Rigid protein motion as a model for crystallographic temperature factors

Parameterizing elastic network models to capture the dynamics of proteins

Coarse-grained normal mode analyses of protein dynamics rely on the idea that the geometry of a protein structure contains enough information for computing its fluctuations around its equilibrium conformation. This geometry is captured in the form of an elastic network (EN), namely a network of edges between its residues. The normal modes of a protein are then identified with the normal modes of its EN. Different approaches have been proposed to construct ENs, focusing on the choice of the edges that they are comprised of, and on their parameterizations by the force constants associated with those edges. Here we propose new tools to guide choices on these two facets of EN. We study first different geometric models for ENs. We compare cutoff-based ENs, whose edges have lengths that are smaller than a cutoff distance, with Delaunay-based ENs and find that the latter provide better representations of the geometry of protein structures. We then derive an analytical method for the parameterization of the EN such that its dynamics leads to atomic fluctuations that agree with experimental B-factors. To limit overfitting, we attach a parameter referred to as flexibility constant to each atom instead of to each edge in the EN. The parameterization is expressed as a non-linear optimization problem whose parameters describe both rigid-body and internal motions. We show that this parameterization leads to improved ENs, whose dynamics mimic MD simulations better than ENs with uniform force constants, and reduces the number of normal modes needed to reproduce functional conformational changes.

Elasticity-Associated Functionality and Inhibition of the HIV Protease

HIV protease plays a critical role in the life cycle of the virus through the generation of mature and infectious virions. Detailed knowledge of the structure of the enzyme and its substrate has led to the development of protease inhibitors. However, the development of resistance to all currently available protease inhibitors has contributed greatly to the decreased success of antiretroviral therapy. When therapy failure occurs, multiple mutations are found within the protease sequence starting with primary mutations, which directly impact inhibitor binding, which can also negatively impact viral fitness and replicative capacity by decreasing the binding affinity of the natural substrates to the protease. As such, secondary mutations which are located outside of the active site region accumulate to compensate for the recurrently deleterious effects of primary mutations. However, the resistance mechanism of these secondary mutations is not well understood, but what is known is that these secondary mutations contribute to resistance in one of two ways, either through increasing the energetic penalty associated with bringing the protease into the closed conformation, or, through decreasing the stability of the protein/drug complex in a manner that increases the dissociation rate of the drug, leading to diminished inhibition. As a result, the elasticity of the enzyme-substrate complex has been implicated in the successful recognition and catalysis of the substrates which may be inferred to suggest that the elasticity of the enzyme/drug complex plays a role in resistance. A realistic representation of the dynamic nature of the protease may provide a more powerful tool in structure-based drug design algorithms.

Conformational Plasticity of HLA-B27 Molecules Correlates Inversely With Efficiency of Negative T Cell Selection

The development of autoimmune disorders is incompletely understood. Inefficient thymic T cell selection against self-peptides presented by major histocompatibility antigens (HLA in humans) may contribute to the emergence of auto-reactive effector cells, and molecular mimicry between foreign and self-peptides could promote T cell cross-reactivity. A pair of class I subtypes, HLA-B2705 and HLA-B2709, have previously been intensely studied, because they are distinguished from each other only by a single amino acid exchange at the floor of the peptide-binding groove, yet are differentially associated with the autoinflammatory disorder ankylosing spondylitis. Using X-ray crystallography in combination with ensemble refinement, we find that the non-disease-associated subtype HLA-B2709, when presenting the self-peptide pGR (RRRWHRWRL), exhibits elevated conformational dynamics, and the complex can also be recognized by T cells. Both features are not observed in case of the sequence-related self-peptide pVIPR (RRKWRRWHL) in complex with this subtype, and T cell cross-reactivity between pGR, pVIPR, and the viral peptide pLMP2 (RRRWRRLTV) is only rarely observed. The disease-associated subtype HLA-B2705, however, exhibits extensive conformational flexibility in case of the three complexes, all of which are also recognized by frequently occurring cross-reactive T cells. A comparison of the structural and dynamic properties of the six HLA-B27 complexes, together with their individual ability to interact with T cells, permits us to correlate the flexibility of HLA-B27 complexes with effector cell reactivity. The results suggest the existence of an inverse relationship between conformational plasticity of peptide-HLA-B27 complexes and the efficiency of negative selection of self-reactive cells within the thymus.

Are crystallographic B-factors suitable for calculating protein conformational entropy?

It is not possible to obtain reliable entropy estimates from crystallographic B-factors even with re-refined or room-temperature crystal structures.

Slow normal modes of proteins are accurately reproduced across different platforms

The Protein data bank (PDB) (Berman et al 2000 Nucl. Acids Res. 28 235-42) contains the atomic structures of over 10⁵ biomolecules with better than 2.8 Å resolution. The listing of the identities and coordinates of the atoms comprising each macromolecule permits an analysis of the slow-time vibrational response of these large systems to minor perturbations. 3D video animations of individual modes of oscillation demonstrate how regions interdigitate to create cohesive collective motions, providing a comprehensive framework for and familiarity with the overall 3D architecture. Furthermore, the isolation and representation of the softest, slowest deformation coordinates provide opportunities for the development of mechanical models of enzyme function. The eigenvector decomposition, therefore, must be accurate, reliable as well as rapid to be generally reported upon. We obtain the eigenmodes of a 1.2 Å 34 kDa PDB entry using either exclusively heavy atoms or partly or fully reduced atomic sets; Cartesian or internal coordinates; interatomic force fields derived either from a full Cartesian potential, a reduced atomic potential or a Gaussian distance-dependent potential; and independently developed software. These varied technologies are similar in that each maintains proper stereochemistry either by use of dihedral degrees of freedom which freezes bond lengths and bond angles, or by use of a full atomic potential that includes realistic bond length and angle restraints. We find that the shapes of the slowest eigenvectors are nearly identical, not merely similar.

From deep TLS validation to ensembles of atomic models built from elemental motions. II. Analysis of TLS refinement results by explicit interpretation

TLS modelling was developed by Schomaker and Trueblood to describe atomic displacement parameters through concerted (rigid-body) harmonic motions of an atomic group [Schomaker & Trueblood (1968), Acta Cryst. B24, 63-76]. The results of a TLS refinement are T, L and S matrices that provide individual anisotropic atomic displacement parameters (ADPs) for all atoms belonging to the group. These ADPs can be calculated analytically using a formula that relates the elements of the TLS matrices to atomic parameters. Alternatively, ADPs can be obtained numerically from the parameters of concerted atomic motions corresponding to the TLS matrices. Both procedures are expected to produce the same ADP values and therefore can be used to assess the results of TLS refinement. Here, the implementation of this approach in PHENIX is described and several illustrations, including the use of all models from the PDB that have been subjected to TLS refinement, are provided.

The maximum penalty criterion for ridge regression: application to the calibration of the force constant in elastic network models

Tikhonov regularization, or ridge regression, is a popular technique to deal with collinearity in multivariate regression. We unveil a formal analogy between ridge regression and statistical mechanics, where the objective function is comparable to a free energy, and the ridge parameter plays the role of temperature. This analogy suggests two novel criteria for selecting a suitable ridge parameter: specific-heat (C_v) and maximum penalty (MP). We apply these fits to evaluate the relative contributions of rigid-body and internal fluctuations, which are typically highly collinear, to crystallographic B-factors. This issue is particularly important for computational models of protein dynamics, such as the elastic network model (ENM), since the amplitude of the predicted internal motion is commonly calibrated using B-factor data. After validation on simulated datasets, our results indicate that rigid-body motions account on average for more than 80% of the amplitude of B-factors. Furthermore, we evaluate the ability of different fits to reproduce the amplitudes of internal fluctuations in X-ray ensembles from the B-factors in the corresponding single X-ray structures. The new ridge criteria are shown to be markedly superior to the commonly used two-parameter fit that neglects rigid-body rotations and to the full fits regularized under generalized cross-validation. In conclusion, the proposed fits ensure a more robust calibration of the ENM force constant and should prove valuable in other applications.

FF12MC: A revised AMBER forcefield and new protein simulation protocol

Specialized to simulate proteins in molecular dynamics (MD) simulations with explicit solvation, FF12MC is a combination of a new protein simulation protocol employing uniformly reduced atomic masses by tenfold and a revised AMBER forcefield FF99 with (i) shortened CH bonds, (ii) removal of torsions involving a nonperipheral sp(3) atom, and (iii) reduced 1-4 interaction scaling factors of torsions ϕ and ψ. This article reports that in multiple, distinct, independent, unrestricted, unbiased, isobaric-isothermal, and classical MD simulations FF12MC can (i) simulate the experimentally observed flipping between left- and right-handed configurations for C14-C38 of BPTI in solution, (ii) autonomously fold chignolin, CLN025, and Trp-cage with folding times that agree with the experimental values, (iii) simulate subsequent unfolding and refolding of these miniproteins, and (iv) achieve a robust Z score of 1.33 for refining protein models TMR01, TMR04, and TMR07. By comparison, the latest general-purpose AMBER forcefield FF14SB locks the C14-C38 bond to the right-handed configuration in solution under the same protein simulation conditions. Statistical survival analysis shows that FF12MC folds chignolin and CLN025 in isobaric-isothermal MD simulations 2-4 times faster than FF14SB under the same protein simulation conditions. These results suggest that FF12MC may be used for protein simulations to study kinetics and thermodynamics of miniprotein folding as well as protein structure and dynamics. Proteins 2016; 84:1490-1516. © 2016 The Authors Proteins: Structure, Function, and Bioinformatics Published by Wiley Periodicals, Inc.

Use of multiple picosecond high-mass molecular dynamics simulations to predict crystallographic B-factors of folded globular proteins

Predicting crystallographic B-factors of a protein from a conventional molecular dynamics simulation is challenging, in part because the B-factors calculated through sampling the atomic positional fluctuations in a picosecond molecular dynamics simulation are unreliable, and the sampling of a longer simulation yields overly large root mean square deviations between calculated and experimental B-factors. This article reports improved B-factor prediction achieved by sampling the atomic positional fluctuations in multiple picosecond molecular dynamics simulations that use uniformly increased atomic masses by 100-fold to increase time resolution. Using the third immunoglobulin-binding domain of protein G, bovine pancreatic trypsin inhibitor, ubiquitin, and lysozyme as model systems, the B-factor root mean square deviations (mean ± standard error) of these proteins were 3.1 ± 0.2–9 ± 1 Ų for Cα and 7.3 ± 0.9–9.6 ± 0.2 Ų for Cγ, when the sampling was done for each of these proteins over 20 distinct, independent, and 50-picosecond high-mass molecular dynamics simulations with AMBER forcefield FF12MC or FF14SB. These results suggest that sampling the atomic positional fluctuations in multiple picosecond high-mass molecular dynamics simulations may be conducive to a priori prediction of crystallographic B-factors of a folded globular protein.

Characterization and Prediction of Protein Flexibility Based on Structural Alphabets

Motivation. To assist efforts in determining and exploring the functional properties of proteins, it is desirable to characterize and predict protein flexibilities. Results. In this study, the conformational entropy is used as an indicator of the protein flexibility. We first explore whether the conformational change can capture the protein flexibility. The well-defined decoy structures are converted into one-dimensional series of letters from a structural alphabet. Four different structure alphabets, including the secondary structure in 3-class and 8-class, the PB structure alphabet (16-letter), and the DW structure alphabet (28-letter), are investigated. The conformational entropy is then calculated from the structure alphabet letters. Some of the proteins show high correlation between the conformation entropy and the protein flexibility. We then predict the protein flexibility from basic amino acid sequence. The local structures are predicted by the dual-layer model and the conformational entropy of the predicted class distribution is then calculated. The results show that the conformational entropy is a good indicator of the protein flexibility, but false positives remain a problem. The DW structure alphabet performs the best, which means that more subtle local structures can be captured by large number of structure alphabet letters. Overall this study provides a simple and efficient method for the characterization and prediction of the protein flexibility.

X-ray refinement significantly underestimates the level of microscopic heterogeneity in biomolecular crystals

Biomolecular X-ray structures typically provide a static, time- and ensemble-averaged view of molecular ensembles in crystals. In the absence of rigid-body motions and lattice defects, B-factors are thought to accurately reflect the structural heterogeneity of such ensembles. In order to study the effects of averaging on B-factors, we employ molecular dynamics simulations to controllably manipulate microscopic heterogeneity of a crystal containing 216 copies of villin headpiece. Using average structure factors derived from simulation, we analyse how well this heterogeneity is captured by high-resolution molecular-replacement-based model refinement. We find that both isotropic and anisotropic refined B-factors often significantly deviate from their actual values known from simulation: even at high 1.0 Å resolution and Rfree of 5.9%, B-factors of some well-resolved atoms underestimate their actual values even sixfold. Our results suggest that conformational averaging and inadequate treatment of correlated motion considerably influence estimation of microscopic heterogeneity via B-factors, and invite caution in their interpretation.

From deep TLS validation to ensembles of atomic models built from elemental motions

The translation-libration-screw model first introduced by Cruickshank, Schomaker and Trueblood describes the concerted motions of atomic groups. Using TLS models can improve the agreement between calculated and experimental diffraction data. Because the T, L and S matrices describe a combination of atomic vibrations and librations, TLS models can also potentially shed light on molecular mechanisms involving correlated motions. However, this use of TLS models in mechanistic studies is hampered by the difficulties in translating the results of refinement into molecular movement or a structural ensemble. To convert the matrices into a constituent molecular movement, the matrix elements must satisfy several conditions. Refining the T, L and S matrix elements as independent parameters without taking these conditions into account may result in matrices that do not represent concerted molecular movements. Here, a mathematical framework and the computational tools to analyze TLS matrices, resulting in either explicit decomposition into descriptions of the underlying motions or a report of broken conditions, are described. The description of valid underlying motions can then be output as a structural ensemble. All methods are implemented as part of the PHENIX project.

Conformational dynamics of a crystalline protein from microsecond-scale molecular dynamics simulations and diffuse X-ray scattering

X-ray diffraction from protein crystals includes both sharply peaked Bragg reflections and diffuse intensity between the peaks. The information in Bragg scattering is limited to what is available in the mean electron density. The diffuse scattering arises from correlations in the electron density variations and therefore contains information about collective motions in proteins. Previous studies using molecular-dynamics (MD) simulations to model diffuse scattering have been hindered by insufficient sampling of the conformational ensemble. To overcome this issue, we have performed a 1.1-μs MD simulation of crystalline staphylococcal nuclease, providing 100-fold more sampling than previous studies. This simulation enables reproducible calculations of the diffuse intensity and predicts functionally important motions, including transitions among at least eight metastable states with different active-site geometries. The total diffuse intensity calculated using the MD model is highly correlated with the experimental data. In particular, there is excellent agreement for the isotropic component of the diffuse intensity, and substantial but weaker agreement for the anisotropic component. Decomposition of the MD model into protein and solvent components indicates that protein-solvent interactions contribute substantially to the overall diffuse intensity. We conclude that diffuse scattering can be used to validate predictions from MD simulations and can provide information to improve MD models of protein motions.

The effects of thermal disorder on the solution-scattering profiles of macromolecules

The solution-scattering profiles of macromolecules are significantly affected by the thermal motions of their atoms, especially at wide scattering angles, even when only a single conformational state is significantly populated in solution. Here it is shown that the impact thermal motions have on the molecular component of the solution-scattering profile of a single-state macromolecule can be predicted accurately if the variances and covariances of the thermal excursions of its atoms from their average positions are known.

All-atom empirical potential for molecular modeling and dynamics studies of proteins

New protein parameters are reported for the all-atom empirical energy function in the CHARMM program. The parameter evaluation was based on a self-consistent approach designed to achieve a balance between the internal (bonding) and interaction (nonbonding) terms of the force field and among the solvent-solvent, solvent-solute, and solute-solute interactions. Optimization of the internal parameters used experimental gas-phase geometries, vibrational spectra, and torsional energy surfaces supplemented with ab initio results. The peptide backbone bonding parameters were optimized with respect to data for N-methylacetamide and the alanine dipeptide. The interaction parameters, particularly the atomic charges, were determined by fitting ab initio interaction energies and geometries of complexes between water and model compounds that represented the backbone and the various side chains. In addition, dipole moments, experimental heats and free energies of vaporization, solvation and sublimation, molecular volumes, and crystal pressures and structures were used in the optimization. The resulting protein parameters were tested by applying them to noncyclic tripeptide crystals, cyclic peptide crystals, and the proteins crambin, bovine pancreatic trypsin inhibitor, and carbonmonoxy myoglobin in vacuo and in crystals. A detailed analysis of the relationship between the alanine dipeptide potential energy surface and calculated protein φ, χ angles was made and used in optimizing the peptide group torsional parameters. The results demonstrate that use of ab initio structural and energetic data by themselves are not sufficient to obtain an adequate backbone representation for peptides and proteins in solution and in crystals. Extensive comparisons between molecular dynamics simulations and experimental data for polypeptides and proteins were performed for both structural and dynamic properties. Energy minimization and dynamics simulations for crystals demonstrate that the latter are needed to obtain meaningful comparisons with experimental crystal structures. The presented parameters, in combination with the previously published CHARMM all-atom parameters for nucleic acids and lipids, provide a consistent set for condensed-phase simulations of a wide variety of molecules of biological interest.

TLS from fundamentals to practice

The Translation-Libration-Screw-rotation (TLS) model of rigid-body harmonic displacements introduced in crystallography by Schomaker & Trueblood (1968) is now a routine tool in macromolecular studies and is a feature of most modern crystallographic structure refinement packages. In this review we consider a number of simple examples that illustrate important features of the TLS model. Based on these examples simplified formulae are given for several special cases that may occur in structure modeling and refinement. The derivation of general TLS formulae from basic principles is also provided. This manuscript describes the principles of TLS modeling, as well as some select algorithmic details for practical application. An extensive list of applications references as examples of TLS in macromolecular crystallography refinement is provided.

Substrate envelope-designed potent HIV-1 protease inhibitors to avoid drug resistance

The rapid evolution of HIV under selective drug pressure has led to multidrug resistant (MDR) strains that evade standard therapies. We designed highly potent HIV-1 protease inhibitors (PIs) using the substrate envelope model, which confines inhibitors within the consensus volume of natural substrates, providing inhibitors less susceptible to resistance because a mutation affecting such inhibitors will simultaneously affect viral substrate processing. The designed PIs share a common chemical scaffold but utilize various moieties that optimally fill the substrate envelope, as confirmed by crystal structures. The designed PIs retain robust binding to MDR protease variants and display exceptional antiviral potencies against different clades of HIV as well as a panel of 12 drug-resistant viral strains. The substrate envelope model proves to be a powerful strategy to develop potent and robust inhibitors that avoid drug resistance.

Elastic network models: theoretical and empirical foundations

Fifteen years ago, Monique Tirion showed that the low-frequency normal modes of a protein are not significantly altered when nonbonded interactions are replaced by Hookean springs, for all atom pairs whose distance is smaller than a given cutoff value. Since then, it has been shown that coarse-grained versions of Tirion's model are able to provide fair insights on many dynamical properties of biological macromolecules. In this chapter, theoretical tools required for studying these so-called Elastic Network Models are described, focusing on practical issues and, in particular, on possible artifacts. Then, an overview of some typical results that have been obtained by studying such models is given.

Design, synthesis, and biological and structural evaluations of novel HIV-1 protease inhibitors to combat drug resistance

A series of new HIV-1 protease inhibitors (PIs) were designed using a general strategy that combines computational structure-based design with substrate-envelope constraints. The PIs incorporate various alcohol-derived P2 carbamates with acyclic and cyclic heteroatomic functionalities into the (R)-hydroxyethylamine isostere. Most of the new PIs show potent binding affinities against wild-type HIV-1 protease and three multidrug resistant (MDR) variants. In particular, inhibitors containing the 2,2-dichloroacetamide, pyrrolidinone, imidazolidinone, and oxazolidinone moieties at P2 are the most potent with K(i) values in the picomolar range. Several new PIs exhibit nanomolar antiviral potencies against patient-derived wild-type viruses from HIV-1 clades A, B, and C and two MDR variants. Crystal structure analyses of four potent inhibitors revealed that carbonyl groups of the new P2 moieties promote extensive hydrogen bond interactions with the invariant Asp29 residue of the protease. These structure-activity relationship findings can be utilized to design new PIs with enhanced enzyme inhibitory and antiviral potencies.

The relation of the X-ray B-factor to protein dynamics: insights from recent dynamic solid-state NMR data

In addressing the potential use of B-factors derived from X-ray scattering data of proteins for the understanding the (functional) dynamics of proteins, we present a comparison of B-factors of five different proteins (SH3 domain, Crh, GB1, ubiquitin and thioredoxin) with data from recent solid-state nuclear magnetic resonance experiments reflecting true (rotational) dynamics on well-defined timescales. Apart from trivial correlations involving mobile loop regions and chain termini, we find no significant correlation of B-factors with the dynamic data on any of the investigated timescales, concluding that there is no unique and general correlation of B-factors with the internal reorientational dynamics of proteins.

TMC310911, a novel human immunodeficiency virus type 1 protease inhibitor, shows in vitro an improved resistance profile and higher genetic barrier to resistance compared with current protease inhibitors

TMC310911 is a novel human immunodeficiency virus type 1 (HIV-1) protease inhibitor (PI) structurally closely related to darunavir (DRV) but with improved virological characteristics. TMC310911 has potent activity against wild-type (WT) HIV-1 (median 50% effective concentration [EC(50)], 14 nM) and a wide spectrum of recombinant HIV-1 clinical isolates, including multiple-PI-resistant strains with decreased susceptibility to currently approved PIs (fold change [FC] in EC(50), >10). For a panel of 2,011 recombinant clinical isolates with decreased susceptibility to at least one of the currently approved PIs, the FC in TMC310911 EC(50) was ≤ 4 for 82% of isolates and ≤ 10 for 96% of isolates. The FC in TMC310911 EC(50) was ≤ 4 and ≤ 10 for 72% and 94% of isolates with decreased susceptibility to DRV, respectively. In vitro resistance selection (IVRS) experiments with WT virus and TMC310911 selected for mutations R41G or R41E, but selection of resistant virus required a longer time than IVRS performed with WT virus and DRV. IVRS performed with r13025, a multiple-PI-resistant recombinant clinical isolate, and TMC310911 selected for mutations L10F, I47V, and L90M (FC in TMC310911 EC(50) = 16). IVRS performed with r13025 in the presence of DRV required less time and resulted in more PI resistance-associated mutations (V32I, I50V, G73S, L76V, and V82I; FC in DRV EC(50) = 258). The activity against a comprehensive panel of PI-resistant mutants and the limited in vitro selection of resistant viruses under drug pressure suggest that TMC310911 represents a potential drug candidate for the management of HIV-1 infection for a broad range of patients, including those with multiple PI resistance.

Dynamics may significantly influence the estimation of interatomic distances in biomolecular X-ray structures

Atomic positions obtained by X-ray crystallography are time and space averages over many molecules in the crystal. Importantly, interatomic distances, calculated between such average positions and frequently used in structural and mechanistic analyses, can be substantially different from the more appropriate time-average and ensemble-average interatomic distances. Using crystallographic B-factors, one can deduce corrections, which have so far been applied exclusively to small molecules, to obtain correct average distances as a function of the type of atomic motion. Here, using 4774 high-quality protein X-ray structures, we study the significance of such corrections for different types of atomic motion. Importantly, we show that for distances shorter than 5 Å, corrections greater than 0.5 Å may apply, especially for noncorrelated or anticorrelated motion. For example, 14% of the studied structures have at least one pair of atoms with a correction of ≥ 0.5 Å in the case of noncorrelated motion. Using molecular dynamics simulations of villin headpiece, ubiquitin, and SH3 domain unit cells, we demonstrate that the majority of average interatomic distances in these proteins agree with noncorrelated corrections, suggesting that such deviations may be truly relevant. Importantly, we demonstrate that the corrections do not significantly affect stereochemistry and the overall quality of final refined X-ray structures, but can provide marked improvements in starting unrefined models obtained from low-resolution X-ray data. Finally, we illustrate the potential mechanistic and biological significance of the calculated corrections for KcsA ion channel and show that they provide indirect evidence that motions in its selectivity filter are highly correlated.

Immunoglobulin Structure Exhibits Control over CDR Motion

Motions of the IgG structure are evaluated using normal mode analysis of an elastic network model to detect hinges, the dominance of low frequency modes, and the most important internal motions. One question we seek to answer is whether or not IgG hinge motions facilitate antigen binding. We also evaluate the protein crystal and packing effects on the experimental temperature factors and disorder predictions. We find that the effects of the protein environment on the crystallographic temperature factors may be misleading for evaluating specific functional motions of IgG. The extent of motion of the antigen binding domains is computed to show their large spatial sampling. We conclude that the IgG structure is specifically designed to facilitate large excursions of the antigen binding domains. Normal modes are shown as capable of computationally evaluating the hinge motions and the spatial sampling by the structure. The antigen binding loops and the major hinge appear to behave similarly to the rest of the structure when we consider the dominance of the low frequency modes and the extent of internal motion. The full IgG structure has a lower spectral dimension than individual F_ab domains, pointing to more efficient information transfer through the antibody than through each domain. This supports the claim that the IgG structure is specifically constructed to facilitate antigen binding by coupling motion of the antigen binding loops with the large scale hinge motions.

Structure-based design, synthesis, and structure-activity relationship studies of HIV-1 protease inhibitors incorporating phenyloxazolidinones

A series of new HIV-1 protease inhibitors with the hydroxyethylamine core and different phenyloxazolidinone P2 ligands were designed and synthesized. Variation of phenyl substitutions at the P2 and P2' moieties significantly affected the binding affinity and antiviral potency of the inhibitors. In general, compounds with 2- and 4-substituted phenyloxazolidinones at P2 exhibited lower binding affinities than 3-substituted analogues. Crystal structure analyses of ligand-enzyme complexes revealed different binding modes for 2- and 3-substituted P2 moieties in the protease S2 binding pocket, which may explain their different binding affinities. Several compounds with 3-substituted P2 moieties demonstrated picomolar binding affinity and low nanomolar antiviral potency against patient-derived viruses from HIV-1 clades A, B, and C, and most retained potency against drug-resistant viruses. Further optimization of these compounds using structure-based design may lead to the development of novel protease inhibitors with improved activity against drug-resistant strains of HIV-1.

Normal mode analysis and applications in biological physics

Normal mode analysis has become a popular and often used theoretical tool in the study of functional motions in enzymes, viruses, and large protein assemblies. The use of normal modes in the study of these motions is often extremely fruitful since many of the functional motions of large proteins can be described using just a few normal modes which are intimately related to the overall structure of the protein. In this review, we present a broad overview of several popular methods used in the study of normal modes in biological physics including continuum elastic theory, the elastic network model, and a new all-atom method, recently developed, which is capable of computing a subset of the low frequency vibrational modes exactly. After a review of the various methods, we present several examples of applications of normal modes in the study of functional motions, with an emphasis on viral capsids.

Determination of ensemble-average pairwise root mean-square deviation from experimental B-factors

Root mean-square deviation (RMSD) after roto-translational least-squares fitting is a measure of global structural similarity of macromolecules used commonly. On the other hand, experimental x-ray B-factors are used frequently to study local structural heterogeneity and dynamics in macromolecules by providing direct information about root mean-square fluctuations (RMSF) that can also be calculated from molecular dynamics simulations. We provide a mathematical derivation showing that, given a set of conservative assumptions, a root mean-square ensemble-average of an all-against-all distribution of pairwise RMSD for a single molecular species, <RMSD(2)>(1/2), is directly related to average B-factors (<B>) and <RMSF(2)>(1/2). We show this relationship and explore its limits of validity on a heterogeneous ensemble of structures taken from molecular dynamics simulations of villin headpiece generated using distributed-computing techniques and the Folding@Home cluster. Our results provide a basis for quantifying global structural diversity of macromolecules in crystals directly from x-ray experiments, and we show this on a large set of structures taken from the Protein Data Bank. In particular, we show that the ensemble-average pairwise backbone RMSD for a microscopic ensemble underlying a typical protein x-ray structure is approximately 1.1 A, under the assumption that the principal contribution to experimental B-factors is conformational variability.

All-atom normal-mode analysis reveals an RNA-induced allostery in a bacteriophage coat protein

Assembly of the T=3 bacteriophage MS2 is initiated by the binding of a 19 nucleotide RNA stem loop from within the phage genome to a symmetric coat protein dimer. This binding event effects a folding of the FG loop in one of the protein subunits of the dimer and results in the formation of an asymmetric dimer. Since both the symmetric and asymmetric forms of the dimer are needed for the assembly of the protein container, this allosteric switch plays an important role in the life cycle of the phage. We provide here details of an all-atom normal-mode analysis of this allosteric effect. The results suggest that asymmetric contacts between the A -duplex RNA phosphodiester backbone of the stem loop with the EF loop in one coat protein subunit results in an increased dynamic behavior of its FG loop. The four lowest-frequency modes, which encompass motions predominantly on the FG loops, account for over 90% of the increased dynamic behavior due to a localization of the vibrational pattern on a single FG loop. Finally, we show that an analysis of the allosteric effect using an elastic network model fails to predict this localization effect, highlighting the importance of using an all-atom full force field method for this problem.

On the relationship between diffraction patterns and motions in macromolecular crystals

The quality of many macromolecular crystal structures published recently has been enhanced through the use of new methods for treating the effects of molecular motion and disorder on diffraction patterns, among them a technique called translation, libration, screw-axis (TLS) parameterization. TLS parameterization rationalizes those effects in terms of domain-scale, rigid-body motions and, interestingly, the models for molecular motion that emerge when macromolecular diffraction data are analyzed this way often make sense biochemically. Here it is pointed out that all such models should be treated with caution until it is shown that they are consistent with the diffuse scatter produced by the crystals that provided the diffraction data from which they derive.

REACH coarse-grained normal mode analysis of protein dimer interaction dynamics

The REACH (realistic extension algorithm via covariance Hessian) coarse-grained biomolecular simulation method is a self-consistent multiscale approach directly mapping atomistic molecular dynamics simulation results onto a residue-scale model. Here, REACH is applied to calculate the dynamics of protein-protein interactions. The intra- and intermolecular fluctuations and the intermolecular vibrational densities of states derived from atomistic molecular dynamics are well reproduced by the REACH normal modes. The phonon dispersion relations derived from the REACH lattice dynamics model of crystalline ribonuclease A are also in satisfactory agreement with the corresponding all-atom results. The REACH model demonstrates that increasing dimer interaction strength decreases the translational and rotational intermolecular vibrational amplitudes, while their vibrational frequencies are relatively unaffected. A comparative study of functionally interacting biological dimers with crystal dimers, which are formed artificially via crystallization, reveals a relation between their static structures and the interprotein dynamics: i.e., the consequence of the extensive interfaces of biological dimers is reduction of the intermonomer translational and rotational amplitudes, but not the frequencies.

All-atom contact model for understanding protein dynamics from crystallographic B-factors

An all-atom local contact model is described that can be used to predict protein motions underlying isotropic crystallographic B-factors. It uses a mean-field approximation to represent the motion of an atom in a harmonic potential generated by the surrounding atoms resting at their equilibrium positions. Based on a 400-ns molecular dynamics simulation of ubiquitin in explicit water, it is found that each surrounding atom stiffens the spring constant by a term that on average scales exponentially with the interatomic distance. This model combines features of the local density model by Halle and the local contact model by Zhang and Brüschweiler. When applied to a nonredundant set of 98 ultra-high resolution protein structures, an average correlation coefficient of 0.75 is obtained for all atoms. The systematic inclusion of crystal contact contributions and fraying effects is found to enhance the performance substantially. Because the computational cost of the local contact model scales linearly with the number of protein atoms, it is applicable to proteins of any size for the prediction of B-factors of both backbone and side-chain atoms. The model performs as well as or better than several other models tested, such as rigid-body motional models, the local density model, and various forms of the elastic network model. It is concluded that at the currently achievable level of accuracy, collective intramolecular motions are not essential for the interpretation of B-factors.

Relative stabilities of conserved and non-conserved structures in the OB-fold superfamily

The OB-fold is a diverse structure superfamily based on a beta-barrel motif that is often supplemented with additional non-conserved secondary structures. Previous deletion mutagenesis and NMR hydrogen exchange studies of three OB-fold proteins showed that the structural stabilities of sites within the conserved beta-barrels were larger than sites in non-conserved segments. In this work we examined a database of 80 representative domain structures currently classified as OB-folds, to establish the basis of this effect. Residue-specific values were obtained for the number of Calpha-Calpha distance contacts, sequence hydrophobicities, crystallographic B-factors, and theoretical B-factors calculated from a Gaussian Network Model. All four parameters point to a larger average flexibility for the non-conserved structures compared to the conserved beta-barrels. The theoretical B-factors and contact densities show the highest sensitivity. Our results suggest a model of protein structure evolution in which novel structural features develop at the periphery of conserved motifs. Core residues are more resistant to structural changes during evolution since their substitution would disrupt a larger number of interactions. Similar factors are likely to account for the differences in stability to unfolding between conserved and non-conserved structures.

Building alternate protein structures using the elastic network model

We describe a method for efficiently generating ensembles of alternate, all-atom protein structures that (a) differ significantly from the starting structure, (b) have good stereochemistry (bonded geometry), and (c) have good steric properties (absence of atomic overlap). The method uses reconstruction from a series of backbone framework structures that are obtained from a modified elastic network model (ENM) by perturbation along low-frequency normal modes. To ensure good quality backbone frameworks, the single force parameter ENM is modified by introducing two more force parameters to characterize the interaction between the consecutive carbon alphas and those within the same secondary structure domain. The relative stiffness of the three parameters is parameterized to reproduce B-factors, while maintaining good bonded geometry. After parameterization, violations of experimental Calpha-Calpha distances and Calpha-Calpha-Calpha pseudo angles along the backbone are reduced to less than 1%. Simultaneously, the average B-factor correlation coefficient improves to R = 0.77. Two applications illustrate the potential of the approach. (1) 102,051 protein backbones spanning a conformational space of 15 A root mean square deviation were generated from 148 nonredundant proteins in the PDB database, and all-atom models with minimal bonded and nonbonded violations were produced from this ensemble of backbone structures using the SCWRL side chain building program. (2) Improved backbone templates for homology modeling. Fifteen query sequences were each modeled on two targets. For each of the 30 target frameworks, dozens of improved templates could be produced In all cases, improved full atom homology models resulted, of which 50% could be identified blind using the D-Fire statistical potential.

HIV-1 protease inhibitors from inverse design in the substrate envelope exhibit subnanomolar binding to drug-resistant variants

The acquisition of drug-resistant mutations by infectious pathogens remains a pressing health concern, and the development of strategies to combat this threat is a priority. Here we have applied a general strategy, inverse design using the substrate envelope, to develop inhibitors of HIV-1 protease. Structure-based computation was used to design inhibitors predicted to stay within a consensus substrate volume in the binding site. Two rounds of design, synthesis, experimental testing, and structural analysis were carried out, resulting in a total of 51 compounds. Improvements in design methodology led to a roughly 1000-fold affinity enhancement to a wild-type protease for the best binders, from a Ki of 30-50 nM in round one to below 100 pM in round two. Crystal structures of a subset of complexes revealed a binding mode similar to each design that respected the substrate envelope in nearly all cases. All four best binders from round one exhibited broad specificity against a clinically relevant panel of drug-resistant HIV-1 protease variants, losing no more than 6-13-fold affinity relative to wild type. Testing a subset of second-round compounds against the panel of resistant variants revealed three classes of inhibitors: robust binders (maximum affinity loss of 14-16-fold), moderate binders (35-80-fold), and susceptible binders (greater than 100-fold). Although for especially high-affinity inhibitors additional factors may also be important, overall, these results suggest that designing inhibitors using the substrate envelope may be a useful strategy in the development of therapeutics with low susceptibility to resistance.

Computational design and experimental study of tighter binding peptides to an inactivated mutant of HIV-1 protease

Drug resistance in HIV-1 protease, a barrier to effective treatment, is generally caused by mutations in the enzyme that disrupt inhibitor binding but still allow for substrate processing. Structural studies with mutant, inactive enzyme, have provided detailed information regarding how the substrates bind to the protease yet avoid resistance mutations; insights obtained inform the development of next generation therapeutics. Although structures have been obtained of complexes between substrate peptide and inactivated (D25N) protease, thermodynamic studies of peptide binding have been challenging due to low affinity. Peptides that bind tighter to the inactivated protease than the natural substrates would be valuable for thermodynamic studies as well as to explore whether the structural envelope observed for substrate peptides is a function of weak binding. Here, two computational methods-namely, charge optimization and protein design-were applied to identify peptide sequences predicted to have higher binding affinity to the inactivated protease, starting from an RT-RH derived substrate peptide. Of the candidate designed peptides, three were tested for binding with isothermal titration calorimetry, with one, containing a single threonine to valine substitution, measured to have more than a 10-fold improvement over the tightest binding natural substrate. Crystal structures were also obtained for the same three designed peptide complexes; they show good agreement with computational prediction. Thermodynamic studies show that binding is entropically driven, more so for designed affinity enhanced variants than for the starting substrate. Structural studies show strong similarities between natural and tighter-binding designed peptide complexes, which may have implications in understanding the molecular mechanisms of drug resistance in HIV-1 protease.

Intrinsic motions along an enzymatic reaction trajectory

The mechanisms by which enzymes achieve extraordinary rate acceleration and specificity have long been of key interest in biochemistry. It is generally recognized that substrate binding coupled to conformational changes of the substrate-enzyme complex aligns the reactive groups in an optimal environment for efficient chemistry. Although chemical mechanisms have been elucidated for many enzymes, the question of how enzymes achieve the catalytically competent state has only recently become approachable by experiment and computation. Here we show crystallographic evidence for conformational substates along the trajectory towards the catalytically competent 'closed' state in the ligand-free form of the enzyme adenylate kinase. Molecular dynamics simulations indicate that these partially closed conformations are sampled in nanoseconds, whereas nuclear magnetic resonance and single-molecule fluorescence resonance energy transfer reveal rare sampling of a fully closed conformation occurring on the microsecond-to-millisecond timescale. Thus, the larger-scale motions in substrate-free adenylate kinase are not random, but preferentially follow the pathways that create the configuration capable of proficient chemistry. Such preferred directionality, encoded in the fold, may contribute to catalysis in many enzymes.

Mutational analysis of the purine riboswitch aptamer domain

The purine riboswitch is one of a number of mRNA elements commonly found in the 5'-untranslated region capable of controlling expression in a cis-fashion via its ability to directly bind small-molecule metabolites. Extensive biochemical and structural analysis of the nucleobase-binding domain of the riboswitch, referred to as the aptamer domain, has revealed that the mRNA recognizes its cognate ligand using an intricately folded three-way junction motif that completely encapsulates the ligand. High-affinity binding of the purine nucleobase is facilitated by a distal loop-loop interaction that is conserved between both the adenine and guanine riboswitches. To understand the contribution of conserved nucleotides in both the three-way junction and the loop-loop interaction of this RNA, we performed a detailed mutagenic survey of these elements in the context of an adenine-responsive variant of the xpt-pbuX guanine riboswitch from Bacillus subtilis. The varying ability of these mutants to bind ligand as measured by isothermal titration calorimetry uncovered the conserved nucleotides whose identity is required for purine binding. Crystallographic analysis of the bound form of five mutants and chemical probing of their free state demonstrate that the identity of several universally conserved nucleotides is not essential for formation of the RNA-ligand complex but rather for maintaining a binding-competent form of the free RNA. These data show that conservation patterns in riboswitches arise from a combination of formation of the ligand-bound complex, promoting an open form of the free RNA, and participating in the secondary structural switch with the expression platform.

Crystallography: crystallographic evidence for deviating C3b structure

Activation of the protein C3 into C3b in the complement pathway is a crucial step in the complement immune response against pathogenic, immunogenic and apoptotic particles. Ajees et al. describe a crystal structure for C3b that deviates from the one reported by Janssen et al. and by Wiesmann et al.. We have reanalysed the data deposited by Ajees et al. and have discovered features that are inconsistent with the known physical properties of macromolecular structures and their diffraction data. Our findings therefore call into question the crystal structure for C3b reported by Ajees et al..

Design and synthesis of HIV-1 protease inhibitors incorporating oxazolidinones as P2/P2' ligands in pseudosymmetric dipeptide isosteres

A series of novel HIV-1 protease inhibitors based on two pseudosymmetric dipeptide isosteres have been synthesized and evaluated. The inhibitors were designed by incorporating N-phenyloxazolidinone-5-carboxamides into the hydroxyethylene and (hydroxyethyl)hydrazine dipeptide isosteres as P2 and P2' ligands. Compounds with (S)-phenyloxazolidinones attached at a position proximal to the central hydroxyl group showed low nM inhibitory activities against wild-type HIV-1 protease. Selected compounds were further evaluated for their inhibitory activities against a panel of multidrug-resistant protease variants and for their antiviral potencies in MT-4 cells. The crystal structures of lopinavir (LPV) and two new inhibitors containing phenyloxazolidinone-based ligands in complex with wild-type HIV-1 protease have been determined. A comparison of the inhibitor-protease structures with the LPV-protease structure provides valuable insight into the binding mode of the new inhibitors to the protease enzyme. Based on the crystal structures and knowledge of structure-activity relationships, new inhibitors can be designed with enhanced enzyme inhibitory and antiviral potencies.

Design of mutation-resistant HIV protease inhibitors with the substrate envelope hypothesis

There is a clinical need for HIV protease inhibitors that can evade resistance mutations. One possible approach to designing such inhibitors relies upon the crystallographic observation that the substrates of HIV protease occupy a rather constant region within the binding site. In particular, it has been hypothesized that inhibitors which lie within this region will tend to resist clinically relevant mutations. The present study offers the first prospective evaluation of this hypothesis, via computational design of inhibitors predicted to conform to the substrate envelope, followed by synthesis and evaluation against wild-type and mutant proteases, as well as structural studies of complexes of the designed inhibitors with HIV protease. The results support the utility of the substrate envelope hypothesis as a guide to the design of robust protease inhibitors.

Crystal structure of lysine sulfonamide inhibitor reveals the displacement of the conserved flap water molecule in human immunodeficiency virus type 1 protease

Human immunodeficiency virus type 1 (HIV-1) protease has been continuously evolving and developing resistance to all of the protease inhibitors. This requires the development of new inhibitors that bind to the protease in a novel fashion. Most of the inhibitors that are on the market are peptidomimetics, where a conserved water molecule mediates hydrogen bonding interactions between the inhibitors and the flaps of the protease. Recently a new class of inhibitors, lysine sulfonamides, was developed to combat the resistant variants of HIV protease. Here we report the crystal structure of a lysine sulfonamide. This inhibitor binds to the active site of HIV-1 protease in a novel manner, displacing the conserved water and making extensive hydrogen bonds with every region of the active site.

Druggability of SCF ubiquitin ligase-protein interfaces

The unique mechanism of the SCF ubiquitin ligase poses a challenge to drug discovery. A central enzymatic small molecule-binding active site is not evident in this multisubunit protein enzyme, as is the case with kinases or proteases. Instead, the SCF ligase seems to accomplish ubiquitylation through a series of cooperative movements dependent on the protein interfaces between its components and its substrate. Activity-modulating small molecules, therefore, need to interact with these protein interfaces. The three-dimensional structure of these interfaces may be the key asset in determining their suitability for small molecule binding. Computational tools and a systematic approach described in detail here can assess the "druggability" of an SCF ligase before the investment of effort in high-throughput screening (HTS), structure-based drug design (SBBD), or virtual library screening (VLS).

Normal mode refinement of anisotropic thermal parameters for a supramolecular complex at 3.42-A crystallographic resolution

Here we report a normal-mode-based protocol for modeling anisotropic thermal motions of proteins in x-ray crystallographic refinement. The foundation for this protocol is a recently developed elastic normal mode analysis that produces much more accurate eigenvectors without the tip effect. The effectiveness of the procedure is demonstrated on the refinement of a 3.42-A structure of formiminotransferase cyclodeaminase, a 0.5-MDa homooctameric enzyme. Using an order of magnitude fewer adjustable thermal parameters than the conventional isotropic refinement, this protocol resulted in a decrease of the values of R(cryst) and R(free) and improvements of the density map. Several poorly resolved regions in the original isotropically refined structure became clearer so that missing side chains were fitted easily and mistraced backbone was corrected. Moreover, the distribution of anisotropic thermal ellipsoids revealed functionally important structure flexibility. This normal-mode-based refinement is an effective way of describing anisotropic thermal motions in x-ray structures and is particularly attractive for the refinement of very large and flexible supramolecular complexes at moderate resolutions.