Yogurtcu Osman N, Johnson Margaret E
Department of Biophysics, The Johns Hopkins University, Baltimore, Maryland 21218, USA.
J Chem Phys. 2015 Aug 28;143(8):084117. doi: 10.1063/1.4929390.
The dynamics of association between diffusing and reacting molecular species are routinely quantified using simple rate-equation kinetics that assume both well-mixed concentrations of species and a single rate constant for parameterizing the binding rate. In two-dimensions (2D), however, even when systems are well-mixed, the assumption of a single characteristic rate constant for describing association is not generally accurate, due to the properties of diffusional searching in dimensions d ≤ 2. Establishing rigorous bounds for discriminating between 2D reactive systems that will be accurately described by rate equations with a single rate constant, and those that will not, is critical for both modeling and experimentally parameterizing binding reactions restricted to surfaces such as cellular membranes. We show here that in regimes of intrinsic reaction rate (ka) and diffusion (D) parameters ka/D > 0.05, a single rate constant cannot be fit to the dynamics of concentrations of associating species independently of the initial conditions. Instead, a more sophisticated multi-parametric description than rate-equations is necessary to robustly characterize bimolecular reactions from experiment. Our quantitative bounds derive from our new analysis of 2D rate-behavior predicted from Smoluchowski theory. Using a recently developed single particle reaction-diffusion algorithm we extend here to 2D, we are able to test and validate the predictions of Smoluchowski theory and several other theories of reversible reaction dynamics in 2D for the first time. Finally, our results also mean that simulations of reactive systems in 2D using rate equations must be undertaken with caution when reactions have ka/D > 0.05, regardless of the simulation volume. We introduce here a simple formula for an adaptive concentration dependent rate constant for these chemical kinetics simulations which improves on existing formulas to better capture non-equilibrium reaction dynamics from dilute to dense systems.
扩散和反应分子物种之间的缔合动力学通常使用简单的速率方程动力学来量化，该动力学假设物种浓度充分混合，并且使用单个速率常数来参数化结合速率。然而，在二维（2D）中，即使系统充分混合，由于d≤2维中扩散搜索的特性，用单个特征速率常数来描述缔合的假设通常也不准确。确定严格的界限，以区分能用单个速率常数的速率方程准确描述的二维反应系统和不能准确描述的系统，对于模拟和实验参数化限于细胞膜等表面的结合反应至关重要。我们在此表明，在本征反应速率（ka）和扩散（D）参数的范围内，ka/D > 0.05时，单个速率常数无法独立于初始条件拟合缔合物种浓度的动力学。相反，需要一种比速率方程更复杂的多参数描述，才能从实验中稳健地表征双分子反应。我们的定量界限源于对从斯莫卢霍夫斯基理论预测的二维速率行为的新分析。使用我们在此扩展到二维的最近开发的单粒子反应扩散算法，我们首次能够测试和验证斯莫卢霍夫斯基理论以及二维中其他几种可逆反应动力学理论的预测。最后，我们的结果还意味着，当反应的ka/D > 0.05时，无论模拟体积如何，使用速率方程对二维反应系统进行模拟时都必须谨慎。我们在此为这些化学动力学模拟引入了一个简单公式，用于自适应浓度依赖的速率常数，该公式改进了现有公式，以更好地捕捉从稀溶液到浓溶液的非平衡反应动力学。
