Feedback Molecular Dynamics Simulations in Proteins

With a known three dimensional structure, experimental vibrational spectra of proteins can be interpreted with the help of Normal Mode Analysis (NMA). In general normal modes computed at energy minimum using harmonic approximation are compared to an experimental spectrum in which the molecule is neither in the energy minimum nor in the limit of harmonic approximation. As a result NMA is not able to explain the coupling between the modes due to the anharmonicity of the potential. As an alternative to NMA we propose to use periodicity restraints during a molecular dynamics simulation which reinforce motions that occur in a specific period. These restraints couple the trajectory of a molecule to its own history. This allows to identify all (also non-linear) periodic motions that are in agreement with a given period and yields generalized vibrational modes. We implemented this type of feedback in GROMACS(4.5) and tested our method with a single amino-acid glycine and two small proteins Trp-cage (1L2Y) and chicken-villin (1QQV). If the given feedback matches the time scale of a generalized vibrational mode, the amplitude of the motion as well as the energy of the system increases and the analysis of such motions often clearly shows the presence of more than one normal mode in it. This knowledge about the time scales and the corresponding composition of normal modes would be helpful in vibrational spectroscopy to design a composite pulse to excite a specific generalized vibrational mode of a biomolecule.