Boltzmann-type distribution of side-chain conformation in proteins

Dry molten globule conformational state of CYP11A1 (SCC) regulates the first step of steroidogenesis in the mitochondrial matrix

Multiple metabolic events occur in mitochondria. Mitochondrial protein translocation from the cytoplasm across compartments depends on the amino acid sequence within the precursor. At the mitochondria associated-ER membrane, misfolding of a mitochondrial targeted protein prior to import ablates metabolism. CYP11A1, cytochrome P450 cholesterol side chain cleavage enzyme (SCC), is imported from the cytoplasm to mitochondrial matrix catalyzing cholesterol to pregnenolone, an essential step for metabolic processes and mammalian survival. Multiple steps regulate the availability of an actively folded SCC; however, the mechanism is unknown. We identified that a dry molten globule state of SCC exists in the matrix by capturing intermediate protein folding steps dictated by its C-terminus. The intermediate dry molten globule state in the mitochondrial matrix of living cells is stable with a limited network of interaction and is inactive. The dry molten globule is activated with hydrogen ions availability, triggering cleavage of cholesterol sidechain, and initiating steroidogenesis.

Mapping protein dynamics at high spatial resolution with temperature-jump X-ray crystallography

Understanding and controlling protein motion at atomic resolution is a hallmark challenge for structural biologists and protein engineers because conformational dynamics are essential for complex functions such as enzyme catalysis and allosteric regulation. Time-resolved crystallography offers a window into protein motions, yet without a universal perturbation to initiate conformational changes the method has been limited in scope. Here we couple a solvent-based temperature jump with time-resolved crystallography to visualize structural motions in lysozyme, a dynamic enzyme. We observed widespread atomic vibrations on the nanosecond timescale, which evolve on the submillisecond timescale into localized structural fluctuations that are coupled to the active site. An orthogonal perturbation to the enzyme, inhibitor binding, altered these dynamics by blocking key motions that allow energy to dissipate from vibrations into functional movements linked to the catalytic cycle. Because temperature jump is a universal method for perturbing molecular motion, the method demonstrated here is broadly applicable for studying protein dynamics.

Side chain flexibility and the symmetry of protein homodimers

A comprehensive analysis of crystallographic data of 565 high-resolution protein homodimers comprised of over 250,000 residues suggests that amino acids form two groups that differ in their tendency to distort or symmetrize the structure of protein homodimers. Residues of the first group tend to distort the protein homodimer and generally have long or polar side chains. These include: Lys, Gln, Glu, Arg, Asn, Met, Ser, Thr and Asp. Residues of the second group contribute to protein symmetry and are generally characterized by short or aromatic side chains. These include: Ile, Pro, His, Val, Cys, Leu, Trp, Tyr, Phe, Ala and Gly. The distributions of the continuous symmetry measures of the proteins and the continuous chirality measures of their building blocks highlight the role of side chain geometry and the interplay between entropy and symmetry in dictating the conformational flexibility of proteins.

77Se NMR Probes the Protein Environment of Selenomethionine

Sulfur is critical for the correct structure and proper function of proteins. Yet, lacking a sensitive enough isotope, nuclear magnetic resonance (NMR) experiments are unable to deliver for sulfur in proteins the usual wealth of chemical, dynamic, and structural information. This limitation can be circumvented by substituting sulfur with selenium, which has similar physicochemical properties and minimal impact on protein structures but possesses an NMR compatible isotope (⁷⁷Se). Here we exploit the sensitivity of ⁷⁷Se NMR to the nucleus' chemical milieu and use selenomethionine as a probe for its proteinaceous environment. However, such selenium NMR spectra of proteins currently resist a reliable interpretation because systematic connections between variations of system variables and changes in ⁷⁷Se NMR parameters are still lacking. To start narrowing this knowledge gap, we report here on a biological ⁷⁷Se magnetic resonance data bank based on a systematically designed library of GB1 variants in which a single selenomethionine was introduced at different locations within the protein. We recorded the resulting isotropic ⁷⁷Se chemical shifts and relaxation times for six GB1 variants by solution-state ⁷⁷Se NMR. For four of the GB1 variants we were also able to determine the chemical shift anisotropy tensor of SeM by solid-state ⁷⁷Se NMR. To enable interpretation of the NMR data, the structures of five of the GB1 variants were solved by X-ray crystallography to a resolution of 1.2 Å, allowing us to unambiguously determine the conformation of the selenomethionine. Finally, we combine our solution- and solid-state NMR data with the structural information to arrive at general insights regarding the execution and interpretation of ⁷⁷Se NMR experiments that exploit selenomethionine to probe proteins.

The Too Many Faces of PD-L1: A Comprehensive Conformational Analysis Study

In the current study, we focused on the immune-checkpoints PD-1 pathway and in particular on the ligand PD-L1. We studied the conformational dynamics of PD-L1 through principal component analysis of existing crystal structures combined with classical and accelerated molecular dynamics simulations. We identified the maximum structural displacements that take place in all PD-L1 crystal structures and in the molecular dynamics trajectories. We found that these displacements are attributed to specific flexible regions in the protein. We also investigated the conformational preference for small molecule binding and highlighted a methionine residue at the binding site, which plays a key role in drug binding. The binding mechanism of PD-L1 to other binding partners is also discussed in detail from a computational perspective. We hope that the data presented here support the ongoing efforts to discover effective therapies targeting the PD-1 immune-checkpoint pathway.

RNA folding pathways in stop motion

We introduce a method for predicting RNA folding pathways, with an application to the most important RNA tetraloops. The method is based on the idea that ensembles of three-dimensional fragments extracted from high-resolution crystal structures are heterogeneous enough to describe metastable as well as intermediate states. These ensembles are first validated by performing a quantitative comparison against available solution nuclear magnetic resonance (NMR) data of a set of RNA tetranucleotides. Notably, the agreement is better with respect to the one obtained by comparing NMR with extensive all-atom molecular dynamics simulations. We then propose a procedure based on diffusion maps and Markov models that makes it possible to obtain reaction pathways and their relative probabilities from fragment ensembles. This approach is applied to study the helix-to-loop folding pathway of all the tetraloops from the GNRA and UNCG families. The results give detailed insights into the folding mechanism that are compatible with available experimental data and clarify the role of intermediate states observed in previous simulation studies. The method is computationally inexpensive and can be used to study arbitrary conformational transitions.

Molprobity's ultimate rotamer-library distributions for model validation

Here we describe the updated MolProbity rotamer-library distributions derived from an order-of-magnitude larger and more stringently quality-filtered dataset of about 8000 (vs. 500) protein chains, and we explain the resulting changes and improvements to model validation as seen by users. To include only side-chains with satisfactory justification for their given conformation, we added residue-specific filters for electron-density value and model-to-density fit. The combined new protocol retains a million residues of data, while cleaning up false-positive noise in the multi- χ datapoint distributions. It enables unambiguous characterization of conformational clusters nearly 1000-fold less frequent than the most common ones. We describe examples of local interactions that favor these rare conformations, including the role of authentic covalent bond-angle deviations in enabling presumably strained side-chain conformations. Further, along with favored and outlier, an allowed category (0.3-2.0% occurrence in reference data) has been added, analogous to Ramachandran validation categories. The new rotamer distributions are used for current rotamer validation in MolProbity and PHENIX, and for rotamer choice in PHENIX model-building and refinement. The multi-dimensional χ distributions and Top8000 reference dataset are freely available on GitHub. These rotamers are termed "ultimate" because data sampling and quality are now fully adequate for this task, and also because we believe the future of conformational validation should integrate side-chain with backbone criteria. Proteins 2016; 84:1177-1189. © 2016 Wiley Periodicals, Inc.

Empirical Corrections to the Amber RNA Force Field with Target Metadynamics

The computational study of conformational transitions in nucleic acids still faces many challenges. For example, in the case of single stranded RNA tetranucleotides, agreement between simulations and experiments is not satisfactory due to inaccuracies in the force fields commonly used in molecular dynamics simulations. We here use experimental data collected from high-resolution X-ray structures to attempt an improvement of the latest version of the AMBER force field. A modified metadynamics algorithm is used to calculate correcting potentials designed to enforce experimental distributions of backbone torsion angles. Replica-exchange simulations of tetranucleotides including these correcting potentials show significantly better agreement with independent solution experiments for the oligonucleotides containing pyrimidine bases. Although the proposed corrections do not seem to be portable to generic RNA systems, the simulations revealed the importance of the α and ζ backbone angles for the modulation of the RNA conformational ensemble. The correction protocol presented here suggests a systematic procedure for force-field refinement.

Aromatic cluster mutations produce focal modulations of β-sheet structure

Site-directed mutagenesis is a powerful tool for altering the structure and function of proteins in a focused manner. Here, we examined how a model β-sheet protein could be tuned by mutation of numerous surface-exposed residues to aromatic amino acids. We designed these aromatic side chain "clusters" at highly solvent-exposed positions in the flat, single-layer β-sheet of Borrelia outer surface protein A (OspA). This unusual β-sheet scaffold allows us to interrogate the effects of these mutations in the context of well-defined structure but in the absence of the strong scaffolding effects of globular protein architecture. We anticipated that the introduction of a cluster of aromatic amino acid residues on the β-sheet surface would result in large conformational changes and/or stabilization and thereby provide new means of controlling the properties of β-sheets. Surprisingly, X-ray crystal structures revealed that the introduction of aromatic clusters produced only subtle conformational changes in the OspA β-sheet. Additionally, despite burying a large degree of hydrophobic surface area, the aromatic cluster mutants were slightly less stable than the wild-type scaffold. These results thereby demonstrate that the introduction of aromatic cluster mutations can serve as a means for subtly modulating β-sheet conformation in protein design.

Perspective: Coarse-grained models for biomolecular systems

By focusing on essential features, while averaging over less important details, coarse-grained (CG) models provide significant computational and conceptual advantages with respect to more detailed models. Consequently, despite dramatic advances in computational methodologies and resources, CG models enjoy surging popularity and are becoming increasingly equal partners to atomically detailed models. This perspective surveys the rapidly developing landscape of CG models for biomolecular systems. In particular, this review seeks to provide a balanced, coherent, and unified presentation of several distinct approaches for developing CG models, including top-down, network-based, native-centric, knowledge-based, and bottom-up modeling strategies. The review summarizes their basic philosophies, theoretical foundations, typical applications, and recent developments. Additionally, the review identifies fundamental inter-relationships among the diverse approaches and discusses outstanding challenges in the field. When carefully applied and assessed, current CG models provide highly efficient means for investigating the biological consequences of basic physicochemical principles. Moreover, rigorous bottom-up approaches hold great promise for further improving the accuracy and scope of CG models for biomolecular systems.

Implications of aberrant temperature-sensitive glucose transport via the glucose transporter deficiency mutant (GLUT1DS) T295M for the alternate-access and fixed-site transport models

In silico glucose docking to the transporter GLUT1 templated to the crystal structure of Escherichia coli XylE, a bacterial homolog of GLUT1-4 (4GBZ.pdb), reveals multiple docking sites. One site in the external vestibule in the exofacial linker between TM7 and -8 is adjacent to a missense T295M and a 4-mer insertion mutation. Glucose docking to the adjacent site is occluded in these mutants. These mutants cause an atypical form of glucose transport deficiency syndrome (GLUT1DS), where transport into the brain is deficient, although unusually transport into erythrocytes at 4 °C appears normal. A model in which glucose traverses the transporter via a network of saturable fixed sites simulates the temperature sensitivity of normal and mutant glucose influx and the mutation-dependent alterations of influx and efflux asymmetry when expressed in Xenopus oocytes at 37 °C. The explanation for the temperature sensitivity is that at 4 °C glucose influx between the external and internal vestibules is slow and causes glucose to accumulate in the external vestibule. This retards net glucose uptake from the external solution via two parallel sites into the external vestibule, consequently masking any transport defect at either one of these sites. At 37 °C glucose transit between the external and internal vestibules is rapid, with no significant glucose buildup in the external vestibule, and thereby unmasks any transport defect at one of the parallel input sites. Monitoring glucose transport in patients' erythrocytes at higher temperatures may improve the diagnostic accuracy of the functional test of GLUT1DS.

Intrinsic energy landscapes of amino acid side-chains

Amino acid side-chain conformational properties influence the overall structural and dynamic properties of proteins and, therefore, their biological functions. In this study, quantum mechanical (QM) potential energy surfaces for the rotation of side-chain χ(1) and χ(2) torsions in dipeptides in the alphaR, beta, and alphaL backbone conformations were calculated. The QM energy surfaces provide a broad view of the intrinsic conformational properties of each amino acid side-chain. The extent to which intrinsic energetics dictates side-chain orientation was studied through comparisons of the QM energy surfaces with χ(1) and χ(2) free energy surfaces from probability distributions obtained from a survey of high resolution crystal structures. In general, the survey probability maxima are centered in minima of the QM surfaces as expected for sp(3) (or sp(2) for χ(2) of Asn, Phe, Trp, and Tyr) atom centers with strong variations between amino acids occurring in the energies of the minima indicating intrinsic differences in rotamer preferences. High correlations between the QM and survey data were found for hydrophobic side-chains except Met, suggesting minimal influence of the protein and solution environments on their conformational distributions. Conversely, low correlations for polar or charged side-chains indicate a dominant role of the environment in stabilizing conformations that are not intrinsically favored. Data also link the presence of off-rotamers in His and Trp to favorable interactions with the backbone. Results also suggest that the intrinsic energetics of the side-chains of Phe and Tyr may play important roles in protein folding and stability. Analyses on whether intrinsic side-chain energetics can influence backbone preference identified a strong correlation for residues in the alphaL backbone conformation. It is suggested that this correlation reflects the intrinsic instability of the alphaL backbone such that assumption of this backbone conformation is facilitated by intrinsically favorable side-chain conformations. Together our results offer a broad overview of the conformational properties of amino acid side-chains and the QM data may be used as target data for force field optimization.

Insights into intramolecular Trp and His side-chain orientation and stereospecific π interactions surrounding metal centers: an investigation using protein metal-site mimicry in solution

Metal-binding scaffolds incorporating a Trp/His-paired epitope are instrumental in giving novel insights into the physicochemical basis of functional and mechanistic versatility conferred by the Trp-His interplay at a metal site. Herein, by coupling biometal site mimicry and (1)H and (13)C NMR spectroscopy experiments, modular constructs EDTA-(L-Trp, L-His) (EWH; EDTA=ethylenediamino tetraacetic acid) and DTPA-(L-Trp, L-His) (DWH; DTPA=diethylenetriamino pentaacetic acid) were employed to dissect the static and transient physicochemical properties of hydrophobic/hydrophilic aromatic interactive modes surrounding biometal centers. The binding feature and identities of the stoichiometric metal-bound complexes in solution were investigated by using (1)H and (13)C NMR spectroscopy, which facilitated a cross-validation of the carboxylate, amide oxygen, and tertiary amino groups as the primary ligands and indole as the secondary ligand, with the imidazole (Im) N3 nitrogen being weakly bound to metals such as Ca(2+) owing to a multivalency effect. Surrounding the metal centers, the stereospecific orientation of aromatic rings in the diastereoisomerism is interpreted with the Ca(2+)-EWH complex. With respect to perturbed Trp side-chain rotamer heterogeneity, drastically restricted Trp side-chain flexibility and thus a dynamically constrained rotamer interconversion due to π interactions is evident from the site-selective (13)C NMR spectroscopic signal broadening of the Trp indolyl C3 atom. Furthermore, effects of Trp side-chain fluctuation on indole/Im orientation were the subject of a 2D NMR spectroscopy study by using the Ca(2+)-bound state; a C-H2(indolyl)/C-H5(Im(+)) connectivity observed in the NOESY spectra captured direct evidence that the N-H1 of the Ca(2+)-Im(+) unit interacted with the pyrrole ring of the indole unit in Ca(2+)-bound EWH but not in DWH, which is assignable to a moderately static, anomalous, T-shaped, interplanar π(+)-π stacking alignment. Nevertheless, a comparative (13)C NMR spectroscopy study of the two homologous scaffolds revealed that the overall response of the indole unit arises predominantly from global attractions between the indole ring and the entire positively charged first coordination sphere. The study thus demonstrates the coordination-sphere/geometry dependence of the Trp/His side-chain interplay, and established that π interactions allow (13)C NMR spectroscopy to offer a new window for investigating Trp rotamer heterogeneity near metal-binding centers.

3D models of lamprey progesterone receptor complexed with progesterone, 7α-hydroxy-progesterone and 15α-hydroxy-progesterone

Sea lamprey, a basal vertebrate, contains a progesterone receptor [PR]. An unusual property of lamprey is that gonadotropin-releasing hormone induces synthesis of 15α-hydroxy-progesterone [15α-OH-P] instead of progesterone. There also is indirect evidence for 7α-OH-P in lamprey serum. To determine if there is a structural basis for the binding of 7α-OH-P and 15α-OH-P to lamprey PR, we constructed 3D models of the lamprey PR complexed with progesterone, 7α-OH-P and 15α-OH-P. These 3D models reveal that Met-277 in lamprey PR has a specific interaction with the 15α-hydroxyl on 15α-OH-P and with Met-192, which also contacts the 15α-hydroxyl group. We also find that 7α-OH-P has favorable contacts with side-chains in lamprey PR. BLAST searches reveal that Met-277 on lamprey PR is unique among vertebrate PRs. This unique site on lamprey PR could be a target for compounds to control reproduction in sea lamprey, an environmental pest in Lake Michigan.

Recovering physical potentials from a model protein databank

Knowledge-based approaches frequently employ empirical relations to determine effective potentials for coarse-grained protein models directly from protein databank structures. Although these approaches have enjoyed considerable success and widespread popularity in computational protein science, their fundamental basis has been widely questioned. It is well established that conventional knowledge-based approaches do not correctly treat many-body correlations between amino acids. Moreover, the physical significance of potentials determined by using structural statistics from different proteins has remained obscure. In the present work, we address both of these concerns by introducing and demonstrating a theory for calculating transferable potentials directly from a databank of protein structures. This approach assumes that the databank structures correspond to representative configurations sampled from equilibrium solution ensembles for different proteins. Given this assumption, this physics-based theory exactly treats many-body structural correlations and directly determines the transferable potentials that provide a variationally optimized approximation to the free energy landscape for each protein. We illustrate this approach by first constructing a databank of protein structures using a model potential and then quantitatively recovering this potential from the structure databank. The proposed framework will clarify the assumptions and physical significance of knowledge-based potentials, allow for their systematic improvement, and provide new insight into many-body correlations and cooperativity in folded proteins.

Conformational dependence of 13C shielding and coupling constants for methionine methyl groups

Methionine residues fulfill a broad range of roles in protein function related to conformational plasticity, ligand binding, and sensing/mediating the effects of oxidative stress. A high degree of internal mobility, intrinsic detection sensitivity of the methyl group, and low copy number have made methionine labeling a popular approach for NMR investigation of selectively labeled protein macromolecules. However, selective labeling approaches are subject to more limited information content. In order to optimize the information available from such studies, we have performed DFT calculations on model systems to evaluate the conformational dependence of (3)J (CSCC), (3)J (CSCH), and the isotropic shielding, sigma(iso). Results have been compared with experimental data reported in the literature, as well as data obtained on [methyl-(13)C]methionine and on model compounds. These studies indicate that relative to oxygen, the presence of the sulfur atom in the coupling pathway results in a significantly smaller coupling constant, (3)J (CSCC)/(3)J (COCC) approximately 0.7. It is further demonstrated that the (3)J (CSCH) coupling constant depends primarily on the subtended CSCH dihedral angle, and secondarily on the CSCC dihedral angle. Comparison of theoretical shielding calculations with the experimental shift range of the methyl group for methionine residues in proteins supports the conclusion that the intra-residue conformationally-dependent shift perturbation is the dominant determinant of delta(13)Cepsilon. Analysis of calmodulin data based on these calculations indicates that several residues adopt non-standard rotamers characterized by very large approximately 100 degrees chi(3) values. The utility of the delta(13)Cepsilon as a basis for estimating the gauche/trans ratio for chi(3) is evaluated, and physical and technical factors that limit the accuracy of both the NMR and crystallographic analyses are discussed.

Improved side-chain torsion potentials for the Amber ff99SB protein force field

Recent advances in hardware and software have enabled increasingly long molecular dynamics (MD) simulations of biomolecules, exposing certain limitations in the accuracy of the force fields used for such simulations and spurring efforts to refine these force fields. Recent modifications to the Amber and CHARMM protein force fields, for example, have improved the backbone torsion potentials, remedying deficiencies in earlier versions. Here, we further advance simulation accuracy by improving the amino acid side-chain torsion potentials of the Amber ff99SB force field. First, we used simulations of model alpha-helical systems to identify the four residue types whose rotamer distribution differed the most from expectations based on Protein Data Bank statistics. Second, we optimized the side-chain torsion potentials of these residues to match new, high-level quantum-mechanical calculations. Finally, we used microsecond-timescale MD simulations in explicit solvent to validate the resulting force field against a large set of experimental NMR measurements that directly probe side-chain conformations. The new force field, which we have termed Amber ff99SB-ILDN, exhibits considerably better agreement with the NMR data. Proteins 2010. © 2010 Wiley-Liss, Inc.

Backbone statistical potential from local sequence-structure interactions in protein loops

Native proteins have been optimized by evolution simultaneously for structure and sequence. Structural databases reflect this interdependency. In this paper, we present a new statistical potential for a reduced backbone representation that has both structure and sequence characteristics as variables. We use information from structural data available in the Protein Coil Library, selected on the basis of resolution and refinement factor. In these structures, the nonlocal interactions are randomly distributed and, thus, average out in statistics, so structural propensities due to local backbone-based interactions can be studied separately. We collect data in the form of local sequence-specific phi-psi backbone dihedral pairs. From these data, we construct dihedral probability density functions (DPDFs) that quantify any adjacent phi-psi pair distribution in the context of all possible combinations of local residue types. We use a probabilistic analysis to deduce how the correlations encoded in the various DPDFs as well as in residue frequencies propagate along the sequence and can be cumulated in a statistical potential capable of efficiently scoring a loop by its backbone conformation and sequence only. Our potential is able to identify with high accuracy the native structure of a loop with a given sequence among possible alternative conformations from sets of well-constructed decoys. Conversely, the potential can also be used for sequence prediction problems and is shown to score the native sequence of a given loop structure among the most fit of the possible sequence combinations. Applications for both structure prediction and sequence design are discussed.

A preliminary survey of the peptoid folding landscape

We present an analysis of the conformational preferences of N-substituted glycine peptoid oligomers. We survey the backbone conformations observed in experimentally determined peptoid structures and provide a comparison with high-level quantum mechanics calculations of short peptoid oligomers. The dominant sources of structural variation derive from: side-chain dependent cis/trans isomerization of backbone amide bonds, side chain stereochemistry, and flexibility in the psi dihedral angle. We find good agreement between the clustering of experimentally determined peptoid torsion angles and local torsional minima predicted by theory for a disarcosine model. The calculations describe a well-defined conformational map featuring distinct energy minima. The general features of the peptoid backbone conformational landscape are consistent across a range of N-alkyl glycine side chains. Alteration of side chain types, however, creates subtle but potentially significant variations in local folding propensities. We identify a limited number of low energy local conformations, which may be preferentially favored by incorporation of particular monomer units. Greater variation in backbone dihedral angles are accessible in peptoids featuring trans amide bond geometries. These results confirm that computational approaches can play a valuable role in guiding the design of complex peptoid architectures and may lead to strategies for introducing constraints that select among a limited number of low energy local conformations.

Using quantum mechanics to improve estimates of amino acid side chain rotamer energies

Amino acid side chains adopt a discrete set of favorable conformations typically referred to as rotamers. The relative energies of rotamers partially determine which side chain conformations are more often observed in protein structures and accurate estimates of these energies are important for predicting protein structure and designing new proteins. Protein modelers typically calculate side chain rotamer energies by using molecular mechanics (MM) potentials or by converting rotamer probabilities from the protein database (PDB) into relative free energies. One limitation of the knowledge-based energies is that rotamer preferences observed in the PDB can reflect internal side chain energies as well as longer-range interactions with the rest of the protein. Here, we test an alternative approach for calculating rotamer energies. We use three different quantum mechanics (QM) methods (second order Møller-Plesset (MP2), density functional theory (DFT) energy calculation using the B3LYP functional, and Hartree-Fock) to calculate the energy of amino acid rotamers in a dipeptide model system, and then use these pre-calculated values in side chain placement simulations. Energies were calculated for over 36,000 different conformations of leucine, isoleucine, and valine dipeptides with backbone torsion angles from the helical and strand regions of the Ramachandran plot. In a subset of cases these energies differ significantly from those calculated with standard molecular mechanics potentials or those derived from PDB statistics. We find that in these cases the energies from the QM methods result in more accurate placement of amino acid side chains in structure prediction tests.

Effects of amino acid composition, finite size of proteins, and sparse statistics on distance-dependent statistical pair potentials

Statistical distance dependent pair potentials are frequently used in a variety of folding, threading, and modeling studies of proteins. The applicability of these types of potentials is tightly connected to the reliability of statistical observations. We explored the possible origin and extent of false positive signals in statistical potentials by analyzing their distance dependence in a variety of randomized protein-like models. While on average potentials derived from such models are expected to equal zero at any distance, we demonstrate that systematic and significant distortions exist. These distortions originate from the limited statistical counts in local environments of proteins and from the limited size of protein structures at large distances. We suggest that these systematic errors in statistical potentials are connected to the dependence of amino acid composition on protein size and to variation in protein sizes. Additionally, atom-based potentials are dominated by a false positive signal that is due to correlation among distances measured from atoms of one residue to atoms of another residue. The significance of residue-based pairwise potentials at various spatial pair separations was assessed in this study and it was found that as few as approximately 50% of potential values were statistically significant at distances below 4 A, and only at most approximately 80% of them were significant at larger pair separations. A new definition for reference state, free of the observed systematic errors, is suggested. It has been demonstrated to generate statistical potentials that compare favorably to other publicly available ones.

Approximate Values for Force Constant and Wave Number Associated with a Low-Frequency Concerted Motion in Proteins Can Be Evaluated by a Comparison of X-ray Structures

Low-frequency internal motions in protein molecules play a key role in biological functions. A direct relationship between low-frequency motions and enzymatic activity has been suggested for bovine pancreatic ribonuclease (RNase A). The flexibility-function relationship in this enzyme has been attributed to a subtle and concerted breathing motion of the beta-sheet regions occurring upon substrate binding and release. Here, we calculate an approximate value for the force constant and the wave number of the low-frequency beta-sheet breathing motion of RNase A, by using the Boltzmann hypothesis on a set of data derived from a simple conventional structural superimposition of an unusual large number of X-ray structures available for the protein. The results agree with previous observations and with theoretical predictions on the basis of normal-mode analysis. To the best of our knowledge, this is the first example in which the wave number and the force constant of a low-frequency concerted motion in a protein are directly derived from X-ray structures.

Structural Effects of Naturally Occurring Human Blood Group B Galactosyltransferase Mutations Adjacent to the DXD Motif

Human blood group A and B antigens are produced by two closely related glycosyltransferase enzymes. An N-acetylgalactosaminyltransferase (GTA) utilizes UDP-GalNAc to extend H antigen acceptors (Fuc alpha(1-2)Gal beta-OR) producing A antigens, whereas a galactosyltransferase (GTB) utilizes UDP-Gal as a donor to extend H structures producing B antigens. GTA and GTB have a characteristic (211)DVD(213) motif that coordinates to a Mn(2+) ion shown to be critical in donor binding and catalysis. Three GTB mutants, M214V, M214T, and M214R, with alterations adjacent to the (211)DVD(213) motif have been identified in blood banking laboratories. From serological phenotyping, individuals with the M214R mutation show the B(el) variant expressing very low levels of B antigens, whereas those with M214T and M214V mutations give rise to A(weak)B phenotypes. Kinetic analysis of recombinant mutant GTB enzymes revealed that M214R has a 1200-fold decrease in k(cat) compared with wild type GTB. The crystal structure of M214R showed that DVD motif coordination to Mn(2+) was disrupted by Arg-214 causing displacement of the metal by a water molecule. Kinetic characterizations of the M214T and M214V mutants revealed they both had GTA and GTB activity consistent with the serology. The crystal structure of the M214T mutant showed no change in DVD coordination to Mn(2+). Instead a critical residue, Met-266, which is responsible for determining donor specificity, had adopted alternate conformations. The conformation with the highest occupancy opens up the active site to accommodate the larger A-specific donor, UDP-GalNAc, accounting for the dual specificity.

Protein design simulations suggest that side-chain conformational entropy is not a strong determinant of amino acid environmental preferences

Loss of side-chain conformational entropy is an important force opposing protein folding and the relative preferences of the amino acids for being buried or solvent exposed may be partially determined by which amino acids lose more side-chain entropy when placed in the core of a protein. To investigate these preferences, we have incorporated explicit modeling of side-chain entropy into the protein design algorithm, RosettaDesign. In the standard version of the program, the energy of a particular sequence for a fixed backbone depends only on the lowest energy side-chain conformations that can be identified for that sequence. In the new model, the free energy of a single amino acid sequence is calculated by evaluating the average energy and entropy of an ensemble of structures generated by Monte Carlo sampling of amino acid side-chain conformations. To evaluate the impact of including explicit side-chain entropy, sequences were designed for 110 native protein backbones with and without the entropy model. In general, the differences between the two sets of sequences are modest, with the largest changes being observed for the longer amino acids: methionine and arginine. Overall, the identity between the designed sequences and the native sequences does not increase with the addition of entropy, unlike what is observed when other key terms are added to the model (hydrogen bonding, Lennard-Jones energies, and solvation energies). These results suggest that side-chain conformational entropy has a relatively small role in determining the preferred amino acid at each residue position in a protein.

Intrinsic backbone preferences are fully present in blocked amino acids

The preferences of amino acid residues for ,psi backbone angles vary strikingly among the amino acids, as shown by the backbone angle found from the (3)J(H(alpha),H(N)) coupling constant for short peptides in water. New data for the (3)J(H(alpha),H(N)) values of blocked amino acids (dipeptides) are given here. Dipeptides exhibit the full range of coupling constants shown by longer peptides such as GGXGG and dipeptides present the simplest system for analyzing backbone preferences. The dipeptide coupling constants are surprisingly close to values computed from the coil library (conformations of residues not in helices and not in sheets). Published coupling constants for GGXGG peptides agree closely with dipeptide values for all nonpolar residues and for some polar residues but not for X = D, N, T, and Y, which are probably affected by polar side chain-backbone interactions in GGXGG peptides. Thus, intrinsic backbone preferences are already determined at the dipeptide level and remain almost unchanged in GGXGG peptides and are strikingly similar in the coil library of conformations from protein structures. The simplest explanation for the backbone preferences is that backbone conformations are strongly affected by electrostatic dipole-dipole interactions in the peptide backbone and by screening of these interactions with water, which depends on nearby side chains. Strong backbone electrostatic interactions occur in dipeptides. This is shown by calculations both of backbone electrostatic energy for different conformers of the alanine dipeptide in the gas phase and by electrostatic solvation free energies of amino acid dipeptides.

Characterizing conserved structural contacts by pair-wise relative contacts and relative packing groups

To adequately deal with the inherent complexity of interactions between protein side-chains, we develop and describe here a novel method for characterizing protein packing within a fold family. Instead of approaching side-chain interactions absolutely from one residue to another, we instead consider the relative interactions of contacting residue pairs. The basic element, the pair-wise relative contact, is constructed from a sequence alignment and contact analysis of a set of structures and consists of a cluster of similarly oriented, interacting, side-chain pairs. To demonstrate this construct's usefulness in analyzing protein structure, we used the pair-wise relative contacts to analyze two sets of protein structures as defined by SCOP: the diverse globin-like superfamily (126 structures) and the more uniform heme binding globin family (a 94 structure subset of the globin-like superfamily). The superfamily structure set produced 1266 unique pair-wise relative contacts, whereas the family structure subset gave 1001 unique pair-wise relative contacts. For both sets, we show that these constructs can be used to accurately and automatically differentiate between fold classes. Furthermore, these pair-wise relative contacts correlate well with sequence identity and thus provide a direct relationship between changes in sequence and changes in structure. To capture the complexity of protein packing, these pair-wise relative contacts can be superimposed around a single residue to create a multi-body construct called a relative packing group. Construction of convex hulls around the individual packing groups provides a measure of the variation in packing around a residue and defines an approximate volume of space occupied by the groups interacting with a residue. We find that these relative packing groups are useful in understanding the structural quality of sequence or structure alignments. Moreover, they provide context to calculate a value for structural randomness, which is important in properly assessing the quality of a structural alignment. The results of this study provide the framework for future analysis for correlating sequence changes to specific structure changes.

Sterics and solvation winnow accessible conformational space for unfolded proteins

The magnitude of protein conformational space is over-estimated by the traditional random-coil model, in which local steric restrictions arise exclusively from interactions between adjacent chain neighbors. Using a five-state model, we assessed the extent to which steric hindrance and hydrogen bond satisfaction, energetically significant factors, impose additional conformational restrictions on polypeptide chains, beyond adjacent residues. Steric hindrance is repulsive: the distance of closest approach between any two atoms cannot be less than the sum of their van der Waals radii. Hydrogen bond satisfaction is attractive: polar backbone atoms must form hydrogen bonds, either intramolecularly or to solvent water. To gauge the impact of these two factors on the magnitude of conformational space, we systematically enumerated and classified the disfavored conformations that restrict short polyalanyl backbone chains. Applying such restrictions to longer chains, we derived a scaling law to estimate conformational restriction as a function of chain length. Disfavored conformations predicted by the model were tested against experimentally determined structures in the coil library, a non-helix, non-strand subset of the PDB. These disfavored conformations are usually absent from the coil library, and exceptions can be uniformly rationalized.

Do all backbone polar groups in proteins form hydrogen bonds?

Evidence from proteins and peptides supports the conclusion that intrapeptide hydrogen bonds stabilize the folded form of proteins. Paradoxically, evidence from small molecules supports the opposite conclusion, that intrapeptide hydrogen bonds are less favorable than peptide-water hydrogen bonds. A related issue-often lost in this debate about comparing peptide-peptide to peptide- water hydrogen bonds-involves the energetic cost of an unsatisfied hydrogen bond. Here, experiment and theory agree that breaking a hydrogen bond costs between 5 and 6 kcal/mol. Accordingly, the likelihood of finding an unsatisfied hydrogen bond in a protein is insignificant. This realization establishes a powerful rule for evaluating protein conformations.

Intraresidue Distribution of Energy in Proteins

Boltzmann-like distributions appear in many properties and energy-related quantities of proteins. A few examples are hydrophobicity, various types of side-chain/side-chain interactions, proline isomerization, hydrogen bonds, internal cavities, interactions at the level of specific atom types, and the propensity of the phi/'phi' ratio. Here, we conjecture that the Boltzmann hypothesis also holds for the intra-residue energy distribution. We confirm the conjecture by calculating the energies of 41,672 residues of the structures of highly resolved proteins, where at least 12 out of 20 naturally occurring amino acids follow Boltzmann's law. We further examine the entire set of all residue energies and find that the convolution of the individual distributions gives a Poisson function, which is followed by approximately 50% of individual proteins' structures.

Origin of the neighboring residue effect on peptide backbone conformation

Unfolded peptides in water have some residual structure that may be important in the folding process, and the nature of the residual structure is currently of much interest. There is a neighboring residue effect on backbone conformation, discovered in 1997 from measurements of (3)J(HN alpha) coupling constants. The neighboring residue effect appears also in the "coil library" of Protein Data Bank structures of residues not in alpha-helix and not in beta-structure. When a neighboring residue (i - 1 or i + 1) belongs to class L (aromatic and beta-branched amino acids, FHITVWY) rather than class S (all others, G and P excluded), then the backbone angle of residue i is more negative for essentially all amino acids. Calculated values of peptide solvation (electrostatic solvation free energy, ESF) predict basic properties of the neighboring residue effect. We show that L amino acids reduce the solvation of neighboring peptide groups more than S amino acids. When tripeptides from the coil library are excised to allow solvation, the central residues have more negative values of but less negative values of with L than with S neighbors. The coil library values of <(3)J(HN alpha)>, which vary strikingly among the amino acids, are correlated with the neighboring residue effect seen by ESF. Moreover, values for the "blocking effect" of side chains on the hydrogen exchange rates of peptide NH protons are correlated with ESF values.