Mode projected dynamics of globular and membrane proteins

In this work, we performed simulations of opsin as a model membrane protein and ovalbumin using CHARMM35b2 to understand the projected mode dynamics, which is useful to analyze intramolecular energy transfer in proteins. We projected the few selective low-frequency normal modes into the molecular dynamics trajectories of opsin in solvent and vacuum. The hydration effect of normal modes in proteins was evaluated.To calculate the projected mode dynamics, normal mode analysis was used to store each vibrational mode and its respective eigenvectors, L_i ^j (i = 1,2,3,....3N ), which represent a set of eigenvectors for the corresponding j^th normal mode (1 < j < 3N-6, i.e., apart from rigid rotations and translations). In general, the coupling of these normal modes is present during a molecular dynamics trajectory. Taking a suitable linear combination of these modes, we can generate a set of new modes. We then calculated the projections of the two MD trajectories in both vacuum and solvent of our model proteins onto the normal modes of the respective proteins. First, we determined the linear transformations of these modes into each velocity trajectory for which a new set of trajectories was generated based on the specific normal mode. These transformations were applied to each time step to obtain the trajectories R^s_vel ( n*?t) (solvated proteins) and R^v_vel (n*?t) (protein in vacuum) aligned to the normal modes, where n enumerates the time steps and R_vel is a 3N-dimensional vector encompassing the velocity of the N atoms in the protein. Moreover, the newly created velocity trajectories for the selective mode L_i^j are used to interpret the vibrational density of states projected onto the mode. Our comparison of the internal dynamics of solvated and non-solvated proteins has shown that the dynamic influence of the solvent is significant for the skeletal motions of the proteins. Using this method, we can calculate the boson frequency and its influence on the solvent at different cryogenic temperatures.