Free Energy Calculations using a Swarm-Enhanced Sampling Molecular Dynamics Approach

Abstract

Free energy simulations are an established computational tool in modelling chemical change in the condensed phase. However, sampling of kinetically distinct substates remains a challenge to these approaches. As a route to addressing this, we link the methods of thermodynamic integration (TI) and swarm-enhanced sampling molecular dynamics (sesMD), where simulation replicas interact cooperatively to aid transitions over energy barriers. We illustrate the approach by using alchemical alkane transformations in solution, comparing them with the multiple independent trajectory TI (IT-TI) method. Free energy changes for transitions computed by using IT-TI grew increasingly inaccurate as the intramolecular barrier was heightened. By contrast, swarm-enhanced sampling TI (sesTI) calculations showed clear improvements in sampling efficiency, leading to more accurate computed free energy differences, even in the case of the highest barrier height. The sesTI approach, therefore, has potential in addressing chemical change in systems where conformations exist in slow exchange.

Keywords: enhanced sampling; free energy calculations; kinetic substates; molecular dynamics; swarm.

Figure 1. Figure

Butane-to-butane alchemical transformation through the dual topology approach. Active groups (in red) and inactive groups (in green) coexist and alter as mixing parameter λ evolves from state 0 to 1. Corresponding central C-C-C-C dihedrals φ_0, and φ₁ for states 0 and 1 are also shown.

Figure 2. Figure

Sampling of dihedral angle φ₀ at λ=0.01 in butane systems a) b1, b) b2 and c) b3 from 5 ns of 12 independent trajectories for IT-TI (MD) and 12-replica swarm trajectories (sesMD); snapshots at 50 ps intervals and individually coloured for clarity.

Figure 3. Figure

Population of φ₀φ₁ rotamers of butane during IT-TI or sesTI transformation in b1, b2 and b3 systems a) as a function of λ (combined replicas) and b) as a function of replicas r01 to r12 (for λ= 0.01) and their sum (“all”). Abscissa is φ₀ and ordinate is φ₁. Both axes range from −180° to 180°.

Figure 4. Figure

Time series of dihedral angle φ₀ at λ=0.05 for butane systems a) b1, b) b2 and c) b3 systems for IT-TI and sesTI alchemical transformations. Windows include all replica contributions.

Figure 5. Figure

Time series of dihedral angle φ₀ of a) b1, b) b2 and c) b3 systems across λ for a single replica of IT-TI (TI-01) and a single replica of sesTI (r01) alchemical transformation.

Figure 6. Figure

Convergence of free energy difference estimates as a function of simulation length of 12 independent replica TI calculations for systems a) b1, b) b2 and c) b3.

Figure 7. Figure

Convergence of free energy difference estimates as a function of simulation length for butane-to-butane transitions of a) b1, b) b2 and c) b3 systems from IT-TI (blue) and sesTI by using Equation (4) (red) and Equation (5) (green).