Hidden Regularity and Universal Classification of Fast Side Chain Motions in Proteins Rajitha Rajeshwar T., † Jeremy C. Smith, ‡,§ and Marimuthu Krishnan* ,† † Center for Computational Natural Sciences and Bioinformatics, International Institute of Information Technology, Gachibowli, Hyderabad 500 032, India ‡ UT/ORNL Center for Molecular Biophysics, Oak Ridge National Laboratory, P.O. Box 2008 Oak Ridge, Tennessee 37831-6309, United States § Department of Biochemistry and Molecular and Cellular Biology, University of Tennessee, M407 Walters Life Sciences, 1414 Cumberland Avenue, Knoxville, Tennessee 37996, United States * S Supporting Information ABSTRACT: Proteins display characteristic dynamical signatures that appear to be universal across all proteins regardless of topology and size. Here, we systematically characterize the universal features of fast side chain motions in proteins by examining the conformational energy surfaces of individual residues obtained using enhanced sampling molecular dynamics simulation (618 free energy surfaces obtained from 0.94 μs MD simulation). The side chain conformational free energy surfaces obtained using the adaptive biasing force (ABF) method for a set of eight proteins with different molecular weights and secondary structures are used to determine the methyl axial NMR order parameters (O axis 2 ), populations of side chain rotamer states (ρ), conformational entropies (S conf ), probability fluxes, and activation energies for side chain inter- rotameric transitions. The free energy barriers separating side chain rotamer states range from 0.3 to 12 kcal/mol in all proteins and follow a trimodal distribution with an intense peak at ∼5 kcal/mol and two shoulders at ∼3 and ∼7.5 kcal/mol, indicating that some barriers are more favored than others by proteins to maintain a balance between their conformational stability and flexibility. The origin and the influences of the trimodal barrier distribution on the distribution of O axis 2 and the side chain conformational entropy are discussed. A hierarchical grading of rotamer states based on the conformational free energy barriers, entropy, and probability flux reveals three distinct classes of side chains in proteins. A unique nonlinear correlation is established between O axis 2 and the side chain rotamer populations (ρ). The apparent universality in O axis 2 versus ρ correlation, trimodal barrier distribution, and distinct characteristics of three classes of side chains observed among all proteins indicates a hidden regularity (or commonality) in the dynamical heterogeneity of fast side chain motions in proteins. ■ INTRODUCTION The startling diversity in the structure and dynamics of proteins illustrates the complexity and richness of protein-mediated biological processes and also demands a molecular-level understanding of the fundamental principles underpinning these processes. 1-5 The notion that structure and dynamics are governed by the underlying energy surface underscores the intricate connection between heterogeneity in functional dynamical processes and the hierarchical conformational substates of proteins. 6-10 The interactions within proteins and with surrounding species (such as other proteins, solvent molecules, and counterions) give rise to a complex energy landscape resulting in a wide spectrum of dynamics, ranging from localized atomic vibrations to large-scale collective conformational transitions. 2,7,11,12 The high-frequency harmon- ic motions do not alter the equilibrium structure of the protein, while significant structural changes occur during conforma- tional transitions. These anharmonic, barrier-crossing motions enable the protein to visit different regions of the conforma- tional space and thus play critical roles in protein function. 6,7,9-11,13-15 Conformational transitions in proteins occur at various length- (domain- to side chain-level) and time- scales (fast (ps-ns) to slow (μs-ms)). 1,8,16,17 Many research efforts directed toward understanding the functional roles of internal motions primarily rely on experimental techniques that probed the average dynamics (i.e., dynamics averaged over all residues or probes) of proteins. For instance, fluorescence spectroscopy measures the average lifetime or relaxation rate of different fluorophores in a protein, 18-20 neutron scattering experiments determine the average mean-square displacement of the nonexchangeable protein hydrogen atoms, 2,21,22 and infrared (IR) and Raman spectroscopies probe the overall vibrational modes of different functional groups in proteins. 23,24 Although these experimental techniques are non-site-specific, they play critical roles in Received: August 29, 2013 Published: May 20, 2014 Article pubs.acs.org/JACS © 2014 American Chemical Society 8590 dx.doi.org/10.1021/ja5024783 | J. Am. Chem. Soc. 2014, 136, 8590-8605