Efficient Nonequilibrium Method for Binding Free Energy Calculations in Molecular Dynamics Simulations

Abstract

We introduce an effective technique for the calculation of the binding free energy in drug-receptor systems using nonequilibrium molecular dynamics and application of the Jarzynski theorem. In essence, this novel methodology constitutes the nonequilibrium adaptation of an ancient free energy perturbation technique called Double Annihilation Method, invented more than 25 years ago [J. Chem. Phys. 1988, 89, 3742-3746] and upon which modern approaches of binding free energy computation in drug-receptor systems are heavily based. The proposed computational approach, termed Fast Switching Double Annihilation Methods (FS-DAM) in honor of its ancient ancestor, is applied to a prototypical example system with multiple binding sites, proving its computational potential and versatility in unraveling multiple site or allosteric binding processes.

I. Dissociation free energies of drug–receptor systems via non-equilibrium alchemical simulations: a theoretical framework

“…The distance between the forward and reverse distribution is of the order of the V box dependent dissociation free energy so that, for tight binding ligand, P (W 1→0 ) and P (−W 0→1 ) have a negligible overlap. [38] In the Figure The pattern shown in Figure 1 closely resembles that seen in systems where one direction of the τ -NE experiment envisages the entrance in a funnel, like in the folding of a small polipeptide. [32] The entrance in the exclusion zone (that for the case of the Zn(MBET306) + complex reported in Figure 1 corresponds roughly to the volume surrounding the central tartrate core of the molecule), via fast-growth from randomly sampled positions in a volume that is much larger than V site , is a far more dissipative process than the alchemically driven escape of the ligand from the binding site.…”

“…Jorgensen and C. Ravimohan [18], as a limiting case of a general non equilibrium (NE) theory of alchemical processes, specifically addressing some controversial and elusive issues like the volume dependence of the decoupling free energy of the bound state. [31,34,37] We further show that most of pitfalls and entanglements in the equilibrium approach can be resolved by using the recently proposed non-equilibrium variant of the alchemical method, named Fast Switching Double Annihilation Method (FS-DAM) [38] relying on the production of many independent non-equilibrium trajectories with a continuous dynamical evolution of an externally driven alchemical coordinate, [39] completing the alchemical decoupling of the ligand in a matter of few tens of picoseconds rather than nanoseconds. The absolute binding free energy is recovered from the annihilation work distributions by applying an unidirectional free energy estimate, on the assumption that any observed work distribution is given by a mixture of Gaussian distributions, [32] whose normal components are identical in either direction of the non-equilibrium process, with weights regulated by the Crooks theorem.…”

“…We have also seen, in the preceding section that, given a spread of the work distribution of few kcal mol −1 for speeds of the decoupling process lasting in the order of 50:300 picoseconds, few hundreds of τ -NE trajectories are sufficient for getting an accuracy within 0.5 kcal mol −1 in the dissociation free energy. [38] In the scheme reported in Figure 2 we have implicitly assumed that the bound state free energy is independent of the orientation of the ligand in the binding site. In reality, the ligand could be found in the exclusion zone with, e.g., several competing and mutually exclusive orientational poses (or free energy basins), with one of such poses being much more favorable than all the others (see Eq.…”

Reproducibility of Free Energy Calculations across Different Molecular Simulation Software Packages

“…The method has gained renewed attention in recent years -concomitant with improvements in computer hardware designwithin the traditional equilibrium framework [16][17][18] and also increasingly in combination with non-equilibrium techniques. [19][20][21] The name "alchemical" comes from the nonphysical intermediates that often need to be created to obtain reliable estimates of free energy differences between physical end states, and because parts or all of a molecule may effectively appear or disappear in a transformation. In the context of force field methods the transformation takes place in parameter space, i.e.…”

Unbiased free energy estimates in fast nonequilibrium transformations using Gaussian mixtures

“…20,30,32,33 In practice, however, in many instances where the ideal Markovian distribution was manifestly violated, Eq. (3) has been proved to be surprisingly accurate, even at high pulling speed, when applied on a particular direction of the process as in the NE double annihilation method 34 for evaluating the binding free energies via fast switching alchemical transformations, 21 and in the prototypical unfolding of deca-alanine. 11,29,31,32 This is somewhat puzzling given that in the opposite direction, e.g., in the NE refolding of deca-alanine, Eq.…”