-limited reaction rates and its consequences
摘要：
扩散限制缔合反应在自然界中普遍存在。它们对于生物反应特别重要，其中反应速率通常由分子在二维表面（例如细胞膜）上的扩散运输决定。二维表面上扩散的特殊性可能导致非平凡的反应动力学，例如两个分子之间的浓度依赖性缔合速率。然而，传统上，生物分子缔合反应的动力学已经使用质量作用定律建模，该定律假设反应速率是浓度无关的常数。本文利用多尺度分子模拟方法研究了二维表面上扩散限制缔合反应的浓度依赖性。特别是，我们量化的短程对相互作用的反应速率的浓度依赖性的影响，并将其编入一个经验法则。在化学动力学模型中应用这一定律，我们发现简单化学体系的稳态行为会因浓度依赖速率的存在而发生剧烈的改变。特别地，我们发现，它导致抑制的内在噪声在二聚反应和不稳定的鲁棒振荡Lotka-Volterra捕食系统。事实上，我们在后者中看到了从健壮到微调行为的转变。此外，我们发现，浓度依赖的反应速率自然出现在随机捕食系统由于固有噪声。我们评论这些结果的后果，并讨论其在复杂的化学和生物系统建模的影响。特别是，我们评论的质量作用定律，这是在所有这些系统的理论建模主食的有效性范围。
英文摘要：
Diffusion-limited association reactions are ubiquitous in nature. They are particularly important for biological reactions, where the reaction rates are often determined by the diffusive transport of the molecules on two-dimensional surfaces, such as the cell membrane. The peculiarities of diffusion on two-dimensional surfaces may lead to nontrivial reaction kinetics, such as concentration dependent rate of association between two molecules. However, traditionally, the kinetics of biomolecular association reactions has been modeled using the law of mass action, which assumes that the rate of reaction is a concentration independent constant. In this paper, using multiscale molecular simulation, we investigate the concentration dependence of diffusion-limited association reactions on 2D surfaces. In particular, we quantify the influence of short-ranged pair interactions on the concentration dependence of the reaction rates and codify it in an empirical law. Using this law in a chemical kinetic model, we find that the the steady state behaviors of simple chemical systems are drastically modified by the presence of concentration dependent rates. In particular, we find that it leads to suppression of intrinsic noise in dimerization reaction and destabilizes robust oscillation in Lotka-Volterra predator-prey systems. In fact, we see a transition from robust to fine-tuned behavior in the latter. In addition, we show that concentration dependent reaction rates arise naturally in stochastic predator-prey systems due to intrinsic noise. We comment on the consequences of these results and discuss their implications in the modeling of complex chemical and biological systems. In particular, we comment on the range of validity of the law of mass action, which is a staple in all theoretical modeling of these systems.
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