Rate constants for proteins binding to substrates with multiple binding sites using a generalized forward flux sampling expression

Abstract

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.

Unbiased Atomistic Insight in the Mechanisms and Solvent Role for Globular Protein Dimer Dissociation

“…Our findings of direct, sliding and rebinding paths for the non-specific dissociation for the B U, suggests that these atomistic mechanisms of protein unbinding, also occurring in the specific N U are general dissociation mechanisms. Indeed recent numerical work highlights these mechanisms using simplified models of protein binding [25,26]. These findings are also fully compatible with previous MD simulations [6,53].…”

“…This finding suggests that the mechanism of direct dissociation, sliding and rebinding are general dissociation mechanisms. Indeed, theoretical and numerical work on simple models shows that indeed protein association is influenced by rebinding [25,26]. The sliding mechanism can thus be viewed as rebinding to a non-specific state without full solvation.…”

“…[23] state that water assists binding through stabilization of a diffusion encounter complex which increases the rebinding probability. Association via rebinding increases for stronger isotropic (dispersion) interactions, which smooth the rugged energy landscape due to anisotropic (charged) interactions [25,26]. In fact, water could also play such a smoothing role, e. g. by screening anisotropic salt bridges at the interface.…”

Unbiased Atomistic Insight into the Mechanisms and Solvent Role for Globular Protein Dimer Dissociation

“…These findings are in agreement with the existing literature on sliding and rebinding mechanisms, wherein dimers exhibit early intermediates that effectively increase the binding rate. 17,19,25,26 However, the nature of interactions participating in such mechanisms has not been addressed in detail. To gain further insight, we define several collective variables (CVs) that are important for the dissociation mechanisms.…”

“…Theoretical and numerical work on simple models shows that indeed protein association is influenced by rebinding. 25,26 The sliding mechanism can thus be viewed as rebinding to a nonspecific state without full solvation.…”