Abstract
The free energy of a process is the fundamental quantity that determines its spontaneity or propensity at a given temperature. In particular, the binding free energy of a drug candidate to its biomolecular target is used as an objective quantity in drug design. Recently, binding kinetics—rates of association (kon) and dissociation (koff)—have also demonstrated utility for their ability to predict efficacy and in some cases have been shown to be more predictive than the binding free energy alone. Some methods exist to calculate binding kinetics from molecular simulations, although these are typically more difficult to calculate than the binding affinity as they depend on details of the transition path ensemble. Assessing these rate constants can be difficult, due to uncertainty in the definition of the bound and unbound states, large error bars and the lack of experimental data. As an additional consistency check, rate constants from simulation can be used to calculate free energies (using the log of their ratio) which can then be compared to free energies obtained experimentally or using alchemical free energy perturbation. However, in this calculation it is not straightforward to account for common, practical details such as the finite simulation volume or the particular definition of the “bound” and “unbound” states. Here we derive a set of correction terms that can be applied to calculations of binding free energies using full reactive trajectories. We apply these correction terms to revisit the calculation of binding free energies from rate constants for a host-guest system that was part of a blind prediction challenge, where significant deviations were observed between free energies calculated with rate ratios and those calculated from alchemical perturbation. The correction terms combine to significantly decrease the error with respect to computational benchmarks, from 3.4 to 0.76 kcal/mol. Although these terms were derived with weighted ensemble simulations in mind, some of the correction terms are generally applicable to free energies calculated using physical pathways via methods such as Markov state modeling, metadynamics, milestoning, or umbrella sampling.
Highlights
Γ does not appear in the internal energy function, and cannot affect thermodynamic properties such as the binding free energy, we examine whether lower friction coefficients can accelerate the convergence of unbinding simulations
To generate an ensemble of ligand unbinding events, we need to employ enhanced sampling as the timescale of ligand unbinding events in this system is prohibitively long: we found in previous studies a mean first passage time of 2.1 s (Dixon et al, 2018), which is six orders of magnitude longer than the reach of conventional MD sampling
We derive a more accurate expression for the binding free energy that accounts for the finite box size in a typical MD simulation
Summary
In recent years there is a growing appreciation for the utility of binding kinetics in the prediction of drug efficacy (Lu and Tonge, 2010; Carroll et al, 2012; Vauquelin et al, 2012; Pei et al, 2014; Ayaz et al, 2016; Copeland, 2016; Costa et al, 2016; Guo et al, 2016; Tonge, 2017; Bruce et al, 2018; Lee et al, 2019; NunesAlves et al, 2020). Kinetic constants of binding and release—beyond just the equilibrium constants of binding—are required to model drug action when the timescales of binding and release cannot be separated from the other competing processes (Bernetti et al, 2017). It is important to note that changes in kinetics are not always tied to changes in affinity (Guo et al, 2014), and that to accurately predict changes in kinetics, models of the ligandbinding transition state are needed to estimate transition-state stabilization or destabilization (Spagnuolo et al, 2017)
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