Estimation of vibrational spectra of Trp-cage protein from nonequilibrium metadynamics simulations.

The development of methods that allow a structural interpretation of linear and nonlinear vibrational spectra is of great importance, both for spectroscopy and for optimizing force field quality. The experimentally measured signals are ensemble averages over all accessible configurations, which complicates spectral calculations. To account for this, we present a recipe for calculating vibrational amide-I spectra of proteins based on metadynamics molecular dynamics simulations. For each frame, a one-exciton Hamiltonian is set up for the backbone amide groups, in which the couplings are estimated with the transition-charge coupling model for nonnearest neighbors, and with a parametrized map of ab initio calculations that give the coupling as a function of the dihedral angles for nearest neighbors. The local-mode frequency variations due to environmental factors such as hydrogen bonds are modeled by exploiting the linear relationship between the amide C-O bond length and the amide-I frequency. The spectra are subsequently calculated while taking into account the equilibrium statistical weights of the frames that are determined using a previously published reweighting procedure. By implementing all these steps in an efficient Fortran code, the spectra can be averaged over very large amounts of structures, thereby extensively covering the phase space of proteins. Using this recipe, the spectral responses of 2.5 million frames of a metadynamics simulation of the miniprotein Trp-cage are averaged to reproduce the experimental temperature-dependent IR spectra very well. The spectral calculations provide new insight into the origin of the various spectral signatures (which are typically challenging to disentangle in the congested amide-I region), and allow for a direct structural interpretation of the experimental spectra and for validation of the molecular dynamics simulations of ensembles.