Elastic Barrier Dynamical Freezing in Free Energy Calculations: A Way To Speed Up Nonequilibrium Molecular Dynamics Simulations by Orders of Magnitude

Abstract

An important issue concerning computer simulations addressed to free energy estimates via nonequilibrium work theorems, such as the Jarzynski equality [Phys. Rev. Lett. 1997, 78, 2690], is the computational effort required to achieve results with acceptable accuracy. In this respect, the dynamical freezing approach [Phys. Rev. E 2009, 80, 041124] has been shown to improve the efficiency of this kind of simulations, by blocking the dynamics of particles located outside an established mobility region. In this report, we show that dynamical freezing produces a systematic spurious decrease of the particle density inside the mobility region. As a consequence, the requirements to apply nonequilibrium work theorems are only approximately met. Starting from these considerations, we have developed a simulation scheme, called "elastic barrier dynamical freezing", according to which a stiff potential-energy barrier is enforced at the boundaries of the mobility region, preventing the particles from leaving this region of space during the nonequilibrium trajectories. The method, tested on the calculation of the distance-dependent free energy of a dimer immersed into a Lennard-Jones fluid, provides an accuracy comparable to the conventional steered molecular dynamics, with a computational speedup exceeding a few orders of magnitude.

Local Resampling Trick for Focused Molecular Dynamics

“…If we repeatedly select all particles i where ∥ x i ∥ < r , resampling the positions of these particles while freezing the rest, then eventually we will remove all particles from the region of interest, as illustrated in Figure . A similar observation was made by Giovannelli et al in ref …”

“…The last panel shows the fraction of particles within that region. A similar observation was made in ref …”

“…In molecular simulation, it is often useful to focus sampling effort on small parts of a large system. Examples may include: (1) cases where a small perturbation is introduced to a large system, such as relative binding free energy calculations in explicit solvent, (2) cases where a more efficient sampler can be implemented for a subsystem than for the system overall, and (3) cases where the observable being computed depends most sensitively on fluctuations in a small region of the system.…”

Binding Free Energies of Host–Guest Systems by Nonequilibrium Alchemical Simulations with Constrained Dynamics: Illustrative Calculations and Numerical Validation

“…The ligand-constrained state, namely the final state of the decoupling process, could be recovered with an analytical reweighting procedure. Finally, some methodology inspired to QM/MM simulations developed in the framework of nonequilibrium simulations, such as dynamical freezing , or configurational freezing , could somehow be integrated in the alchemical machinery to decrease further the dissipation and hence to improve the accuracy. Nothing prevents, in principle, the methodologies described above being combined in a unique nonequilibrium alchemical protocol.…”

Binding Free Energies of Host–Guest Systems by Nonequilibrium Alchemical Simulations with Constrained Dynamics: Theoretical Framework

“…Nonetheless, this type of problem is common to all the double-decoupling based methods. In such cases, one must introduce an a priori knowledge of possible poses of the ligand or to resort to some advanced sampling technique based, for example, on replica exchange or serial generalized ensemble schemes. ,− Techniques based on the freezing of atoms far from the binding site could also be implemented to speed up the nonequilibrium trajectories. − …”