Acceleration of biomolecular kinetics in Gaussian accelerated molecular dynamics

Abstract

Recent studies demonstrated that Gaussian accelerated molecular dynamics (GaMD) is a robust computational technique, which provides simultaneous unconstrained enhanced sampling and free energy calculations of biomolecules. However, the exact acceleration of biomolecular dynamics or speedup of kinetic rates in GaMD simulations and, more broadly, in enhanced sampling methods, remains a challenging task to be determined. Here, the GaMD acceleration is examined using alanine dipeptide in explicit solvent as a biomolecular model system. Relative to long conventional molecular dynamics simulation, GaMD simulations exhibited ∼36-67 times speedup for sampling of the backbone dihedral transitions. The acceleration depended on level of the GaMD boost potential. Furthermore, Kramers' rate theory was applied to estimate GaMD acceleration using simulation-derived diffusion coefficients, curvatures and barriers of free energy profiles. In most cases, the calculations also showed significant speedup of dihedral transitions in GaMD, although the GaMD acceleration factors tended to be underestimated by ∼3-96 fold. Because greater boost potential can be applied in GaMD simulations of systems with increased sizes, which potentially leads to higher acceleration, it is subject to future studies on accelerating the dynamics and recovering kinetic rates of larger biomolecules such as proteins and protein-protein/nucleic acid complexes.

Fig. 1

(A) Schematic representation of backbone dihedrals Φ and Ψ in alanine dipeptide. (B) 2D potential of mean force (PMF) of backbone dihedrals (Φ, Ψ) calculated from 1000 ns cMD simulation. Low energy wells are labeled corresponding to the right-handed α helix (α_R), left-handed α helix (α_L), β-sheet (β) and polyproline II (P_II) conformations. (C) Time course and (D) 1D PMF of dihedral Φ obtained from the 1000 ns cMD simulation.

Fig. 2

Accelerated conformational sampling of alanine dipeptide in dihedral GaMD simulations: (A) Recovered 2D PMF of backbone dihedrals (Φ, Ψ) calculated from reweighting three 30 ns dihedral GaMD simulations combined using cumulant expansion to the 2^nd order. Low energy wells are labeled as in Fig. 1B. (B) 2D PMF of backbone dihedrals (Φ, Ψ) calculated directly from the three 30 ns dihedral GaMD simulations combined without energetic reweighting. (C) Time course of dihedral Φ obtained from the three 30 ns dihedral GaMD simulations. (D) 1D PMF of dihedral Φ obtained from the three 30 ns dihedral GaMD simulations without and with energetic reweighting (denoted “Modified” and “Reweighted”, respectively) compared with that of the 1000 ns cMD simulation. For GaMD, 1D PMF profiles were calculated separately for each simulation, and their average and standard deviation (error bars) were plotted here.

Fig. 3

Accelerated conformational sampling of alanine dipeptide in dual-boost GaMD simulations: (A) Recovered 2D PMF of backbone dihedrals (Φ, Ψ) calculated from reweighting three 30 ns dual-boost GaMD simulations combined using cumulant expansion to the 2^nd order. Low energy wells are labeled as in Fig. 1B. (B) 2D PMF of backbone dihedrals (Φ, Ψ) calculated directly from the three 30 ns dual-boost GaMD simulations combined without energetic reweighting. (C) Time course of dihedral Φ obtained from the three 30 ns dual-boost GaMD simulations. (D) 1D PMF of dihedral Φ obtained from the three 30 ns dual-boost GaMD simulations without and with energetic reweighting (denoted “Modified” and “Reweighted”, respectively) compared with that of the 1000 ns cMD simulation. For GaMD, 1D PMF profiles were calculated separately for each simulation, and their average and standard deviation (error bars) were plotted here.

Fig. 4

(A-B) Exponential decay of survival functions S(t) for the forward transition of dihedral Φ across the 0º energy barrier obtained from: (A) direct calculation using the transition time series collected from the simulations and (B) numerically solving the Smoluchowski equation along the 1D PMF profile of Φ. (C-D) Exponential decay of the survival functions S(t) for backward transition of dihedral Φ across the 0º energy barrier obtained from: (C) direct calculation using the transition time series collected from the simulations and (D) numerically solving the Smoluchowski equation along the 1D PMF profile of Φ. The survival functions were calculated using the cMD, dihedral GaMD and dual-boost GaMD simulations.