Conformational substates in enzyme mechanism: the 120 K structure of alpha-lytic protease at 1.5 A resolution

Highly scalable maximum likelihood and conjugate Bayesian inference for ERGMs on graph sets with equivalent vertices

The exponential family random graph modeling (ERGM) framework provides a highly flexible approach for the statistical analysis of networks (i.e., graphs). As ERGMs with dyadic dependence involve normalizing factors that are extremely costly to compute, practical strategies for ERGMs inference generally employ a variety of approximations or other workarounds. Markov Chain Monte Carlo maximum likelihood (MCMC MLE) provides a powerful tool to approximate the maximum likelihood estimator (MLE) of ERGM parameters, and is generally feasible for typical models on single networks with as many as a few thousand nodes. MCMC-based algorithms for Bayesian analysis are more expensive, and high-quality answers are challenging to obtain on large graphs. For both strategies, extension to the pooled case—in which we observe multiple networks from a common generative process—adds further computational cost, with both time and memory scaling linearly in the number of graphs. This becomes prohibitive for large networks, or cases in which large numbers of graph observations are available. Here, we exploit some basic properties of the discrete exponential families to develop an approach for ERGM inference in the pooled case that (where applicable) allows an arbitrarily large number of graph observations to be fit at no additional computational cost beyond preprocessing the data itself. Moreover, a variant of our approach can also be used to perform Bayesian inference under conjugate priors, again with no additional computational cost in the estimation phase. The latter can be employed either for single graph observations, or for observations from graph sets. As we show, the conjugate prior is easily specified, and is well-suited to applications such as regularization. Simulation studies show that the pooled method leads to estimates with good frequentist properties, and posterior estimates under the conjugate prior are well-behaved. We demonstrate the usefulness of our approach with applications to pooled analysis of brain functional connectivity networks and to replicated x-ray crystal structures of hen egg-white lysozyme.

Evolutionary repurposing of a sulfatase: A new Michaelis complex leads to efficient transition state charge offset

The recruitment and evolutionary optimization of promiscuous enzymes is key to the rapid adaptation of organisms to changing environments. Our understanding of the precise mechanisms underlying enzyme repurposing is, however, limited: What are the active-site features that enable the molecular recognition of multiple substrates with contrasting catalytic requirements? To gain insights into the molecular determinants of adaptation in promiscuous enzymes, we performed the laboratory evolution of an arylsulfatase to improve its initially weak phenylphosphonate hydrolase activity. The evolutionary trajectory led to a 100,000-fold enhancement of phenylphosphonate hydrolysis, while the native sulfate and promiscuous phosphate mono- and diester hydrolyses were only marginally affected (≤50-fold). Structural, kinetic, and in silico characterizations of the evolutionary intermediates revealed that two key mutations, T50A and M72V, locally reshaped the active site, improving access to the catalytic machinery for the phosphonate. Measured transition state (TS) charge changes along the trajectory suggest the creation of a new Michaelis complex (E•S, enzyme-substrate), with enhanced leaving group stabilization in the TS for the promiscuous phosphonate (β_leavinggroup from -1.08 to -0.42). Rather than altering the catalytic machinery, evolutionary repurposing was achieved by fine-tuning the molecular recognition of the phosphonate in the Michaelis complex, and by extension, also in the TS. This molecular scenario constitutes a mechanistic alternative to adaptation solely based on enzyme flexibility and conformational selection. Instead, rapid functional transitions between distinct chemical reactions rely on the high reactivity of permissive active-site architectures that allow multiple substrate binding modes.

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.

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.

Predicting X-ray diffuse scattering from translation-libration-screw structural ensembles

Identifying the intramolecular motions of proteins and nucleic acids is a major challenge in macromolecular X-ray crystallography. Because Bragg diffraction describes the average positional distribution of crystalline atoms with imperfect precision, the resulting electron density can be compatible with multiple models of motion. Diffuse X-ray scattering can reduce this degeneracy by reporting on correlated atomic displacements. Although recent technological advances are increasing the potential to accurately measure diffuse scattering, computational modeling and validation tools are still needed to quantify the agreement between experimental data and different parameterizations of crystalline disorder. A new tool, phenix.diffuse, addresses this need by employing Guinier's equation to calculate diffuse scattering from Protein Data Bank (PDB)-formatted structural ensembles. As an example case, phenix.diffuse is applied to translation-libration-screw (TLS) refinement, which models rigid-body displacement for segments of the macromolecule. To enable the calculation of diffuse scattering from TLS-refined structures, phenix.tls_as_xyz builds multi-model PDB files that sample the underlying T, L and S tensors. In the glycerophosphodiesterase GpdQ, alternative TLS-group partitioning and different motional correlations between groups yield markedly dissimilar diffuse scattering maps with distinct implications for molecular mechanism and allostery. These methods demonstrate how, in principle, X-ray diffuse scattering could extend macromolecular structural refinement, validation and analysis.

One Crystal, Two Temperatures: Cryocooling Penalties Alter Ligand Binding to Transient Protein Sites

Interrogating fragment libraries by X-ray crystallography is a powerful strategy for discovering allosteric ligands for protein targets. Cryocooling of crystals should theoretically increase the fraction of occupied binding sites and decrease radiation damage. However, it might also perturb protein conformations that can be accessed at room temperature. Using data from crystals measured consecutively at room temperature and at cryogenic temperature, we found that transient binding sites could be abolished at the cryogenic temperatures employed by standard approaches. Changing the temperature at which the crystallographic data was collected could provide a deliberate perturbation to the equilibrium of protein conformations and help to visualize hidden sites with great potential to allosterically modulate protein function.

Integrative, dynamic structural biology at atomic resolution--it's about time

Biomolecules adopt a dynamic ensemble of conformations, each with the potential to interact with binding partners or perform the chemical reactions required for a multitude of cellular functions. Recent advances in X-ray crystallography, nuclear magnetic resonance (NMR) spectroscopy and other techniques are helping us realize the dream of seeing--in atomic detail--how different parts of biomolecules shift between functional substates using concerted motions. Integrative structural biology has advanced our understanding of the formation of large macromolecular complexes and how their components interact in assemblies by leveraging data from many low-resolution methods. Here, we review the growing opportunities for integrative, dynamic structural biology at the atomic scale, contending there is increasing synergistic potential between X-ray crystallography, NMR and computer simulations to reveal a structural basis for protein conformational dynamics at high resolution.

E pluribus unum, no more: from one crystal, many conformations

Several distinct computational approaches have recently been implemented to represent conformational heterogeneity from X-ray crystallography datasets that are averaged in time and space. As these modeling methods mature, newly discovered alternative conformations are being used to derive functional protein mechanisms. Room temperature X-ray data collection is emerging as a key variable for sampling functionally relevant conformations also observed in solution studies. Although concerns about radiation damage are warranted with higher temperature data collection, 'diffract and destroy' strategies on X-ray free electron lasers may permit radiation damage-free data collection. X-ray crystallography need not be confined to 'static unique snapshots'; these experimental and computational advances are revealing how the many conformations populated within a single crystal are used in biological mechanisms.

Automated identification of functional dynamic contact networks from X-ray crystallography

Protein function often depends on the exchange between conformational substates. Allosteric ligand binding or distal mutations can stabilize specific active site conformations and consequently alter protein function. In addition to comparing independently determined X-ray crystal structures, alternative conformations observed at low levels of electron density have the potential to provide mechanistic insights into conformational dynamics. Here, we report a new multi-conformer contact network algorithm (CONTACT) that identifies networks of conformationally heterogeneous residues directly from high-resolution X-ray crystallography data. Contact networks in Escherichia coli dihydrofolate reductase (ecDHFR) predict the long-range pattern of NMR chemical shift perturbations of an allosteric mutation. A comparison of contact networks in wild type and mutant ecDHFR suggests how mutations that alter optimized networks of coordinated motions can impair catalytic function. Thus, CONTACT-guided mutagenesis will allow the structure-dynamics-function relationship to be exploited in protein engineering and design.

X-ray evidence of a native state with increased compactness populated by tryptophan-less B. licheniformis β-lactamase

β-lactamases confer antibiotic resistance, one of the most serious world-wide health problems, and are an excellent theoretical and experimental model in the study of protein structure, dynamics and evolution. Bacillus licheniformis exo-small penicillinase (ESP) is a Class-A β-lactamase with three tryptophan residues located in the protein core. Here, we report the 1.7-Å resolution X-ray structure, catalytic parameters, and thermodynamic stability of ESP(ΔW), an engineered mutant of ESP in which phenylalanine replaces the wild-type tryptophan residues. The structure revealed no qualitative conformational changes compared with thirteen previously reported structures of B. licheniformis β-lactamases (RMSD = 0.4-1.2 Å). However, a closer scrutiny showed that the mutations result in an overall more compact structure, with most atoms shifted toward the geometric center of the molecule. Thus, ESP(ΔW) has a significantly smaller radius of gyration (R(g)) than the other B. licheniformis β-lactamases characterized so far. Indeed, ESP(ΔW) has the smallest R(g) among 126 Class-A β-lactamases in the Protein Data Bank (PDB). Other measures of compactness, like the number of atoms in fixed volumes and the number and average of noncovalent distances, confirmed the effect. ESP(ΔW) proves that the compactness of the native state can be enhanced by protein engineering and establishes a new lower limit to the compactness of the Class-A β-lactamase fold. As the condensation achieved by the native state is a paramount notion in protein folding, this result may contribute to a better understanding of how the sequence determines the conformational variability and thermodynamic stability of a given fold.

Accessing protein conformational ensembles using room-temperature X-ray crystallography

Modern protein crystal structures are based nearly exclusively on X-ray data collected at cryogenic temperatures (generally 100 K). The cooling process is thought to introduce little bias in the functional interpretation of structural results, because cryogenic temperatures minimally perturb the overall protein backbone fold. In contrast, here we show that flash cooling biases previously hidden structural ensembles in protein crystals. By analyzing available data for 30 different proteins using new computational tools for electron-density sampling, model refinement, and molecular packing analysis, we found that crystal cryocooling remodels the conformational distributions of more than 35% of side chains and eliminates packing defects necessary for functional motions. In the signaling switch protein, H-Ras, an allosteric network consistent with fluctuations detected in solution by NMR was uncovered in the room-temperature, but not the cryogenic, electron-density maps. These results expose a bias in structural databases toward smaller, overpacked, and unrealistically unique models. Monitoring room-temperature conformational ensembles by X-ray crystallography can reveal motions crucial for catalysis, ligand binding, and allosteric regulation.

Mining electron density for functionally relevant protein polysterism in crystal structures

This review focuses on conceptual and methodological advances in our understanding and characterization of the conformational heterogeneity of proteins. Focusing on X-ray crystallography, we describe how polysterism, the interconversion of pre-existing conformational substates, has traditionally been analyzed by comparing independent crystal structures or multiple chains within a single crystal asymmetric unit. In contrast, recent studies have focused on mining electron density maps to reveal previously ‘hidden’ minor conformational substates. Functional tests of the importance of minor states suggest that evolutionary selection shapes the entire conformational landscape, including uniquely configured conformational substates, the relative distribution of these substates, and the speed at which the protein can interconvert between them. An increased focus on polysterism may shape the way protein structure and function is studied in the coming years.

Computational identification of slow conformational fluctuations in proteins

Conformational flexibility of proteins has been linked to their designated functions. Slow conformational fluctuations occurring at the microsecond to millisecond time scale, in particular, have recently attracted considerable interest in connection to the mechanism of enzyme catalysis. Computational methods are providing valuable insights into the connection between protein structure, flexibility, and function. In this report, we present studies on identification and characterization of microsecond flexibility of ubiquitin, based on quasi-harmonic analysis (QHA) and normal-mode analysis (NMA). The results indicate that the slowest 10 QHA modes, computed from the 0.5 mus molecular dynamics ensemble, contribute over 78% of all motions. The identified slow movements show over 75% similarity with the conformational fluctuations observed in nuclear magnetic resonance ensemble and also agree with displacements in the set of X-ray structures. The slowest modes show high flexibility in the beta1-beta2, alpha1-beta3, and beta3-beta4 loop regions, with functional implications in the mechanism of binding other proteins. NMA of ubiquitin structures was not able to reproduce the long time scale fluctuations, as they were found to strongly depend on the reference structures. Further, conformational fluctuations coupled to the cis/trans isomerization reaction catalyzed by the enzyme cyclophilin A (CypA), occurring at the microsecond to millisecond time scale, have also been identified and characterized on the basis of QHA of conformations sampled along the reaction pathway. The results indicate that QHA covers the same conformational landscape as the experimentally observed CypA flexibility. Overall, the identified slow conformational fluctuations in ubiquitin and CypA indicate that the intrinsic flexibility of these proteins is closely linked to their designated functions.

Modeling discrete heterogeneity in X-ray diffraction data by fitting multi-conformers

The native state of a protein is regarded to be an ensemble of conformers, which allows association with binding partners. While some of this structural heterogeneity is retained upon crystallization, reliably extracting heterogeneous features from diffraction data has remained a challenge. In this study, a new algorithm for the automatic modelling of discrete heterogeneity is presented. At high resolution, the authors' single multi-conformer model, with correlated structural features to represent heterogeneity, shows improved agreement with the diffraction data compared with a single-conformer model. The model appears to be representative of the set of structures present in the crystal. In contrast, below 2 A resolution representing ambiguous electron density by correlated multi-conformers in a single model does not yield better agreement with the experimental data. Consistent with previous studies, this suggests that variability in multi-conformer models at lower resolution levels reflects uncertainty more than coordinated motion.

Exploring structural variability in X-ray crystallographic models using protein local optimization by torsion-angle sampling

Modeling structural variability is critical for understanding protein function and for modeling reliable targets for in silico docking experiments. Because of the time-intensive nature of manual X-ray crystallographic refinement, automated refinement methods that thoroughly explore conformational space are essential for the systematic construction of structurally variable models. Using five proteins spanning resolutions of 1.0-2.8 A, it is demonstrated how torsion-angle sampling of backbone and side-chain libraries with filtering against both the chemical energy, using a modern effective potential, and the electron density, coupled with minimization of a reciprocal-space X-ray target function, can generate multiple structurally variable models which fit the X-ray data well. Torsion-angle sampling as implemented in the Protein Local Optimization Program (PLOP) has been used in this work. Models with the lowest R(free) values are obtained when electrostatic and implicit solvation terms are included in the effective potential. HIV-1 protease, calmodulin and SUMO-conjugating enzyme illustrate how variability in the ensemble of structures captures structural variability that is observed across multiple crystal structures and is linked to functional flexibility at hinge regions and binding interfaces. An ensemble-refinement procedure is proposed to differentiate between variability that is a consequence of physical conformational heterogeneity and that which reflects uncertainty in the atomic coordinates.

Ensemble refinement of protein crystal structures: validation and application

X-ray crystallography typically uses a single set of coordinates and B factors to describe macromolecular conformations. Refinement of multiple copies of the entire structure has been previously used in specific cases as an alternative means of representing structural flexibility. Here, we systematically validate this method by using simulated diffraction data, and we find that ensemble refinement produces better representations of the distributions of atomic positions in the simulated structures than single-conformer refinements. Comparison of principal components calculated from the refined ensembles and simulations shows that concerted motions are captured locally, but that correlations dissipate over long distances. Ensemble refinement is also used on 50 experimental structures of varying resolution and leads to decreases in R(free) values, implying that improvements in the representation of flexibility observed for the simulated structures may apply to real structures. These gains are essentially independent of resolution or data-to-parameter ratio, suggesting that even structures at moderate resolution can benefit from ensemble refinement.

Subangstrom crystallography reveals that short ionic hydrogen bonds, and not a His-Asp low-barrier hydrogen bond, stabilize the transition state in serine protease catalysis

To address questions regarding the mechanism of serine protease catalysis, we have solved two X-ray crystal structures of alpha-lytic protease (alphaLP) that mimic aspects of the transition states: alphaLP at pH 5 (0.82 A resolution) and alphaLP bound to the peptidyl boronic acid inhibitor, MeOSuc-Ala-Ala-Pro-boroVal (0.90 A resolution). Based on these structures, there is no evidence of, or requirement for, histidine-flipping during the acylation step of the reaction. Rather, our data suggests that upon protonation of His57, Ser195 undergoes a conformational change that destabilizes the His57-Ser195 hydrogen bond, preventing the back-reaction. In both structures the His57-Asp102 hydrogen bond in the catalytic triad is a normal ionic hydrogen bond, and not a low-barrier hydrogen bond (LBHB) as previously hypothesized. We propose that the enzyme has evolved a network of relatively short hydrogen bonds that collectively stabilize the transition states. In particular, a short ionic hydrogen bond (SIHB) between His57 Nepsilon2 and the substrate's leaving group may promote forward progression of the TI1-to-acylenzyme reaction. We provide experimental evidence that refutes use of either a short donor-acceptor distance or a downfield 1H chemical shift as sole indicators of a LBHB.

Structure and dynamics of UDP-glucose pyrophosphorylase from Arabidopsis thaliana with bound UDP-glucose and UTP

The structure of the UDP-glucose pyrophosphorylase encoded by Arabidopsis thaliana gene At3g03250 has been solved to a nominal resolution of 1.86 Angstroms. In addition, the structure has been solved in the presence of the substrates/products UTP and UDP-glucose to nominal resolutions of 1.64 Angstroms and 1.85 Angstroms. The three structures revealed a catalytic domain similar to that of other nucleotidyl-glucose pyrophosphorylases with a carboxy-terminal beta-helix domain in a unique orientation. Conformational changes are observed between the native and substrate-bound complexes. The nucleotide-binding loop and the carboxy-terminal domain, including the suspected catalytically important Lys360, move in and out of the active site in a concerted fashion. TLS refinement was employed initially to model conformational heterogeneity in the UDP-glucose complex followed by the use of multiconformer refinement for the entire molecule. Normal mode analysis generated atomic displacement predictions in good agreement in magnitude and direction with the observed conformational changes and anisotropic displacement parameters generated by TLS refinement. The structures and the observed dynamic changes provide insight into the ordered mechanism of this enzyme and previously described oligomerization effects on catalytic activity.

Role of Protein Dynamics in Reaction Rate Enhancement by Enzymes

An integrated view of protein structure, dynamics, and function is emerging, where proteins are considered as dynamically active assemblies and internal motions are closely linked to function such as enzyme catalysis. Further, the motion of solvent bound to external regions of protein impacts internal motions and, therefore, protein function. Recently, we discovered a network of protein vibrations in enzyme cyclophilin A, coupled to its catalytic activity of peptidyl-prolyl cis-trans isomerization. Detailed studies suggest that this network, extending from surface regions to active site, is a conserved part of enzyme structure and has a role in promoting catalysis. In this report, theoretical investigations of concerted conformational fluctuations occurring on microsecond and longer time scales within the discovered network are presented. Using a new technique, kinetic energy was added to protein vibrational modes corresponding to conformational fluctuations in the network. The results reveal that protein dynamics promotes catalysis by altering transition state barrier crossing behavior of reaction trajectories. An increase in transmission coefficient and number of productive trajectories with increasing amounts of kinetic energy in vibrational modes is observed. Variations in active site enzyme-substrate interactions near transition state are found to be correlated with barrier recrossings. Simulations also showed that energy transferred from first solvation shell to surface residues impacts catalysis through network fluctuations. The detailed characterization of network presented here indicates that protein dynamics plays a role in rate enhancement by enzymes. Therefore, coupled networks in enzymes have wide implications in understanding allostericity and cooperative effects, as well as protein engineering and drug design.

Modeling correlated main-chain motions in proteins for flexible molecular recognition

We describe a new method for modeling protein and ligand main-chain flexibility, and show its ability to model flexible molecular recognition. The goal is to sample the full conformational space, including large-scale motions that typically cannot be reached in molecular dynamics simulations due to the computational intensity, as well as conformations that have not been observed yet by crystallography or NMR. A secondary goal is to assess the degree of flexibility consistent with protein-ligand recognition. Flexibility analysis of the target protein is performed using the graph-theoretic algorithm FIRST, which also identifies coupled networks of covalent and noncovalent bonds within the protein. The available conformations of the flexible regions are then explored with ROCK by random-walk sampling of the rotatable bonds. ROCK explores correlated motions by only sampling dihedral angles that preserve the coupled bond networks in the protein and generates conformers with good stereochemistry, without using a computationally expensive potential function. A representative set of the conformational ensemble generated this way can be used as targets for docking with SLIDE, which handles the flexibility of protein and ligand side-chains. The realism of this protein main-chain conformational sampling is assessed by comparison with time-resolved NMR studies of cyclophilin A motions. ROCK is also effective for modeling the flexibility of large cyclic and polycyclic ligands, as demonstrated for cyclosporin and zearalenol. The use of this combined approach to perform docking with main-chain flexibility is illustrated for the cyclophilin A-cyclosporin complex and the estrogen receptor in complex with zearalenol, while addressing the question of how much flexibility is allowed without hindering molecular recognition.

Cis/trans isomerization in HIV-1 capsid protein catalyzed by cyclophilin A: insights from computational and theoretical studies

A network of protein vibrations has recently been identified in the enzyme cyclophilin A (CypA) that is associated with its peptidyl-prolyl cis/trans isomerization activity of small peptide substrates. It has been suggested that this network may have a role in promoting the catalytic step during the isomerization reaction. This work presents the results from the characterization of this network during the isomerization of the Gly89-Pro90 peptide bond in the N-terminal domain of the capsid protein (CA(N)) from human immunodeficiency virus type 1 (HIV-1), which is a naturally occurring, biologically relevant protein substrate for CypA. A variety of computational and theoretical studies are utilized to investigate the protein dynamics of the CypA-CA(N) complex, at multiple time scales, during the isomerization step. The results provide insights into the detailed mechanism of isomerization and confirm the presence of previously reported network of protein vibrations coupled to the reaction. Conserved CypA residues at the complex interface and at positions distal to the interface form parts of this network. There is HIV-1 related medical interest in CypA; incorporation of CypA, complexed with the capsid protein, into the virion is required for the infectious activity of HIV-1. Interaction energy and dynamical cross-correlation calculations are used for a detailed investigation of the protein-protein interactions in the CypA-CA(N) complex. The results show that CA(N) residues His87-Ala-Gly-Pro-Ile-Ala92 form the majority of the interactions with CypA residues. New protein-protein interactions distal to the active site (CypA Arg148-CA(N) Gln95 and CypA Arg148-CA(N) Asn121) are also identified.

Helical Shifts Generate Two Distinct Conformers in the Atomic Resolution Structure of the CheA Phosphotransferase Domain from Thermotoga maritima

Helical histidine phosphotransferase (HPt) domains play a central role in many aspects of bacterial signal transduction. The 0.98 A resolution crystallographic structure of the amino-terminal HPt domain (P1) from the chemotaxis kinase CheA of Thermotoga maritima reveals a remarkable degree of structural heterogeneity within a four-helix bundle. Two of the four helices have alternate main-chain conformations that differ by a 1.3-1.7A shift along the bundle axis. These dual conformers were only resolved with atomic resolution diffraction data and their inclusion significantly improved refinement statistics. Neither conformer optimizes packing within the helical core, consistent with their nearly equal refined occupancies. Altered hydrogen bonding within an inter-helical loop may facilitate transition between conformers. Two discrete structural states rather than a continuum of closely related conformations indicates an energetic barrier to conversion between conformers in the crystal at 100K, although many more states are expected in solution at physiological temperatures. Anisotropic atomic thermal B factors within the two conformers indicate modest overall atomic displacement that is largest perpendicular to the helical bundle and not along the direction of apparent motion. Despite the conformational heterogeneity of P1 in the crystal at low temperature, the protein displays high thermal stability in solution (T(m)=100 degrees C). Addition of a variable C-terminal region that corresponds to a mobile helix in other CheA structures significantly narrows the temperature width of the unfolding transition and may affect domain dynamics. Helices that compose the kinase recognition site and contain the phospho-accepting His45 do not have alternate conformations. In this region, atomic resolution provides detailed structural parameters for a conserved hydrogen-bonding network that tunes the reactivity of His45. A neighboring glutamate (E67), essential for phosphotransferase activity hydrogen bonds directly to His45 N(delta1). E67 generates a negative electrostatic surface surrounding the reactive His that is conserved by most CheA kinases, but absent in related phosphotransferase proteins. The P1 conformations that we observe are likely relevant to other helical or coiled-coil proteins and may be important for generating switches in signaling processes.

The 0.83 A resolution crystal structure of alpha-lytic protease reveals the detailed structure of the active site and identifies a source of conformational strain

The crystal structure of the extracellular bacterial serine protease alpha-lytic protease (alphaLP) has been solved at 0.83 A resolution at pH 8. This ultra-high resolution structure allows accurate analysis of structural elements not possible with previous structures. Hydrogen atoms are visible, and confirm active-site hydrogen-bonding interactions expected for the apo enzyme. In particular, His57 N(delta1) participates in a normal hydrogen bond with Asp102 in the catalytic triad, with a hydrogen atom visible 0.83(+/-0.06)A from the His N(delta1). The catalytic Ser195 occupies two conformations, one corresponding to a population of His57 that is doubly protonated, the other to the singly protonated His57. Based on the occupancy of these conformations, the pKa of His57 is calculated to be approximately 8.8 when a sulfate ion occupies the active site. This 0.83 A structure has allowed critical analysis of geometric distortions within the structure. Interestingly, Phe228 is significantly distorted from planarity. The distortion of Phe228, buried in the core of the C-terminal domain, occurs at an estimated energetic cost of 4.1 kcal/mol. The conformational space for Phe228 is severely limited by the presence of Trp199, which prevents Phe228 from adopting the rotamer observed in many other chymotrypsin family members. In alphaLP, the only allowed rotamer leads to the deformation of Phe228 due to steric interactions with Thr181. We hypothesize that tight packing of co-evolved residues in this region, and the subsequent deformation of Phe228, contributes to the high cooperativity and large energetic barriers for folding and unfolding of alphaLP. The kinetic stability imparted by the large, cooperative unfolding barrier plays a critical role in extending the lifetime of the protease in its harsh environment.

Heterogeneity and Inaccuracy in Protein Structures Solved by X-Ray Crystallography

Proteins are dynamic molecules, exhibiting structural heterogeneity in the form of anisotropic motion and discrete conformational substates, often of functional importance. In protein structure determination by X-ray crystallography, the observed diffraction pattern results from the scattering of X-rays by an ensemble of heterogeneous molecules, ordered and oriented by packing in a crystal lattice. The majority of proteins diffract to resolutions where heterogeneity is difficult to identify and model, and are therefore approximated by a single, average conformation with isotropic variance. Here we show that disregarding structural heterogeneity introduces degeneracy into the structure determination process, as many single, isotropic models exist that explain the diffraction data equally well. The large differences among these models imply that the accuracy of crystallographic structures has been widely overestimated. Further, it suggests that analyses that depend on small differences in the relative positions of atoms may be flawed.

Assessment of the role of computations in structural biology

Computations are now an integrated part of structural biology and are used in data gathering, data processing, and data storage as well as in a full spectrum of theoretical pursuits. In this review, we focus on areas of great promise and call attention to important issues of internal consistency and error analysis.

Flexibility analysis of enzyme active sites by crystallographic temperature factors

Protein flexibility is inherent to protein structural behavior. Experimental evidence for protein flexibility is extensive both in solution and in the solid state. A major question is whether the flexibility observed in enzymes is simply an inherent property of proteins that must always be borne in mind or is essential for catalysis or substrate binding. The temperature factors or B-values, as determined crystallographically, are linearly related to the mean square displacement of an atom and give an indication of atomic flexibility in the crystalline state. In this paper, we describe the frequency distributions of the normalized B-factor (B'-factor) for the active site and non-active site residues in the selected 69 apo-enzymes. This analysis was performed over the entire sequences and for different structural subsets defined by the three-dimensional structure of proteins, as alpha-helices, beta-structures and coil conformation and buried and non-buried residues. The results show that in all cases, the active site residues predominantly occur in region of low B'-factor and the non-active site residues have a tendency to exist in the high B'-factor region. This observation suggests that the active site residues, in general, are less flexible than the non-active site residues and therefore the vibrational and the fast collective motions of the C(alpha) atoms of proteins appear not to have clear biological significance.

Structural basis for mobility in the 1.1 A crystal structure of the NG domain of Thermus aquaticus Ffh

The NG domain of the prokaryotic signal recognition protein Ffh is a two-domain GTPase that comprises part of the prokaryotic signal recognition particle (SRP) that functions in co-translational targeting of proteins to the membrane. The interface between the N and G domains includes two highly conserved sequence motifs and is adjacent in sequence and structure to one of the conserved GTPase signature motifs. Previous structural studies have shown that the relative orientation of the two domains is dynamic. The N domain of Ffh has been proposed to function in regulating the nucleotide-binding interactions of the G domain. However, biochemical studies suggest a more complex role for the domain in integrating communication between signal sequence recognition and interaction with receptor. Here, we report the structure of the apo NG GTPase of Ffh from Thermus aquaticus refined at 1.10 A resolution. Although the G domain is very well ordered in this structure, the N domain is less well ordered, reflecting the dynamic relationship between the two domains previously inferred. We demonstrate that the anisotropic displacement parameters directly visualize the underlying mobility between the two domains, and present a detailed structural analysis of the packing of the residues, including the critical alpha4 helix, that comprise the interface. Our data allows us to propose a structural explanation for the functional significance of sequence elements conserved at the N/G interface.

Reversible lattice repacking illustrates the temperature dependence of macromolecular interactions

Flash-freezing, which has become routine in macromolecular X-ray crystallography, causes the crystal to contract substantially. In the case of Escherichia coli beta-galactosidase the changes are reversible and are shown to be due to lattice repacking. On cooling, the area of the protein surface involved in lattice contacts increases by 50 %. There are substantial alterations in intermolecular contacts, these changes being dominated by the long, polar side-chains. For entropic reasons such side-chains, as well as surface solvent molecules, tend to be somewhat disordered at room temperature but can form extensive hydrogen-bonded networks on cooling. Low-temperature density measurements suggest that, at least in some cases, the beneficial effect of cryosolvents may be due to a density increase on vitrification which reduces the volume of bulk solvent that needs to be expelled from the crystal. Analysis of beta-galactosidase and several other proteins suggests that both intramolecular and intermolecular contact interfaces can be perturbed by cryocooling but that the changes tend to be more dramatic in the latter case. The temperature-dependence of the intermolecular interactions suggests that caution may be necessary in interpreting protein-protein and protein-nucleic acid interactions based on low-temperature crystal structures.

Dynamics of the substrate binding pocket in the presence of an inhibitor covalently attached to a fungal lipase

To gain insight into the mobility of the occupied ligand-binding pocket of the Rhizomucor miehei lipase we have conducted a rigorous molecular dynamics analysis. The covalently attached inhibitor, ethylhexylphosphonate, was employed as a mimic of the putative tetrahedral intermediate in the esterolytic reaction. Our results show that in this lipase, ligand recognition is influenced by the flexibility of the binding pocket, a feature that is common to many other enzymes. Several regions around the active site were found to move significantly to adapt to the inhibitor. These motions are correlated to the flexibility of the inhibitor. In particular, the hexyl chain of the inhibitor shows considerable mobility, and adjacent residues in the binding cleft accommodate to this flexibility. Pronounced fluctuations in the binding pocket induced by the flexibility of the inhibitor are observed in the hinge region F79-S82, the active site loop region W88-V95 and the protein regions P209-F215/H257-Y260. The flexibility in the regions F79-S82 and H257-Y260, where the shorter ethyl chain is located, indicates that additional space in this binding cleft region is available for accommodating a larger moiety. Fluctuations in the region W88-V95 and P209-F215 are due to the relatively short flexible hexyl carbon chain. This part of the binding pocket could be stiffened by the presence of a longer carbon chain. Though the inhibitor is covalently attached through the phosphonate moiety, interaction of the remainder of the molecule and the enzyme are determined by hydrophobic interactions, where the Van der Waals energies are approximately 25% lower than the electrostatic contributions.

Ratiometric single-molecule studies of freely diffusing biomolecules

We outline recent developments in biological single-molecule fluorescence detection with particular emphasis on observations by ratiometric fluorescence resonance energy transfer (FRET) of biomolecules freely diffusing in solution. Single-molecule-diffusion methodologies were developed to minimize perturbations introduced by interactions between molecules and surfaces. Confocal microscopy is used in combination with sensitive detectors to observe bursts of photons from fluorescently labeled biomolecules as they diffuse through the focal volume. These bursts are analyzed to extract ratiometric observables such as FRET efficiency and polarization anisotropy. We describe the development of single-molecule FRET methodology and its application to the observation of the Förster distance dependence and the study of protein folding and polymer physics problems. Finally, we discuss future advances in data acquisition and analysis techniques that can provide a more complete picture of the accessible molecular information.

Enzyme specificity under dynamic control II: Principal component analysis of alpha-lytic protease using global and local solvent boundary conditions

The contributions of conformational dynamics to substrate specificity have been examined by the application of principal component analysis to molecular dynamics trajectories of alpha-lytic protease. The wild-type alpha-lytic protease is highly specific for substrates with small hydrophobic side chains at the specificity pocket, while the Met190-->Ala binding pocket mutant has a much broader specificity, actively hydrolyzing substrates ranging from Ala to Phe. Based on a combination of multiconformation analysis of cryo-X-ray crystallographic data, solution nuclear magnetic resonance (NMR), and normal mode calculations, we had hypothesized that the large alteration in specificity of the mutant enzyme is mainly attributable to changes in the dynamic movement of the two walls of the specificity pocket. To test this hypothesis, we performed a principal component analysis using 1-nanosecond molecular dynamics simulations using either a global or local solvent boundary condition. The results of this analysis strongly support our hypothesis and verify the results previously obtained by in vacuo normal mode analysis. We found that the walls of the wild-type substrate binding pocket move in tandem with one another, causing the pocket size to remain fixed so that only small substrates are recognized. In contrast, the M190A mutant shows uncoupled movement of the binding pocket walls, allowing the pocket to sample both smaller and larger sizes, which appears to be the cause of the observed broad specificity. The results suggest that the protein dynamics of alpha-lytic protease may play a significant role in defining the patterns of substrate specificity. As shown here, concerted local movements within proteins can be efficiently analyzed through a combination of principal component analysis and molecular dynamics trajectories using a local solvent boundary condition to reduce computational time and matrix size.

Backbone dynamics of barstar: a (15)N NMR relaxation study

Backbone dynamics of uniformly (15)N-labeled barstar have been studied at 32 degrees C, pH 6.7, by using (15)N relaxation data obtained from proton-detected 2D (1)H-(15)N NMR spectroscopy. (15)N spin-lattice relaxation rate constants (R(1)), spin-spin relaxation rate constants (R(2)), and steady-state heteronuclear (1)H-(15)N NOEs have been determined for 69 of the 86 (excluding two prolines and the N-terminal residue) backbone amide (15)N at a magnetic field strength of 14.1 Tesla. The primary relaxation data have been analyzed by using the model-free formalism of molecular dynamics, using both isotropic and axially symmetric diffusion of the molecule, to determine the overall rotational correlation time (tau(m)), the generalized order parameter (S(2)), the effective correlation time for internal motions (tau(e)), and NH exchange broadening contributions (R(ex)) for each residue. As per the axially symmetric diffusion, the ratio of diffusion rates about the unique and perpendicular axes (D( parallel)/D( perpendicular)) is 0.82 +/- 0.03. The two results have only marginal differences. The relaxation data have also been used to map reduced spectral densities for the NH vectors of these residues at three frequencies: 0, omega(H), and omega(N), where omega(H),(N) are proton and nitrogen Larmor frequencies. The value of tau(m) obtained from model-free analysis of the relaxation data is 5.2 ns. The reduced spectral density analysis, however, yields a value of 5.7 ns. The tau(m) determined here is different from that calculated previously from time-resolved fluorescence data (4.1 ns). The order parameter ranges from 0.68 to 0.98, with an average value of 0.85 +/- 0.02. A comparison of the order parameters with the X-ray B-factors for the backbone nitrogens of wild-type barstar does not show any considerable correlation. Model-free analysis of the relaxation data for seven residues required the inclusion of an exchange broadening term, the magnitude of which ranges from 2 to 9.1 s(-1), indicating the presence of conformational averaging motions only for a small subset of residues.

The 1.0 A crystal structure of Ca(2+)-bound calmodulin: an analysis of disorder and implications for functionally relevant plasticity

Calmodulin (CaM) is a highly conserved 17 kDa eukaryotic protein that can bind specifically to over 100 protein targets in response to a Ca(2+) signal. Ca(2+)-CaM requires a considerable degree of structural plasticity to accomplish this physiological role; however, the nature and extent of this plasticity remain poorly characterized. Here, we present the 1.0 A crystal structure of Paramecium tetraurelia Ca(2+)-CaM, including 36 discretely disordered residues and a fifth Ca(2+) that mediates a crystal contact. The 36 discretely disordered residues are located primarily in the central helix and the two hydrophobic binding pockets, and reveal correlated side-chain disorder that may assist target-specific deformation of the binding pockets. Evidence of domain displacements and discrete backbone disorder is provided by translation-libration-screw (TLS) analysis and multiconformer models of protein disorder, respectively. In total, the evidence for disorder at every accessible length-scale in Ca(2+)-CaM suggests that the protein occupies a large number of hierarchically arranged conformational substates in the crystalline environment and may sample a quasi-continuous spectrum of conformations in solution. Therefore, we propose that the functionally distinct forms of CaM are less structurally distinct than previously believed, and that the different activities of CaM in response to Ca(2+) may result primarily from Ca(2+)-mediated alterations in the dynamics of the protein.

Solution structure and dynamics of biomolecules from Raman optical activity

Raman optical activity (ROA) measures vibrational optical activity by means of a small difference in the intensity of Raman scattering from chiral molecules in right and left circularly polarized incident laser light. The ROA spectra of a wide range of biomolecules in aqueous solution can now be measured routinely. Because of its sensitivity to the chiral elements of biomolecular structure, ROA provides new information about solution structure and dynamics complementary to that supplied by conventional spectroscopic techniques. This article provides a brief introduction to the theory and practice of ROA spectroscopy followed by a review of recent ROA results on polypeptides, proteins, carbohydrates, nucleic acids and viruses which illustrate how new insight into current problems of structure, folding and function may be obtained from ROA studies.

Protein structure alignment using a genetic algorithm

We have developed a novel, fully automatic method for aligning the three-dimensional structures of two proteins. The basic approach is to first align the proteins' secondary structure elements and then extend the alignment to include any equivalent residues found in loops or turns. The initial secondary structure element alignment is determined by a genetic algorithm. After refinement of the secondary structure element alignment, the protein backbones are superposed and a search is performed to identify any additional equivalent residues in a convergent process. Alignments are evaluated using intramolecular distance matrices. Alignments can be performed with or without sequential connectivity constraints. We have applied the method to proteins from several well-studied families: globins, immunoglobulins, serine proteases, dihydrofolate reductases, and DNA methyltransferases. Agreement with manually curated alignments is excellent. A web-based server and additional supporting information are available at http://engpub1.bu.edu/-josephs.

Non-Boltzmann thermodynamic integration (NBTI) for macromolecular systems: relative free energy of binding of trypsin to benzamidine and benzylamine

The relative free energies of binding of trypsin to two amine inhibitors, benzamidine (BZD) and benzylamine (BZA), were calculated using non-Boltzmann thermodynamic integration (NBTI). Comparison of the simulations with the crystal structures of both complexes, trypsin-BZD and trypsin-BZA, shows that NBTI simulations better sample conformational space relative to thermodynamic integration (TI) simulations. The relative binding free energy calculated using NBTI was much closer to the experimentally determined value than that obtained using TI. The error in the TI simulation was found to be primarily due to incorrect sampling of BZA's conformation in the binding pocket. In contrast, NBTI produces a smooth mutation from BZD to BZA using a surrogate potential, resulting in a much closer agreement between the inhibitors' conformations and the omit electron density maps. This superior agreement between experiment and simulation, of both relative binding free energy differences and conformational sampling, demonstrates NBTI's usefulness for free energy calculations in macromolecular simulations.

Rotamer strain as a determinant of protein structural specificity

We present direct evidence for a change in protein structural specificity due to hydrophobic core packing. High resolution structural analysis of a designed core variant of ubiquitin reveals that the protein is in slow exchange between two conformations. Examination of side-chain rotamers indicates that this dynamic response and the lower stability of the protein are coupled to greater strain and mobility in the core. The results suggest that manipulating the level of side-chain strain may be one way of fine tuning the stability and specificity of proteins.

Effect of hydrophobic core packing on sidechain dynamics

The effect of hydrophobic core packing on sidechain dynamics was analyzed by comparing the dynamics of wild-type (WT) ubiquitin to those of a variant which has seven core mutations. This variant, 1D7, was designed to resemble WT by having a well-packed core of similar volume, and we find that its overall level of dynamics is only subtly different from WT. However, the mutations caused a redistribution in the positions of core residues that are dynamic. This correlates with the tendency of these residues to populate unfavorable rotamers, suggesting that strain from poor sidechain conformations may promote increased flexibility as a mechanism to relieve unfavorable steric interactions. The results demonstrate that even when core volume is conserved, different packing arrangements in mutants can alter dynamic behavior.

New insight into the pH-dependent conformational changes in bovine beta-lactoglobulin from Raman optical activity

We have studied the conformation of beta-lactoglobulin in aqueous solution at room temperature over the pH range approximately 2.0-9.0 using vibrational Raman optical activity (ROA). The ROA spectra clearly show that the basic up and down beta-barrel core is preserved over the entire pH range, in agreement with other studies. However, from the shift of a sharp positive ROA band at approximately 1268 to approximately 1294 cm(-1) on going from pH values below that of the Tanford transition, which is centered at pH approximately 7.5, to values above, the Tanford transition appears to be associated with changes in the local conformations of residues in loop sequences possibly corresponding to a migration into the alpha-helical region of the Ramachandran surface from a nearby region. These changes may be related to those detected in X-ray crystal structures which revealed that the Tanford transition is associated with conformational changes in loops which form a doorway to the interior of the protein. The results illustrate how the ability of ROA to detect loop and turn structure separately from secondary structure is useful for studying conformational plasticity in proteins.

Enzyme specificity under dynamic control: a normal mode analysis of alpha-lytic protease

We have used alpha-lytic protease as a model system for exploring the relationship between the internal dynamics of an enzyme and its substrate specificity. The wild-type enzyme is highly specific for small substrates in its primary specificity pocket, while the M190A mutant has a much broader specificity, efficiently catalyzing cleavage of both large and small substrates. Normal modes have been calculated for both the wild-type and the mutant enzyme to determine how internal vibrations contribute to these contrasting specificity profiles. We find that for the atoms lining the walls of the specificity pocket, the wild-type normal modes have a more symmetric character, with the walls vibrating in phase, and the size of the pocket remaining relatively fixed. This is in agreement with X-ray crystallographic data on conformational substates trapped at 120 K. In contrast, we find that in the mutant, the binding pocket normal modes have a more antisymmetric character, with the walls vibrating out of phase, and the pocket able to expand and contract. These results suggest that the internal vibrations of a molecule may play an important role in determining substrate binding and specificity. A small change in protein structure can have a significant effect on the pattern of molecular vibrations, and thus on enzymatic properties, even if the overall amplitudes of the vibrations, as measured by NMR relaxation or crystallographic B-factors, remain largely unchanged.

A pH-dependent stabilization of an active site loop observed from low and high pH crystal structures of mutant monomeric glycinamide ribonucleotide transformylase at 1.8 to 1.9 A

A mutation in the dimer interface of Escherichia coli glycinamide ribonucleotide transformylase (GarTfase) disrupts the observed pH-dependent association of the wild-type enzyme, but has no observable effect on the enzyme activity. Here, we assess whether a pH effect on the enzyme's conformation is sufficient by itself to explain the pH-dependence of the GarTfase reaction. A pH-dependent conformational change is observed between two high-resolution crystal structures of the Glu70Ala mutant GarTfase at pH 3.5 (1.8 A) and 7.5 (1.9 A). Residues 110 to 131 in GarTfase undergo a transformation from a disordered loop at pH 3.5, where the enzyme is inactive, to an ordered loop-helix structure at pH 7.5, where the enzyme is active. The ordering of this flexible loop-helix has a direct effect on catalytic residues in the active site, binding of the folate cofactor and shielding of the active site from solvent. A main-chain carbonyl oxygen atom from Tyr115 in the ordered loop forms a hydrogen bond with His108, and thereby provides electronic and structural stabilization of this key active site residue. Kinetic data indicate that the pKa of His108 is in fact raised to 9. 2. The loop movement can be correlated with elevation of the His pKa, but with further stabilization, probably from Asp144, after the binding of folate cofactor. Leu118, also in the loop, becomes positioned near the p-amino benzoic acid binding site, providing additional hydrophobic interactions with the cofactor 10-formyl tetrahydrofolate. Thus, the pH-dependence of the enzyme activity appears to arise from local active site rearrangements and not from differences due to monomer-dimer association.

Thermodynamics and molecular simulation analysis of hydrophobic substrate recognition by aminotransferases

Aromatic amino acid aminotransferase (AroAT) and aspartate aminotransferase (AspAT) are known as dual-substrate enzymes, which can bind acidic and hydrophobic substrates in the same pocket (Kawaguchi, S., Nobe, Y., Yasuoka, J., Wakamiya, T., Kusumoto, S., and Kuramitsu, S. (1997) J. Biochem. (Tokyo) 122, 55-63). In order to elucidate the mechanism of hydrophobic substrate recognition, kinetic and thermodynamic analyses using substrates with different hydrophobicities were performed. They revealed that 1) amino acid substrate specificity (kmax/Kd) depended on the affinity for the substrate (1/Kd) and 2) binding of the hydrophobic side chain was enthalpy-driven, suggesting that van der Waals interactions between the substrate-binding pocket and hydrophobic substrate predominated. Three-dimensional structures of AspAT and AroAT bound to alpha-aminoheptanoic acid were built using the homology modeling method. A molecular dynamic simulation study suggested that the outward-facing position of the Arg292 side chain was the preferred state to a greater extent in AroAT than AspAT, which would make the hydrophobic substrate bound state of the former more stable. Furthermore, AroAT appeared to have a more flexible conformation than AspAT. Such flexibility would be expected to reduce the energetic cost of conformational rearrangement induced by substrate binding. These two mechanisms (positional preference of Arg and flexible conformation) may account for the high activity of AroAT toward hydrophobic substrates.