Machine learning of single molecule free energy surfaces and the impact of chemistry and environment upon structure and dynamics

The conformational states explored by polymers and proteins can be controlled by environmental conditions (e.g.; temperature, pressure, and solvent) and molecular chemistry (e.g.; molecular weight and side chain identity). We introduce an approach employing the diffusion map nonlinear machine learning technique to recover single molecule free energy landscapes from molecular simulations, quantify changes to the landscape as a function of external conditions and molecular chemistry, and relate these changes to modifications of molecular structure and dynamics. In an application to an n-eicosane chain, we quantify the thermally accessible chain configurations as a function of temperature and solvent conditions. In an application to a family of polyglutamate-derivative homopeptides, we quantify helical stability as a function of side chain length, resolve the critical side chain length for the helix-coil transition, and expose the molecular mechanisms underpinning side chain-mediated helix stability. By quantifying single molecule responses through perturbations to the underlying free energy surface, our approach provides a quantitative bridge between experimentally controllable variables and microscopic molecular behavior, guiding and informing rational engineering of desirable molecular structure and function.