Diffusive and activated contributions in protein dynamics.
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A novel approach is developed to describe the dynamics of proteins, the coarse-grained Langevin Equation for Protein Dynamics (LE4PD). The approach describes proteins as fundamentally semiflexible objects collapsed into the free energy well representing the folded state. This is a multi-scale approach, where structural correlations are used as input to an effectively linear description, which can be solved in diffusive modes. The mode solution to this Langevin equation naturally separates into global modes describing the fully anisotropic tumbling of the macromolecule as a whole, and internal modes which describe local fluctuations about the folded structure. A protein in solution populates a structural ensemble of metastable configurations around the global fold, and we propose a simulation-free coarse-grained approach which utilizes knowledge of the important metastable folded states of the protein to predict the protein dynamics. The accuracy of the LE4PD is verified by analyzing the predicted dynamics across a set of seven different proteins for which both relaxation data and NMR solution structures are available. Using experimental NMR conformers as the input structural ensembles, LE4PD predicts quantitatively accurate results, with correlation coefficient $\rho=.93$ to NMR backbone relaxation measurements for the seven proteins. The NMR solution structure derived ensemble and predicted dynamical relaxation is compared with molecular dynamics simulation-derived structural ensembles and LE4PD predictions, and are consistent in the timescale of the simulations. The use of the experimental NMR conformers frees the approach from computationally demanding simulations. The biological function of proteins is encoded in their structure and expressed through the mediation of their dynamics. We present here a study of how local fluctuation relates to binding and function. This study indicates how local fluctuations are likely to initiate biologically relevant pathways as they cooperatively enhance the dynamics in specific spatial regions of the protein. The picture that emerges is a dynamically heterogenous protein where biologically active regions provide energetically-comparable conformational states that can be trapped by a reacting partner. The slowest, most collective motion localizes directly to highly conserved regions involved in binding partner recognition and active-site regulation. We analyze this possible relation between dynamics and binding mechanism as we calculate the dynamics of monomeric and dimerized HIV protease, free Insulin Growth Factor II Receptor (IGF2R) domain 11 and its IGF2R:IGF2 complex. The long-time dynamics of proteins is controlled by an activated regime where the dynamics of the large amplitude diffusive modes becomes dominated by the presence of energy barriers. We explicitly study the atomistic simulation-derived free energy landscape projected from the diffusive modes of the linear Langevin description of the protein, and obtain a general scaling between the fluctuation lengthscale and complexity. This hierarchical property of the free energy landscape of proteins is shown to be general across a set of six different single-domain monomeric proteins. As a consequence microscopic timescales of sub-angstrom sized fluctuations rapidly propagate out to folding timescales at the nanometer lengthscale of globular single-domain proteins. This glassy activated regime extending from the nanosecond timescale we propose to be set by cooperative rearrangements of the protein-water and protein-protein hydrogen-bonding network. This results in metastable protein configurations with large changes in the protein-solvent hydrogen-bonding network coupled to subtle changes in the protein-protein hydrogen-bonding network. The Langevin formalism predictions are shown to agree with molecular dynamic simulations from the picosecond out to the millisecond timescale.