This study aimed to shed light on the long debate over whether conformational selection (CS) or induced fit (IF) is the governing mechanism for protein-ligand binding. The main difference between the two scenarios is whether the conformational transition of the protein from the unbound form to the bound form occurs before or after encountering the ligand. Here we introduce the IF fraction (i.e., the fraction of binding events achieved via IF), to quantify the binding mechanism. Using simulations of a model protein-ligand system, we demonstrate that both the rate of the conformational transition and the concentration of ligand molecules can affect the IF fraction. CS dominates at slow conformational transition and low ligand concentration. An increase in either quantity results in a higher IF fraction. Despite the many-body nature of the system and the involvement of multiple, disparate types of dynamics (i.e., ligand diffusion, protein conformational transition, and binding reaction), the overall binding kinetics over wide ranges of parameters can be fit to a single exponential, with the apparent rate constant exhibiting a linear dependence on ligand concentration. The present study may guide future kinetics experiments and dynamics simulations in determining the IF fraction.protein-ligand complex | conformational dynamics | diffusion-influenced bimolecular reaction | induced-fit fraction

An analytical expression is derived for the rate constant that describes diffusive transitions between two deep wells of a multidimensional potential. The expression, in contrast to the Kramers-Langer formula for the rate constant, is valid even when the diffusion is highly anisotropic. Our approach is based on a variational principle for the reactive flux and uses a trial function for the splitting probability or commitor. The theoretical result is validated by Brownian dynamics simulations.

A method developed by Northrup et al. [J. Chem. Phys. 80, 1517] for calculating proteinligand binding rate constants (k a ) from Brownian dynamics (BD) simulations has been widely used for rigid molecules. Application to flexible molecules is limited by the formidable computational cost to treat conformational fluctuations during the long BD simulations necessary for k a calculation. Here, we propose a new method called BDflex for k a calculation that circumvents this problem. The basic idea is to separate the whole space into an outer region and an inner region, and formulate k a as the product of k E andη d , which are obtained by separately solving exterior and interior problems. k E is the diffusion-controlled rate constant for the ligand in the outer region to reach the dividing surface between the outer and inner regions; in this exterior problem conformational fluctuations can be neglected.η d is the probability that the ligand, starting from the dividing surface, will react at the binding site rather than escape to infinity. The crucial step in reducing the determination ofη d to a problem confined to the inner region is a radiation boundary condition imposed on the dividing surface; the reactivity on this boundary is proportional to k E . By confining the ligand to the inner region and imposing the radiation boundary condition, we avoid multiple-crossing of the dividing surface before reaction at the binding site and hence dramatically cut down the total simulation time, making the treatment of conformational fluctuations affordable. BDflex is expected to have wide applications in problems where conformational fluctuations of the molecules are crucial for productive ligand binding, such as in cases where transient widening of a bottleneck allows the ligand to access the binding pocket, or the binding site is properly formed only after ligand entrance induces the closure of a lid.