FOM Institute AMOLF, Science Park 104, 1098 XG Amsterdam, The Netherlands.
van't Hoff Institute for Molecular Sciences, University of Amsterdam, P.O. Box 94157, 1090 GD Amsterdam, The Netherlands.
J Chem Phys. 2018 Mar 28;148(12):124109. doi: 10.1063/1.5012854.
To predict the response of a biochemical system, knowledge of the intrinsic and effective rate constants of proteins is crucial. The experimentally accessible effective rate constant for association can be decomposed in a diffusion-limited rate at which proteins come into contact and an intrinsic association rate at which the proteins in contact truly bind. Reversely, when dissociating, bound proteins first separate into a contact pair with an intrinsic dissociation rate, before moving away by diffusion. While microscopic expressions exist that enable the calculation of the intrinsic and effective rate constants by conducting a single rare event simulation of the protein dissociation reaction, these expressions are only valid when the substrate has just one binding site. If the substrate has multiple binding sites, a bound enzyme can, besides dissociating into the bulk, also hop to another binding site. Calculating transition rate constants between multiple states with forward flux sampling requires a generalized rate expression. We present this expression here and use it to derive explicit expressions for all intrinsic and effective rate constants involving binding to multiple states, including rebinding. We illustrate our approach by computing the intrinsic and effective association, dissociation, and hopping rate constants for a system in which a patchy particle model enzyme binds to a substrate with two binding sites. We find that these rate constants increase as a function of the rotational diffusion constant of the particles. The hopping rate constant decreases as a function of the distance between the binding sites. Finally, we find that blocking one of the binding sites enhances both association and dissociation rate constants. Our approach and results are important for understanding and modeling association reactions in enzyme-substrate systems and other patchy particle systems and open the way for large multiscale simulations of such systems.
要预测生化系统的反应，了解蛋白质的固有和有效速率常数至关重要。可接触的关联有效速率常数可以分解为扩散限制速率，即蛋白质接触的速率，以及蛋白质真正结合的固有结合速率。相反，在解离时，结合的蛋白质首先以固有解离速率分离成接触对，然后通过扩散移开。虽然存在微观表达式，可以通过对蛋白质解离反应进行单次稀有事件模拟来计算固有和有效速率常数，但这些表达式仅在底物只有一个结合位点时有效。如果底物有多个结合位点，除了扩散到主体之外，结合的酶还可以跳跃到另一个结合位点。使用正向通量采样计算多个状态之间的跃迁速率常数需要广义的速率表达式。我们在这里提出了这个表达式，并使用它来推导出涉及与多个状态结合的所有固有和有效速率常数的显式表达式，包括再结合。我们通过计算一个带有两个结合位点的底物的有斑点粒子模型酶的固有和有效结合、解离和跳跃速率常数来说明我们的方法。我们发现这些速率常数随着粒子的旋转扩散常数的增加而增加。跳跃速率常数随着结合位点之间的距离的增加而减小。最后，我们发现阻断其中一个结合位点会同时增强结合和解离速率常数。我们的方法和结果对于理解和建模酶-底物系统和其他有斑点粒子系统中的结合反应以及为这些系统的大规模多尺度模拟开辟了道路非常重要。
