The automated optimisation of a coarse-grained force field using free energy data

Abstract

Atomistic models provide a detailed representation of molecular systems, but are sometimes inadequate for simulations of large systems over long timescales. Coarse-grained models enable accelerated simulations by reducing the number of degrees of freedom, at the cost of reduced accuracy. New optimisation processes to parameterise these models could improve their quality and range of applicability. We present an automated approach for the optimisation of coarse-grained force fields, by reproducing free energy data derived from atomistic molecular simulations. To illustrate the approach, we implemented hydration free energy gradients as a new target for force field optimisation in ForceBalance and applied it successfully to optimise the un-charged side-chains and the protein backbone in the SIRAH protein coarse-grain force field. The optimised parameters closely reproduced hydration free energies of atomistic models and gave improved agreement with experiment.

Fig. 1. General workflow for the CG force field optimisation. Free energy gradients are collected from atomistic simulations and used as optimisation targets in ForceBalance. New parameters are obtained and later used in the calculation of hydration free energies for CG beads (side-chains and backbone). Letters from A to D correspond to each of the main stages in the optimisation and validation process (see ESI†).

Fig. 2. Comparison of decoupling HFEs from the new set of optimised parameters (SIRAH-OBAFE) against atomistic simulations (AA), the original SIRAH 1.0 force field, the latest version SIRAH 2.0 and experimental data. (A) Linear regression of predicted ΔG values for AA (blue), SIRAH 1.0 (red), SIRAH 2.0 (orange) and SIRAH-OBAFE (green) force fields, against experimental data. Each point represents a specific side-chain. The grey line represents a perfect fit (y = x), and R² values are given in the inset legends. (B) Bar plot comparison of predicted ΔG values for AA (OPLS and AMBER-14SB) (blue), SIRAH 1.0 (red), SIRAH 2.0 (orange) and SIRAH-OBAFE (green) against experimental data (yellow; y axis) for all the neutral side-chains. Error estimates were calculated as standard errors based on three repeat simulations. For some cases, red bars appear to be missing as they are too small to be seen on the scale of the plot.

Fig. 3. RMSD time series comparison between the original SIRAH 1.0 FF (black), the updated SIRAH 2.0 FF (cyan) and the optimised SIRAH-OBAFE FF (purple). RMSD trajectory analysis is shown as a time series comparison with respect to the Cα carbons of the CG representation to the crystal structure for (A) Serum albumin, (B) GFP protein, (C) Gamma-adaptin domain, (D) L7Ae protein, (E) CRO repressor and (F) the N-terminal domain of phage 434 repressor. PDB codes are shown in the figure titles and legend colours are shown at the bottom of the figure. Protein structures, corresponding to each of the simulated cases, are shown inside each plot. All simulations and analysis were run in GROMACS v.2018.2.