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We aim to automatize the identification of collective variables to simplify and speed up enhanced sampling simulations of conformational dynamics in biomolecules. We focus on anharmonic low-frequency vibrations that exhibit fluctuations on timescales faster than conformational transitions but describe a path of least resistance towards structural change. A key challenge is that harmonic approximations are ill-suited to characterize these vibrations, which are observed at far-infrared frequencies and are easily excited by thermal collisions at room temperature. Here, we approached this problem with a frequency-selective anharmonic (FRESEAN) mode analysis that does not rely on harmonic approximations and successfully isolates anharmonic low-frequency vibrations from short molecular dynamics simulation trajectories. We applied FRESEAN mode analysis to simulations of alanine dipeptide, a common test system for enhanced sampling simulation protocols, and compare the performance of isolated low-frequency vibrations to conventional user-defined collective variables (here backbone dihedral angles) in enhanced sampling simulations. The comparison shows that enhanced sampling along anharmonic low-frequency vibrations not only reproduces known conformational dynamics but can even further improve sampling of slow transitions compared to user-defined collective variables. Notably, free energy surfaces spanned by low-frequency anharmonic vibrational modes exhibit lower barriers associated with conformational transitions relative to representations in backbone dihedral space. We thus conclude that anharmonic low-frequency vibrations provide a promising path for highly effective and fully automated enhanced sampling simulations of conformational dynamics in biomolecules. 

Linear and nonlinear dielectric responses of solutions of intrinsically disordered proteins (IDPs) were analyzed by combining molecular dynamics simulations with formal theories. A large increment of the linear dielectric function over that of the solvent is found and related to large dipole moments of IDPs. The nonlinear dielectric effect (NDE) of the IDP far exceeds that of the bulk electrolyte, offering a route to interrogate protein conformational and rotational statistics and dynamics. Conformational flexibility of the IDP makes the dipole moment statistics consistent with the gamma/log-normal distributions and contributes to the NDE through the dipole moment’s non-Gaussian parameter. The intrinsic non-Gaussian parameter of the dipole moment combines with the protein osmotic compressibility in the nonlinear dielectric susceptibility when dipolar correlations are screened by the electrolyte. The NDE is dominated by dipolar correlations when electrolyte screening is reduced. 

Low-frequency molecular vibrations at far-infrared frequencies are thermally excited at room temperature. As a consequence, thermal fluctuations are not limited to the immediate vicinity of local minima of the potential energy surface and anharmonic properties cannot be ignored. The latter is particularly relevant in molecules with multiple conformations such as proteins and other biomolecules. However, existing theoretical and computational frameworks for the analysis of molecular vibrations have so far been limited by harmonic or quasi-harmonic approximations, which are ill-suited for the description of anharmonic low-frequency vibrations. Here, we developed a fully anharmonic analysis of molecular vibrations based on a time correlation formalism that eliminates the need for harmonic or quasi-harmonic approximations. We use molecular dynamics simulations of a small protein to demonstrate that this new approach, in contrast to harmonic and quasi-harmonic normal modes, correctly identifies the collective degrees of freedom associated with molecular vibrations at any given frequency. This allows us to unambiguously characterize the anharmonic character of low-frequency vibrations in the far-infrared spectrum.