Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, 01-224 Warsaw, Poland.
Department of Mathematics, Box 354350, University of Washington, Seattle, WA 98195, USA.
Phys Chem Chem Phys. 2021 Sep 15;23(35):19343-19351. doi: 10.1039/d1cp02820k.
We simulated Brownian diffusion and reaction-diffusion processes to study the influence of molecular rebinding on the reaction rates of bimolecular reactions. We found that the number of rebinding events, , is proportional to the target's size and inversely proportional to the diffusion coefficient and simulation time-step Δ. We found the proportionality constant close to π. We confirmed that is defined as a ratio of the activation-limited rate constant to the diffusion-limited rate constant, . We provide the formula describing the reactivity coefficient , modelling the transient-native complex transition for the activation-controlled reaction rates. We show that is proportional to (/Δ). Finally, we apply our rebinding-including reaction rate model to the real reactions of photoacid dissociation and protein association. Based on literature data for both types of reactions, we found the Δ time-scale. We show that for the photodissociation of a proton, the Δ is equal to 171 ± 18 fs and the average number of rebinding events is approximately equal to 40. For proteins, Δ is of the order of 100 ps with around 20 rebinding events. In both cases the timescale is similar to the timescale of fluctuation of the solvent molecules surrounding the reactants; vibrations and bending in the case of photoacid dissociation and diffusional motion for proteins.
我们模拟了布朗扩散和反应扩散过程，以研究分子重结合对双分子反应速率的影响。我们发现重结合事件的数量(n)与靶标大小成正比，与扩散系数(D)和模拟时间步长(\Delta)成反比。我们发现比例常数接近(\pi)。我们确认(n)被定义为激活限制速率常数(k_a)与扩散限制速率常数(k_D)的比值，(n=k_a/k_D)。我们提供了描述反应性系数(\alpha)的公式，该公式用于模拟激活控制反应速率的瞬态-天然复合物过渡。我们表明(\alpha)与((1/\Delta))成正比。最后，我们将包含重结合的反应速率模型应用于真实的光酸解反应和蛋白质结合反应。基于这两种类型反应的文献数据，我们发现了(\Delta)时间尺度。我们表明，对于质子的光解反应，(\Delta)等于 171±18 fs，平均重结合事件数约为 40。对于蛋白质，(\Delta)的量级为 100 ps，约有 20 次重结合事件。在这两种情况下，时间尺度都与反应物周围溶剂分子的波动和弯曲时间尺度相似，在光酸解反应中是振动和弯曲，在蛋白质中是扩散运动。
