Rotamer libraries and probabilities of transition between rotamers for the side chains in protein-protein binding

Conformational changes in the side chains are essential for protein-protein binding. Rotameric states and unbound- to-bound conformational changes in the surface residues were systematically studied on a representative set of protein complexes. The side-chain conformations were mapped onto dihedral angles space. The variable threshold algorithm was developed to cluster the dihedral angle distributions and to derive rotamers, defined as the most probable conformation in a cluster. Six rotamer libraries were generated: full surface, surface noninterface, and surface interface-each for bound and unbound states. The libraries were used to calculate the probabilities of the rotamer transitions upon binding. The stability of amino acids was quantified based on the transition maps. The noninterface residues' stability was higher than that of the interface. Long side chains with three or four dihedral angles were less stable than the shorter ones. The transitions between the rotamers at the interface occurred more frequently than on the noninterface surface. Most side chains changed conformation within the same rotamer or moved to an adjacent rotamer. The highest percentage of the transitions was observed primarily between the two most occupied rotamers. The probability of the transition between rotamers increased with the decrease of the rotamer stability. The analysis revealed characteristics of the surface side-chain conformational transitions that can be utilized in flexible docking protocols.     

Side-chain conformational changes upon Protein-Protein Association

Conformational changes upon protein-protein association are the key element of the binding mechanism. The study presents a systematic large-scale analysis of such conformational changes in the side chains. The results indicate that short and long side chains have different propensities for the conformational changes. Long side chains with three or more dihedral angles are often subject to large conformational transition. Shorter residues with one or two dihedral angles typically undergo local conformational changes not leading to a conformational transition. A relationship between the local readjustments and the equilibrium fluctuations of a side chain around its unbound conformation is suggested. Most of the side chains undergo larger changes in the dihedral angle most distant from the backbone. The frequencies of the core-to-surface interface transitions of six nonpolar residues and Tyr are larger than the frequencies of the opposite surface-to-core transitions. The binding increases both polar and nonpolar interface areas. However, the increase of the nonpolar area is larger for all considered classes of protein complexes, suggesting that the protein association perturbs the unbound interfaces to increase the hydrophobic contribution to the binding free energy. To test modeling approaches to side-chain flexibility in protein docking, conformational changes in the X-ray set were compared with those in the docking decoy sets. The results lead to a better understanding of the conformational changes in proteins and suggest directions for efficient conformational sampling in docking protocols.     

How different are structurally flexible and rigid binding sites? Sequence and structural features discriminating proteins that do and do not undergo conformational change upon ligand binding

Proteins are dynamic molecules and often undergo conformational change upon ligand binding. It is widely accepted that flexible loop regions have a critical functional role in enzymes. Lack of consideration of binding site flexibility has led to failures in predicting protein functions and in successfully docking ligands with protein receptors. Here we address the question: which sequence and structural features distinguish the structurally flexible and rigid binding sites? We analyze high-resolution crystal structures of ligand bound (holo) and free (apo) forms of 41 proteins where no conformational change takes place upon ligand binding, 35 examples with moderate conformational change, and 22 cases where a large conformational change has been observed. We find that the number of residue-residue contacts observed per-residue (contact density) does not distinguish flexible and rigid binding sites, suggesting a role for specific interactions and amino acids in modulating the conformational changes. Examination of hydrogen bonding and hydrophobic interactions reveals that cases that do not undergo conformational change have high polar interactions constituting the binding pockets. Intriguingly, the large, aromatic amino acid tryptophan has a high propensity to occur at the binding sites of examples where a large conformational change has been noted. Further, in large conformational change examples, hydrophobic-hydrophobic, aromatic-aromatic, and hydrophobic-polar residue pair interactions are dominant. Further analysis of the Ramachandran dihedral angles (phi, psi) reveals that the residues adopting disallowed conformations are found in both rigid and flexible cases. More importantly, the binding site residues adopting disallowed conformations clustered narrowly into two specific regions of the L-Ala Ramachandran map. Examination of the dihedral angles changes upon ligand binding shows that the magnitude of phi, psi changes are in general minimal, although some large changes particularly between right-handed alpha-helical and extended conformations are seen. Our work further provides an account of conformational changes in the dihedral angles space. The findings reported here are expected to assist in providing a framework for predicting protein-ligand complexes and for template-based prediction of protein function.     

Rotamer strain energy in protein helices - quantification of a major force opposing protein folding

It is widely believed that the dominant force opposing protein folding is the entropic cost of restricting internal rotations. The energetic changes from restricting side-chain torsional motion are more complex than simply a loss of conformational entropy, however. A second force opposing protein folding arises when a side-chain in the folded state is not in its lowest-energy rotamer, giving rotameric strain. chi strain energy results from a dihedral angle being shifted from the most stable conformation of a rotamer when a protein folds. We calculated the energy of a side-chain as a function of its dihedral angles in a poly(Ala) helix. Using these energy profiles, we quantify conformational entropy, rotameric strain energy and chi strain energy for all 17 amino acid residues with side-chains in alpha-helices. We can calculate these terms for any amino acid in a helix interior in a protein, as a function of its side-chain dihedral angles, and have implemented this algorithm on a web page. The mean change in rotameric strain energy on folding is 0.42 kcal mol-1 per residue and the mean chi strain energy is 0.64 kcal mol-1 per residue. Loss of conformational entropy opposes folding by a mean of 1.1 kcal mol-1 per residue, and the mean total force opposing restricting a side-chain into a helix is 2.2 kcal mol-1. Conformational entropy estimates alone therefore greatly underestimate the forces opposing protein folding. The introduction of strain when a protein folds should not be neglected when attempting to quantify the balance of forces affecting protein stability. Consideration of rotameric strain energy may help the use of rotamer libraries in protein design and rationalise the effects of mutations where side-chain conformations change.     

Integrated prediction of one-dimensional structural features and their relationships with conformational flexibility in helical membrane proteins

Background  

Many structural properties such as solvent accessibility, dihedral angles and helix-helix contacts can be assigned to each residue in a membrane protein. Independent studies exist on the analysis and sequence-based prediction of some of these so-called one-dimensional features. However, there is little explanation of why certain residues are predicted in a wrong structural class or with large errors in the absolute values of these features. On the other hand, membrane proteins undergo conformational changes to allow transport as well as ligand binding. These conformational changes often occur via residues that are inherently flexible and hence, predicting fluctuations in residue positions is of great significance.     

Concordance of residual dipolar couplings, backbone order parameters and crystallographic B-factors for a small alpha/beta protein: a unified picture of high probability, fast atomic motions in proteins

Using ensemble refinement of the third immunoglobulin binding domain (GB3) of streptococcal protein G (a small alpha/beta protein of 56 residues), we demonstrate that backbone (N-H, N-C', Calpha-Halpha, Calpha-C') residual dipolar coupling data in five independent alignment media, generalized order parameters from 15N relaxation data, and B-factors from a high-resolution (1.1A), room temperature crystal structure are entirely consistent with one another within experimental error. The optimal ensemble size representation is between four and eight, as assessed by complete cross-validation of the residual dipolar couplings. Thus, in the case of GB3, all three observables reflect the same low-amplitude anisotropic motions arising from fluctuations in backbone phi/psi torsion angles in the picosecond to nanosecond regime in both solution and crystalline environments, yielding a unified picture of fast, high-probability atomic motions in proteins. An understanding of these motions is crucial for understanding the impact of protein dynamics on protein function, since they provide part of the driving force for triggered conformational changes that occur, for example, upon ligand binding, signal transduction and enzyme catalysis.     

Statistical and conformational analysis of the electron density of protein side chains

Protein side chains make most of the specific contacts between proteins and other molecules, and their conformational properties have been studied for many years. These properties have been analyzed primarily in the form of rotamer libraries, which cluster the observed conformations into groups and provide frequencies and average dihedral angles for these groups. In recent years, these libraries have improved with higher resolution structures and using various criteria such as high thermal factors to eliminate side chains that may be misplaced within the crystallographic model coordinates. Many of these side chains have highly non-rotameric dihedral angles. The origin of side chains with high B-factors and/or with non-rotameric dihedral angles is of interest in the determination of protein structures and in assessing the prediction of side chain conformations. In this paper, using a statistical analysis of the electron density of a large set of proteins, it is shown that: (1) most non-rotameric side chains have low electron density compared to rotameric side chains; (2) up to 15% of chi1 non-rotameric side chains in PDB models can clearly be fit to density at a single rotameric conformation and in some cases multiple rotameric conformations; (3) a further 47% of non-rotameric side chains have highly dispersed electron density, indicating potentially interconverting rotameric conformations; (4) the entropy of these side chains is close to that of side chains annotated as having more than one chi(1) rotamer in the crystallographic model; (5) many rotameric side chains with high entropy clearly show multiple conformations that are not annotated in the crystallographic model. These results indicate that modeling of side chains alternating between rotamers in the electron density is important and needs further improvement, both in structure determination and in structure prediction.     

Comparison of normal mode analyses on a small globular protein in dihedral angle space and Cartesian coordinate space

Normal mode analyses on the protein, bovine pancreatic trypsin inhibitor, in dihedral angle space and Cartesian coordinate space are compared. In Cartesian coordinate space it is found that modes of frequencies lower than 30 cm(-1) contribute 80% of the total mean-square fluctuation and are represented almost completely by motions in the dihedral angles. Bond angle and length fluctuations dominate in modes above 200 cm(-1), but contribute less than 2% to the total mean-square fluctuation. In the low-frequency modes a good correspondence between patterns of atomic displacements was found, but on average the root-mean-square fluctuations of the Cartesian coordinate modes are 13% greater than their dihedral angle counterparts. The main effect of fluctuations in the bond angles and lengths, therefore, is to allow the dihedral angles to become more flexible. As the important subspaces determined from the two methods overlap considerably, dihedral angle space analysis can be applied to proteins too large for Cartesian coordinate space analysis.     

The Dynameomics rotamer library: amino acid side chain conformations and dynamics from comprehensive molecular dynamics simulations in water

We have recently completed systematic molecular dynamics simulations of 807 different proteins representing 95% of the known autonomous protein folds in an effort we refer to as Dynameomics. Here we focus on the analysis of side chain conformations and dynamics to create a dynamic rotamer library. Overall this library is derived from 31,000 occurrences of each of 86,217 different residues, or 2.7 × 10(9) rotamers. This dynamic library has 74% overlap of rotamer distributions with rotamer libraries derived from static high-resolution crystal structures. Seventy-five percent of the residues had an assignable primary conformation, and 68% of the residues had at least one significant alternate conformation. The average correlation time for switching between rotamers ranged from 22 ps for Met to over 8 ns for Cys; this time decreased 20-fold on the surface of the protein and modestly for dihedral angles further from the main chain. Side chain S(2) axis order parameters were calculated and they correlated well with those derived from NMR relaxation experiments (R = 0.9). Relationships relating the S(2) axis order parameters to rotamer occupancy were derived. Overall the Dynameomics rotamer library offers a comprehensive depiction of side chain rotamer preferences and dynamics in solution, and more realistic distributions for dynamic proteins in solution at ambient temperature than libraries derived from crystal structures, in particular charged surface residues are better represented. Details of the rotamer library are presented here and the library itself can be downloaded at http://www.dynameomics.org.     

Altered dynamics upon oligomerization corresponds to key functional sites

It is known that over half of the proteins encoded by most organisms function as oligomeric complexes. Oligomerization confers structural stability and dynamics changes in proteins. We investigate the effects of oligomerization on protein dynamics and its functional significance for a set of 145 multimeric proteins. Using coarse‐grained elastic network models, we inspect the changes in residue fluctuations upon oligomerization and then compare with residue conservation scores to identify the functional significance of these changes. Our study reveals conservation of about ½ of the fluctuations, with ¼ of the residues increasing in their mobilities and ¼ having reduced fluctuations. The residues with dampened fluctuations are evolutionarily more conserved and can serve as orthosteric binding sites, indicating their importance. We also use triosephosphate isomerase as a test case to understand why certain enzymes function only in their oligomeric forms despite the monomer including all required catalytic residues. To this end, we compare the residue communities (groups of residues which are highly correlated in their fluctuations) in the monomeric and dimeric forms of the enzyme. We observe significant changes to the dynamical community architecture of the catalytic core of this enzyme. This relates to its functional mechanism and is seen only in the oligomeric form of the protein, answering why proteins are oligomeric structures. Proteins 2017; 85:1422–1434. © 2017 Wiley Periodicals, Inc.     

Proteins will Fold Anyway!!

Abstract

In order to investigate the environmental conditions of amino acid residues in protein molecules, four kinds of packing studies (atomic, geometric, hydrophobic and hydration) were formulated and tested on two proteins; bovine pancreatic trypsin inhibitor (BPTI) and bovine pancreatic ribonuclease S (RNase S). The inter-relationship of these packings on the fluctuations of amino acid residues was analysed by comparing the packing results with the dynamical studies, such as the root-mean-square-deviation values of atomic displacements obtained from the trajectories of molecular dynamics simulation, temperature factor information from crystal structures and residue fluctuations in proteins from continuum model. These analyses yield information about the most fluctuating and most stabilizing residue sites. Comparison of the results obtained by these methods indicate a good agreement, specifying an inverse correlation between the residue packing and fluctuations. This kind of study is helpful in identifying the specific residue sites such as nucleation, receptor binding and antigenic determining sites which in a way indirectly correlates with the functional residues in protein molecules.     

Local propensities and statistical potentials of backbone dihedral angles in proteins

The following three issues concerning the backbone dihedral angles of protein structures are presented. (1) How do the dihedral angles of the 20 amino acids depend on the identity and conformation of their nearest residues? (2) To what extent are the native dihedral angles determined by local (dihedral) potentials? (3) How to build a knowledge-based potential for a residue's dihedral angles, considering the identity and conformation of its nearest residues? We find that the dihedral angle distribution for a residue can significantly depend on the identity and conformation of its adjacent residues. These correlations are in sharp contrast to the Flory isolated-pair hypothesis. Statistical potentials are built for all combinations of residue triplets and depend on the dihedral angles between consecutive residues. First, a low-resolution potential is obtained, which only differentiates between the main populated basins in the dihedral angle density plots. Minimization of the dihedral potential for 125 test proteins reveals that most native alpha-helical residues (89%) and a large fraction of native beta-sheet residues (47%) adopt conformations close to their native one. For native loop residues, the percentage is 48%. It is also found that this fraction is higher for residues away from the ends of alpha or beta secondary structure elements. In addition, a higher resolution potential is built as a function of dihedral angles by a smoothing procedure and continuous functions interpolations. Monte Carlo energy minimization with this potential results in a lower fraction for native beta-sheet residues. Nevertheless, because of the higher flexibility and entropy of beta structures, they could be preferred under the influence of non-local interactions. In general, most alpha-helices and many beta-sheets are strongly determined by the local potential, while the conformations in loops and near the end of beta-sheets are more influenced by non-local interactions.     

Shape of the conformational energy surface near the global minimum and low-frequency vibrations in the native conformation of globular proteins

Based on the assumption that the conformational energy surface of a protein molecule can be approximated near the global minimum point by a multidimensional parabola, conformational fluctuations in the native state are discussed. In this approximation the conformational fluctuations can be viewed as excitations of coupled harmonic oscillations of dihedral angles. For the purpose of estimating the range of frequencies vibrations, globular proteins are assumed to made of homogeneous continuous elastic material. The number of vibrational modes in such an elastic body, with the wavelength no less than the characteristic length of an amino acid residue, are estimated roughly to be three times the number of amino acid residues in a protein, which is slightly less than the number of variable dihedral angles in a protein. Their frequencies, when converted to the wavenumber of corresponding light, are found to range from 1.8 × 10 cm^?1 to 2.1 × 10²cm^?1 for a protein with the diameter d = 40 Å, when Young's E = 10¹¹ dyne/cm² is assumed. A significant fraction of the coupled vibrations of dihedral angles in real globular proteins are collective ones, i.e., those involving the whole protein molecules. Based on these results, it concluded that the depth of the global minimum s at least 150 Kcal/mol.     

A smoothed backbone-dependent rotamer library for proteins derived from adaptive kernel density estimates and regressions

Rotamer libraries are used in protein structure determination, prediction, and design. The backbone-dependent rotamer library consists of rotamer frequencies, mean dihedral angles, and variances as?a function of the backbone dihedral angles. Structure prediction and design methods that employ backbone flexibility would strongly benefit from smoothly varying probabilities and angles. A new version of the?backbone-dependent rotamer library has been developed using adaptive kernel density estimates for the rotamer frequencies and adaptive kernel regression for the mean dihedral angles and variances. This formulation allows for evaluation of the rotamer probabilities, mean angles, and variances as?a smooth and continuous function of phi and psi. Continuous probability density estimates for the nonrotameric degrees of freedom of amides, carboxylates, and aromatic side chains have been modeled as a function of the backbone dihedrals and rotamers of the remaining degrees of freedom. New backbone-dependent rotamer libraries at varying levels of smoothing are available from http://dunbrack.fccc.edu.     

Studying backbone torsional dynamics of intrinsically disordered proteins using fluorescence depolarization kinetics

Intrinsically disordered proteins (IDPs) do not autonomously adopt a stable unique 3D structure and exist as an ensemble of rapidly interconverting structures. They are characterized by significant conformational plasticity and are associated with several biological functions and dysfunctions. The rapid conformational fluctuation is governed by the backbone segmental dynamics arising due to the dihedral angle fluctuation on the Ramachandran ?–ψ conformational space. We discovered that the intrinsic backbone torsional mobility can be monitored by a sensitive fluorescence readout, namely fluorescence depolarization kinetics, of tryptophan in an archetypal IDP such as α-synuclein. This methodology allows us to map the site-specific torsional mobility in the dihedral space within picosecond-nanosecond time range at a low protein concentration under the native condition. The characteristic timescale of ~?1.4 ns, independent of residue position, represents collective torsional dynamics of dihedral angles (? and ψ) of several residues from tryptophan and is independent of overall global tumbling of the protein. We believe that fluorescence depolarization kinetics methodology will find broad application to study both short-range and long-range correlated motions, internal friction, binding-induced folding, disorder-to-order transition, misfolding and aggregation of IDPs.     

The interplay between transient α-helix formation and side chain rotamer distributions in disordered proteins probed by methyl chemical shifts

The peptide backbones of disordered proteins are routinely characterized by NMR with respect to transient structure and dynamics. Little experimental information is, however, available about the side chain conformations and how structure in the backbone affects the side chains. Methyl chemical shifts can in principle report the conformations of aliphatic side chains in disordered proteins and in order to examine this two model systems were chosen: the acid denatured state of acyl-CoA binding protein (ACBP) and the intrinsically disordered activation domain of the activator for thyroid hormone and retinoid receptors (ACTR). We find that small differences in the methyl carbon chemical shifts due to the γ-gauche effect may provide information about the side chain rotamer distributions. However, the effects of neighboring residues on the methyl group chemical shifts obscure the direct observation of γ-gauche effect. To overcome this, we reference the chemical shifts to those in a more disordered state resulting in residue specific random coil chemical shifts. The (13)C secondary chemical shifts of the methyl groups of valine, leucine, and isoleucine show sequence specific effects, which allow a quantitative analysis of the ensemble of χ(2)-angles of especially leucine residues in disordered proteins. The changes in the rotamer distributions upon denaturation correlate to the changes upon helix induction by the co-solvent trifluoroethanol, suggesting that the side chain conformers are directly or indirectly related to formation of transient α-helices.     

A machine learning approach for the prediction of protein surface loop flexibility

Proteins often undergo conformational changes when binding to each other. A major fraction of backbone conformational changes involves motion on the protein surface, particularly in loops. Accounting for the motion of protein surface loops represents a challenge for protein-protein docking algorithms. A first step in addressing this challenge is to distinguish protein surface loops that are likely to undergo backbone conformational changes upon protein-protein binding (mobile loops) from those that are not (stationary loops). In this study, we developed a machine learning strategy based on support vector machines (SVMs). Our SVM uses three features of loop residues in the unbound protein structures-Ramachandran angles, crystallographic B-factors, and relative accessible surface area-to distinguish mobile loops from stationary ones. This method yields an average prediction accuracy of 75.3% compared with a random prediction accuracy of 50%, and an average of 0.79 area under the receiver operating characteristic (ROC) curve using cross-validation. Testing the method on an independent dataset, we obtained a prediction accuracy of 70.5%. Finally, we applied the method to 11 complexes that involve members from the Ras superfamily and achieved prediction accuracy of 92.8% for the Ras superfamily proteins and 74.4% for their binding partners.     

Coordination topology and stability for the native and binding conformers of chymotrypsin inhibitor 2

We demonstrate that the stabilization of the binding region is accomplished at the expense of a loss in the stability of the rest of the protein. A novel molecular mechanics (MM) approach is introduced to distinguish residue stabilities of proteins in a given conformation. As an example, the relative stabilities of folded chymotrypsin inhibitor 2 (CI2) in unbound form, and CI2 in complex with subtilisin novo is investigated. The conformation of the molecule in the two states is almost identical, with an approximately 0.6-A root-mean-square deviation (RMSD) of the Calpha atoms. On binding, the packing density changes only at the binding loop. However, residue fluctuations in the rest of the protein are greatly altered solely due to those contacts, indicating the effective propagation of perturbation and the presence of remotely controlling residues. To quantify the interplay between packing density, packing order, residue fluctuations, and residue stability, we adopt an MM approach whereby small displacements are inserted at selected residues, followed by energy minimization; the displacement of each residue in response to such perturbations are organized in a perturbation-response matrix L. We define residue stability lambda(i) = summation operator((j)L(ij))/ summation operator((j) L(ji)) as the ratio of the amount of change to which the residue is amenable, to the ability of a given residue to induce change. We then define the free energy associated with residue stability, DeltaG(lambda) = -RT ln lambda. DeltaG(lambda) intrinsically selects the residues that are in the folding core. Upon complexation, the binding loop becomes more resistant to perturbation, in contrast to the alpha-helix that favors change. Although the two forms of CI2 are structurally similar, residue fluctuations differ vastly, and the stability of many residues is altered upon binding. The decrease in entropy introduced by binding is thus compensated by these changes.     

Rotamer Dynamics: Analysis of Rotamers in Molecular Dynamics Simulations of Proteins

Given by χ torsional angles, rotamers describe the side-chain conformations of amino acid residues in a protein based on the rotational isomers (hence the word rotamer). Constructed rotamer libraries, based on either protein crystal structures or dynamics studies, are the tools for classifying rotamers (torsional angles) in a way that reflect their frequency in nature. Rotamer libraries are routinely used in structure modeling and evaluation. In this perspective article, we would like to encourage researchers to apply rotamer analyses beyond their traditional use. Molecular dynamics (MD) of proteins highlight the in silico behavior of molecules in solution and thus can identify favorable side-chain conformations. In this article, we used simple computational tools to study rotamer dynamics (RD) in MD simulations. First, we isolated each frame in the MD trajectories in separate Protein Data Bank files via the cpptraj module in AMBER. Then, we extracted torsional angles via the Bio3D module in R language. The classification of torsional angles was also done in R according to the penultimate rotamer library. RD analysis is useful for various applications such as protein folding, study of rotamer-rotamer relationship in protein-protein interaction, real-time correlation between secondary structures and rotamers, study of flexibility of side chains in binding site for molecular docking preparations, use of RD as guide in functional analysis and study of structural changes caused by mutations, providing parameters for improving coarse-grained MD accuracy and speed, and many others. Major challenges facing RD to emerge as a new scientific field involve the validation of results via easy, inexpensive wet-lab methods. This realm is yet to be explored.     

A-site residues move independently from P-site residues in all-atom molecular dynamics simulations of the 70S bacterial ribosome

The ribosome is a large macromolecular machine, and correlated motion between residues is necessary for coordinating function across multiple protein and RNA chains. We ran two all-atom, explicit solvent molecular dynamics simulations of the bacterial ribosome and calculated correlated motion between residue pairs by using mutual information. Because of the short timescales of our simulation (ns), we expect that dynamics are largely local fluctuations around the crystal structure. We hypothesize that residues that show coupled dynamics are functionally related, even on longer timescales. We validate our model by showing that crystallographic B-factors correlate well with the entropy calculated as part of our mutual information calculations. We reveal that A-site residues move relatively independently from P-site residues, effectively insulating A-site functions from P-site functions during translation.