Rigid protein motion as a model for crystallographic temperature factors

Protein structural variation in computational models and crystallographic data

Normal mode analysis offers an efficient way of modeling the conformational flexibility of protein structures. We use anisotropic displacement parameters from crystallography to test the quality of prediction of both the magnitude and directionality of conformational flexibility. Normal modes from four simple elastic network model potentials and from the CHARMM force field are calculated for a data set of 83 diverse, ultrahigh-resolution crystal structures. While all five potentials provide good predictions of the magnitude of flexibility, all-atom potentials have a clear edge at prediction of directionality, and the CHARMM potential has the highest prediction quality. The low-frequency modes from different potentials are similar, but those computed from the CHARMM potential show the greatest difference from the elastic network models. The comprehensive evaluation demonstrates the costs and benefits of using normal mode potentials of varying complexity.

vGNM: a better model for understanding the dynamics of proteins in crystals

The dynamics of proteins are important for understanding their functions. In recent years, the simple coarse-grained Gaussian Network Model (GNM) has been fairly successful in interpreting crystallographic B-factors. However, the model clearly ignores the contribution of the rigid body motions and the effect of crystal packing. The model cannot explain the fact that the same protein may have significantly different B-factors under different crystal packing conditions. In this work, we propose a new GNM, called vGNM, which takes into account both the contribution of the rigid body motions and the effect of crystal packing, by allowing the amplitude of the internal modes to be variables. It hypothesizes that the effect of crystal packing should cause some modes to be amplified and others to become less important. In doing so, vGNM is able to resolve the apparent discrepancy in experimental B-factors among structures of the same protein but with different crystal packing conditions, which GNM cannot explain. With a small number of parameters, vGNM is able to reproduce experimental B-factors for a large set of proteins with significantly better correlations (having a mean value of 0.81 as compared to 0.59 by GNM). The results of applying vGNM also show that the rigid body motions account for nearly 60% of the total fluctuations, in good agreement with previous findings.

Crystal structures of the thi-box riboswitch bound to thiamine pyrophosphate analogs reveal adaptive RNA-small molecule recognition

Riboswitches are noncoding mRNA elements that bind small-molecule metabolites with high affinity and specificity, and they regulate the expression of associated genes. The thi-box riboswitch can exhibit a 1000-fold higher affinity for thiamine pyrophosphate over closely related noncognate compounds such as thiamine monophosphate. To understand the chemical basis of thi-box pyrophosphate specificity, we have determined crystal structures of an E. coli thi-box bound to thiamine pyrophosphate, thiamine monophosphate, and the structural analogs benfotiamine and pyrithiamine. When bound to monophosphorylated compounds, the RNA elements that recognize the thiamine and phosphate moieties of the ligand move closer together. This allows the riboswitch to recognize the monophosphate in a manner similar to how it recognizes the beta-phosphate of thiamine pyrophosphate. In the pyrithiamine complex, the pyrophosphate binding site is largely unstructured. These results show how the riboswitch can bind to various metabolites, and why the thi-box preferentially binds thiamine pyrophosphate.

Role of invariant Thr80 in human immunodeficiency virus type 1 protease structure, function, and viral infectivity

Sequence variability associated with human immunodeficiency virus type 1 (HIV-1) is useful for inferring structural and/or functional constraints at specific residues within the viral protease. Positions that are invariant even in the presence of drug selection define critically important residues for protease function. While the importance of conserved active-site residues is easily understood, the role of other invariant residues is not. This work focuses on invariant Thr80 at the apex of the P1 loop of HIV-1, HIV-2, and simian immunodeficiency virus protease. In a previous study, we postulated, on the basis of a molecular dynamics simulation of the unliganded protease, that Thr80 may play a role in the mobility of the flaps of protease. In the present study, both experimental and computational methods were used to study the role of Thr80 in HIV protease. Three protease variants (T80V, T80N, and T80S) were examined for changes in structure, dynamics, enzymatic activity, affinity for protease inhibitors, and viral infectivity. While all three variants were structurally similar to the wild type, only T80S was functionally similar. Both T80V and T80N had decreased the affinity for saquinavir. T80V significantly decreased the ability of the enzyme to cleave a peptide substrate but maintained infectivity, while T80N abolished both activity and viral infectivity. Additionally, T80N decreased the conformational flexibility of the flap region, as observed by simulations of molecular dynamics. Taken together, these data indicate that HIV-1 protease functions best when residue 80 is a small polar residue and that mutations to other amino acids significantly impair enzyme function, possibly by affecting the flexibility of the flap domain.

Spinach on the ceiling: a theoretical chemist's return to biology

I was born in Vienna and came to the United States as a refugee in October 1938. This experience played an important role in my view of the world and my approach to science: It contributed to my realization that it was safe to stop working in fields that I felt I understood and to focus on different areas of research by asking questions that would teach me and others something new. I describe my experiences that led me from chemistry and physics back to my first love, biology, and outline some of the contributions I have made as part of my ongoing learning experience.

Prediction of protein B-factor profiles

The polypeptide backbones and side chains of proteins are constantly moving due to thermal motion and the kinetic energy of the atoms. The B-factors of protein crystal structures reflect the fluctuation of atoms about their average positions and provide important information about protein dynamics. Computational approaches to predict thermal motion are useful for analyzing the dynamic properties of proteins with unknown structures. In this article, we utilize a novel support vector regression (SVR) approach to predict the B-factor distribution (B-factor profile) of a protein from its sequence. We explore schemes for encoding sequences and various settings for the parameters used in SVR. Based on a large dataset of high-resolution proteins, our method predicts the B-factor distribution with a Pearson correlation coefficient (CC) of 0.53. In addition, our method predicts the B-factor profile with a CC of at least 0.56 for more than half of the proteins. Our method also performs well for classifying residues (rigid vs. flexible). For almost all predicted B-factor thresholds, prediction accuracies (percent of correctly predicted residues) are greater than 70%. These results exceed the best results of other sequence-based prediction methods.

Mechanism of substrate recognition by drug-resistant human immunodeficiency virus type 1 protease variants revealed by a novel structural intermediate

Human immunodeficiency virus type 1 (HIV-1) protease processes and cleaves the Gag and Gag-Pol polyproteins, allowing viral maturation, and therefore is an important target for antiviral therapy. Ligand binding occurs when the flaps open, allowing access to the active site. This flexibility in flap geometry makes trapping and crystallizing structural intermediates in substrate binding challenging. In this study, we report two crystal structures of two HIV-1 protease variants bound with their corresponding nucleocapsid-p1 variant. One of the flaps in each of these structures exhibits an unusual "intermediate" conformation. Analysis of the flap-intermediate and flap-closed crystal structures reveals that the intermonomer flap movements may be asynchronous and that the flap which wraps over the P3 to P1 (P3-P1) residues of the substrate might close first. This is consistent with our hypothesis that the P3-P1 region is crucial for substrate recognition. The intermediate conformation is conserved in both the wild-type and drug-resistant variants. The structural differences between the variants are evident only when the flaps are closed. Thus, a plausible structural model for the adaptability of HIV-1 protease to recognize substrates in the presence of drug-resistant mutations has been proposed.

Fluctuations and correlations in crystalline protein dynamics: a simulation analysis of staphylococcal nuclease

Understanding collective motions in protein crystals is likely to furnish insight into functional protein dynamics and will improve models for refinement against diffraction data. Here, four 10 ns molecular dynamics simulations of crystalline Staphylococcal nuclease are reported and analyzed in terms of fluctuations and correlations in atomic motion. The simulation-derived fluctuations strongly correlate with, but are slightly higher than, the values derived from the experimental B-factors. Approximately 70% of the atomic fluctuations are due to internal protein motion. For 65% of the protein atoms the internal fluctuations converge on the nanosecond timescale. Convergence is much slower for the elements of the interatomic displacement correlation matrix--of these, >80% converge within 1 ns for interatomic distances less, approximately <6 A, but only 10% for separations approximately =12 A. Those collective motions that converged on the nanosecond timescale involve mostly correlations within the beta-barrel or between alpha-helices of the protein. The R-factor with the experimental x-ray diffuse scattering for the crystal, which is determined by the displacement variance-covariance matrix, decreases to 8% after 10 ns simulation. Both the number of converged correlation matrix elements and the R-factor depend logarithmically on time, consistent with a model in which the number of energy minima sampled depends exponentially on the maximum energy barrier crossed. The logarithmic dependence is also extrapolated to predict a convergence time for the whole variance-covariance matrix of approximately 1 micros.

Structural and Thermodynamic Analysis of Human PCNA with Peptides Derived from DNA Polymerase-δ p66 Subunit and Flap Endonuclease-1

Human Proliferating Cellular Nuclear Antigen (hPCNA), a member of the sliding clamp family of proteins, makes specific protein-protein interactions with DNA replication and repair proteins through a small peptide motif termed the PCNA-interacting protein, or PIP-box. We solved the structure of hPCNA bound to PIP-box-containing peptides from the p66 subunit of the human replicative DNA polymerase-delta (452-466) at 2.6 A and of the flap endonuclease (FEN1) (331-350) at 1.85 A resolution. Both structures demonstrate that the pol-delta p66 and FEN1 peptides interact with hPCNA at the same site shown to bind the cdk-inhibitor p21(CIP1). Binding studies indicate that peptides from the p66 subunit of the pol-delta holoenzyme and FEN1 bind hPCNA from 189- to 725-fold less tightly than those of p21. Thus, the PIP-box and flanking regions provide a small docking peptide whose affinities can be readily adjusted in accord with biological necessity to mediate the binding of DNA replication and repair proteins to hPCNA.

Molecular dynamics of biological macromolecules: a brief history and perspective

A description of the origin of my interest in and the development of molecular dynamics simulations of biomolecules is presented with a historical overview, including the role of my interactions with Shneior Lifson and his group in Israel. Some early applications of the methodology by members of my group are summarized, followed by a description of examples of recent applications and some discussion of possible future directions.

Dynamics of proteins in crystals: comparison of experiment with simple models

The dynamic behavior of proteins in crystals is examined by comparing theory and experiments. The Gaussian network model (GNM) and a simplified version of the crystallographic translation libration screw (TLS) model are used to calculate mean square fluctuations of C(alpha) atoms for a set of 113 proteins whose structures have been determined by x-ray crystallography. Correlation coefficients between the theoretical estimations and experiment are calculated and compared. The GNM method gives better correlation with experimental data than the rigid-body libration model and has the added benefit of being able to calculate correlations between the fluctuations of pairs of atoms. By incorporating the effect of neighboring molecules in the crystal the correlation is further improved.

Flexibility and packing in proteins

Structural flexibility is an essential attribute, without which few proteins could carry out their biological functions. Much information about protein flexibility has come from x-ray crystallography, in the form of atomic mean-square displacements (AMSDs) or B factors. Profiles showing the AMSD variation along the polypeptide chain are usually interpreted in dynamical terms but are ultimately governed by the local features of a highly complex energy landscape. Here, we bypass this complexity by showing that the AMSD profile is essentially determined by spatial variations in local packing density. On the basis of elementary statistical mechanics and generic features of atomic distributions in proteins, we predict a direct inverse proportionality between the AMSD and the contact density, i.e., the number of noncovalent neighbor atoms within a local region of approximately 1.5 nm(3) volume. Testing this local density model against a set of high-quality crystal structures of 38 nonhomologous proteins, we find that it accurately and consistently reproduces the prominent peaks in the AMSD profile and even captures minor features, such as the periodic AMSD variation within alpha helices. The predicted rigidifying effect of crystal contacts also agrees with experimental data. With regard to accuracy and computational efficiency, the model is clearly superior to its predecessors. The quantitative link between flexibility and packing density found here implies that AMSDs provide little independent information beyond that contained in the mean atomic coordinates.

Structure-based analysis of protein dynamics: comparison of theoretical results for hen lysozyme with X-ray diffraction and NMR relaxation data

An analytical approach based on Gaussian network model (GNM) is proposed for predicting the rotational dynamics of proteins. The method, previously shown to successfully reproduce X-ray crystallographic temperature factors for a series of proteins is extended here to predict bond torsional mobilities and reorientation of main chain amide groups probed by 15N-H nuclear magnetic resonance (NMR) relaxation. The dynamics of hen egg-white lysozyme (HEWL) in the folded state is investigated using the proposed approach. Excellent agreement is observed between theoretical results and experimental (X-ray diffraction and NMR relaxation) data. The analysis reveals the important role of coupled rotations, or cross-correlations between dihedral angle librations, in defining the relaxation mechanism on a local scale. The crystal and solution structures exhibit some differences in their local motions, but their global motions are identical. Hinge residues mediating the cooperative movements of the alpha- and beta-domains are identified, which comprise residues in helix C, Glu35 and Ser36 on the loop succeeding helix B, Ile55 and Leu56 at the turn between strands II and III. The central part of the beta-domain long loop and the turn between strands I and II display an enhanced mobility. Finally, kinetically hot residues and key interactions are identified, which point at helix B and beta-strand III as the structural elements underlying the stability of the tertiary structure.

The 2.7 A crystal structure of deoxygenated hemoglobin from the sea lamprey (Petromyzon marinus): structural basis for a lowered oxygen affinity and Bohr effect

BACKGROUND

The hemoglobins of the sea lamprey are unusual in that cooperativity and sensitivity to pH arise from an equilibrium between a high-affinity monomer and a low-affinity oligomer. Although the crystal structure of the monomeric cyanide derivative has previously been determined, the manner by which oligomerization acts to lower the oxygen affinity and confer a strong Bohr effect has, until now, been speculative.

RESULTS

We have determined the crystal structure of deoxygenated lamprey hemoglobin V by molecular replacement to 2.7 A resolution, in a crystal form with twelve protomers in the asymmetric unit. The subunits are arranged as six essentially identical dimers, with a novel subunit interface formed by the E helices and the AB corner using the standard hemoglobin helical designations. In addition to nonpolar interactions, the interface includes a striking cluster of four glutamate residues. The proximity of the interface to ligand-binding sites implicates a direct effect on ligand affinity.

CONCLUSIONS

Comparison of the deoxy structure with that of the cyanide derivative revealed conformational changes that appear to be linked to the functional behavior. Oligomerization is coupled with a movement of the first half of the E helix by up to 1.0 A towards the heme, resulting in steric interference of ligand binding to the deoxy structure. The Bohr effect seems to result from proton uptake by glutamate residues as they are buried in the interface. Unlike human and mollusc hemoglobins, in which modulation of function is due to primarily proximal effects, regulation of oxygen affinity in lamprey hemoglobin V seems to depend on changes at the distal (ligand-binding) side of the heme group.

X-ray diffuse scattering and rigid-body motion in crystalline lysozyme probed by molecular dynamics simulation

Rigid-body motions are determined from a 1 ns molecular dynamics simulation of the unit cell of orthorhombic hen egg-white lysozyme and their contribution to X-ray diffuse scattering intensities are examined. Using a dynamical cluster technique, groups of backbone atoms that move as approximately rigid bodies are derived from the intramolecular interatomic fluctuation matrix. These groups tend to be local in the sequence or connected by disulphide bonds, and contain on average five residues each, X-ray diffuse scattering patterns, which are sensitive to collective motions, are calculated from the full simulation trajectory (including all the protein degrees of freedom). The results reproduce the main features of the experimental scattering. Diffuse scattering is also calculated from fitted trajectories of the rigid bodies. The full simulation diffuse scattering and atomic displacements are found to be well reproduced by a model in which the backbone atoms form the rigid groups determined using the dynamical cluster technique and the individual side-chains behave as separate rigid bodies: the resulting R-factor with the full simulation scattering is 5%. Quantitatively poorer agreement is obtained from trajectories in which the secondary structural elements of the protein are considered rigid. Rigid whole-molecule and domain motions make only minor contributions to the protein atom displacements. Finally, correlations in the interatomic fluctuations are examined directly using a canonical method.

Structure and dynamics of calmodulin in solution

To characterize the dynamic behavior of calmodulin in solution, we have carried out molecular dynamics (MD) simulations of the Ca2+-loaded structure. The crystal structure of calmodulin was placed in a solvent sphere of radius 44 A, and 6 Cl- and 22 Na+ ions were included to neutralize the system and to model a 150 mM salt concentration. The total number of atoms was 32,867. During the 3-ns simulation, the structure exhibits large conformational changes on the nanosecond time scale. The central alpha-helix, which has been shown to unwind locally upon binding of calmodulin to target proteins, bends and unwinds near residue Arg74. We interpret this result as a preparative step in the more extensive structural transition observed in the "flexible linker" region 74-82 of the central helix upon complex formation. The major structural change is a reorientation of the two Ca2+-binding domains with respect to each other and a rearrangement of alpha-helices in the N-terminus domain that makes the hydrophobic target peptide binding site more accessible. This structural rearrangement brings the domains to a more favorable position for target binding, poised to achieve the orientation observed in the complex of calmodulin with myosin light-chain kinase. Analysis of solvent structure reveals an inhomogeneity in the mobility of water in the vicinity of the protein, which is attributable to the hydrophobic effect exerted by calmodulin's binding sites for target peptides.

Motions of calmodulin characterized using both Bragg and diffuse X-ray scattering

BACKGROUND

Calmodulin is a calcium-activated regulatory protein which can bind to many different targets. The protein resembles a highly flexible dumbbell, and bends in the middle as it binds. This and other motions must be understood to formulate a realistic model of calmodulin function.

RESULTS

Using the Bragg reflections from X-ray crystallography, a multiple-conformer refinement of a calmodulin-peptide complex shows anisotropic displacements, with high variations of dihedral angles in several nonhelical domains: the flexible linker; three of the four calcium-binding sites (including both of the N-terminal sites); and a turn connecting the C-terminal EF-hand calcium-binding domains. Three-dimensional maps of the large scale diffuse X-ray scattering data show isotropic liquid-like motions with an unusually small correlation length. Three-dimensional maps of the small scale diffuse streaks show highly coupled, anisotropic motions along the head-to-tail molecular packing direction in the unit cell. There is also weak coupling perpendicular to the head-to-tail packing direction, particularly across a cavity occupied by the disordered linker domain of the molecule.

CONCLUSIONS

Together, the Bragg and diffuse scattering present a self-consistent description of the motions in the flexible linker of calmodulin. The other mobile regions of the protein are also of great interest. In particular, the high variations in the calcium-binding sites are likely to influence how strongly they bind ions. This is especially important in the N-terminal sites, which regulate the activity of the molecule.

Ligand-induced conformational changes in ras p21: a normal mode and energy minimization analysis

A normal mode and energy minimization of ras p21 is used to determine the flexibility of the protein and the origin of the conformational differences between GTP and GDP-bound forms. To preserve the integrity of the structures, a hydration shell of water molecules was included as part of the system. Certain low-frequency modes were found to have high involvement coefficients with the conformational transition between the GTP and GDP-bound structures; the involvement coefficients of some of the modes increase when the gamma-phosphate group is removed. Two unstable modes that appear in the GTP-bound structure upon deletion of the gamma-phosphate group were determined and shown to have dominant contributions in the regions of switch I and switch II; there was also a significant displacement of loop 1. The initial motion in these regions is predicted by the modes to be approximately perpendicular to the direction of the transition from the GTP-bound state to the GDP-bound state. The overall conformational change in the switch I and II regions involves rearrangements of the protein backbone within these regions, rather than rigid body motion. Differences in the low-frequency modes of the GTP and GDP-bound forms appear to play a role in ligand binding. A coupling between the helix alpha3 position and the deletion of the gamma-phosphate group may be involved in the interaction with GAP. The oncogenic mutation G12D leads to a global increase in the rigidity of the protein. Thus, the mutant is likely to have a higher barrier for the conformational change to the inactive form; this would slow the transition and could be related to its oncogenic properties.

Molecular dynamics simulation study of DNA dodecamer d(CGCGAATTCGCG) in solution: conformation and hydration

A molecular dynamics simulation of the dodecamer duplex d(CGCGAATTCGCG) using the particle mesh Ewald sum assumed a B-conformation remarkably close to the observed X-ray structure. The Ewald summation method effectively eliminates the usual "cut-off" of long-range interactions and allowed us to evaluate the full effect of the electrostatic forces. This simulation showed remarkable agreement with the Dickerson X-ray structure in both average structure and B-factors; within the EcoRI site itself, the rms deviation between the average theoretical and observed structures was 1.1 A. The width of the minor groove fluctuated between a wide and narrow configuration with the latter corresponding closely to the X-ray structure. The simulation also suggested a strong sequence-dependent signature on the minor groove width in both wide and narrow conformers. Hydration shells in both the major and minor grooves were observed. The "spine of hydration" in the minor groove was clear. In the major groove the first hydration shell appears to be a ribbon-like structure that reproduces the principal features of observed X-ray structures; subtle variations of this hydration pattern suggest sequence dependencies. Sequence-dependent features were also examined for helical and other geometric parameters. The successful reproduction of many experimentally observed fine structural features shows that the Ewald summation significantly improves the fidelity of the calculations.

Binding of the estrogen receptor to DNA. The role of waters

Molecular dynamics simulations are carried out to investigate the binding of the estrogen receptor, a member of the nuclear hormone receptor family, to specific and non-specific DNA. Two systems have been simulated, each based on the crystallographic structure of a complex of a dimer of the estrogen receptor DNA binding domain with DNA. One structure includes the dimer and a consensus segment of DNA, ds(CCAGGTCACAGTGACCTGG); the other structure includes the dimer and a nonconsensus segment of DNA, ds(CCAGAACACAGTGACCTGG). The simulations involve an atomic model of the protein-DNA complex, counterions, and a sphere of explicit water with a radius of 45 A. The molecular dynamics package NAMD was used to obtain 100 ps of dynamics for each system with complete long-range electrostatic interactions. Analysis of the simulations revealed differences in the protein-DNA interactions for consensus and nonconsensus sequences, a bending and unwinding of the DNA, a slight rearrangement of several amino acid side chains, and inclusion of water molecules at the protein-DNA interface region. Our results indicate that binding specificity and stability is conferred by a network of direct and water mediated protein-DNA hydrogen bonds. For the consensus sequence, the network involves three water molecules, residues Glu-25, Lys-28, Lys-32, Arg-33, and bases of the DNA. The binding differs for the nonconsensus DNA sequence in which case the fluctuating network of hydrogen bonds allows water molecules to enter the protein-DNA interface. We conclude that water plays a role in furnishing DNA binding specificity to nuclear hormone receptors.

Three-dimensional diffuse x-ray scattering from crystals of Staphylococcal nuclease

We have developed methods for obtaining and characterizing three-dimensional maps of the reciprocal-space distribution of diffuse x-ray scattering from protein crystals, and have used the methods to study the nature of disorder in crystals of Staphylococcal nuclease. Experimentally obtained maps are 99.5% complete in the reciprocal-space resolution range of 10 A-2.5 A, show symmetry consistent with the P41 space group of the unit cell, and are highly reproducible. Quantitative comparisons of the data with three-dimensional simulations imply liquid-like motions of the protein [Caspar, D. L. D., Clarage, J., Salunke, D. M. & Clarage, M. (1988) Nature (London) 332, 659-662], with a correlation length of 10 A and a root-mean-square displacement of 0.36 A.

Recombinant core streptavidins. A minimum-sized core streptavidin has enhanced structural stability and higher accessibility to biotinylated macromolecules

Two recombinant core streptavidins were designed and characterized to understand the role of the terminal sequences, present in naturally truncated core streptavidins, in the properties of streptavidin. One recombinant core streptavidin, Stv-25, has an amino acid sequence very similar to natural core streptavidins. The other recombinant molecule, Stv-13, has further truncation of the terminal residues and consists essentially of only the beta-barrel structure characteristic of streptavidin. These recombinant core streptavidins are tetrameric and bind four biotins/molecule, as does natural streptavidin. The solubility characteristics of Stv-13, determined by varying the concentration of ammonium sulfate or ethanol, were almost the same as those of Stv-25 and natural core streptavidin. However, Stv-13 showed an enhanced structural stability compared with Stv-25 and natural core streptavidin. For example, Stv-13 retained greater than 80% of its biotin binding ability after incubation in 6 M guanidine hydrochloride at pH 1.5, under which conditions, Stv-25 and natural core streptavidin retained only about 20% of their biotin binding ability. In addition, Stv-13 showed higher accessibility to biotinylated DNA than natural core streptavidin. Apparently, the terminal regions, present on the surface of natural core streptavidin, spatially hinder biotinylated macromolecules from approaching the biotin binding sites.

Diffuse scattering in protein crystallography

The understanding of flexibility and deformability in proteins is one of the current major challenges of structural molecular biology. The knowledge of the average atomic positions of three-dimensional folding of proteins, which is obtained either by X-ray diffraction or n.m.r. spectroscopy, is generally not sufficient to explain their functional mechanisms. Very often it is necessary to consider the existence of other concerted atomic motions as, for example, in the well-known case of the CO molecule fixation at the active site of myoglobin which requires the concerted displacement of a large number of atoms in order to open a channel down to this site. This opening, which depends on the physico-chemical conditions, plays the role of a regulator in the biochemical reactions (Janin & Wodak, 1983; Tainer et al. 1984; Westhof et al. 1984; Ormos et al. 1988).

Intersubunit contacts made by tryptophan 120 with biotin are essential for both strong biotin binding and biotin-induced tighter subunit association of streptavidin

In natural streptavidin, tryptophan 120 of each subunit makes contacts with the biotin bound by an adjacent subunit through the dimer-dimer interface. To understand quantitatively the role of tryptophan 120 and its intersubunit communication in the properties of streptavidin, a streptavidin mutant in which tryptophan 120 is converted to phenylalanine was produced and characterized. The streptavidin mutant forms a tetrameric molecule and binds one biotin per subunit, as does natural streptavidin, indicating that the mutation of tryptophan 120 to phenylalanine has no significant effect on the basic properties of streptavidin. However, its biotin-binding affinity was reduced substantially, to approximately 10(8) M-1, indicating that the contact made by tryptophan 120 to biotin has a considerable contribution to the extremely tight biotin binding by streptavidin. The mutant retained bound biotin over a wide pH range or with the addition of urea up to 6 M at neutral pH. However, bound biotin was efficiently released by the addition of excess free biotin due, presumably, to exchange reactions. Electrophoretic analysis revealed that the intersubunit contact made by tryptophan 120 to biotin through the dimer-dimer interface is the major interaction responsible for the biotin-induced, tighter subunit association of streptavidin. In addition, the mutant has weaker subunit association than natural streptavidin even in the absence of biotin, indicating that tryptophan 120 also contributes to the subunit association of tetramers in the absence of biotin.

Elasticity of globular proteins. The relation between mechanics, thermodynamics and mobility

An analysis of elasticity of lysozyme and myoglobin crystals in terms of thermodynamics has revealed a direct relation between entropy and enthalpy of deformation and delta S* and delta H* terms in the standard free energy change in proteins, delta G(o), (K.P. Murphy, P.L. Privalov, S.J. Gill (1990) Science 247, 559-561), so that at any temperature (between the glass-transition and denaturation temperatures) free energy of deformation is proportional to the hydration independent part of delta G(o). Both energies are characterized with large enthalpy-entropy compensation and tend to zero at the same temperature, Tm = (delta H*/delta S*) = 353 +/- 20 K. Large positive entropy contribution to deformation energy causes large linear decrease in protein elasticity, and increase in thermal mobility of protein atoms with temperature. Being plotted in inverse coordinates, temperature dependence of the mean-square amplitudes, obtained in neutron and mossbauer experiments as well as in molecular dynamic simulations, gives the same 353 +/- 10 K for the temperature, where the amplitudes tend to infinity. Mechanism explaining large positive entropy contribution in deformation energy of native protein molecules presumably involves emergence of more room for motion of protein side-chain groups squeezed between alpha-helices and other rigid skeleton elements, when precise packing of atoms in native protein molecule is distorted as a result of deformation.

Molecular dynamics simulations and rigid body (TLS) analysis of aspartate carbamoyltransferase: evidence for an uncoupled R state

In the R form of ATCase complexed with the bisubstrate analogue, N-(phosphonacetyl)-L-aspartate, large temperature factors are reported for the allosteric domains of the regulatory chains. We studied the conformational flexibility of the holoenzyme with molecular dynamics simulations and rigid body (TLS) analysis. The results of the molecular dynamics simulations suggest that, although local atomic fluctuations account for the temperature factors of the catalytic and zinc domains, they do not account for the large temperature factors of the allosteric regions. However, the temperature factors of the allosteric domains can be satisfactorily analyzed using a rigid body model. The simulations and rigid body analysis support the idea that the allosteric regions are mechanically uncoupled from the rest of the enzyme in the PALA structure. Implications of this uncoupling for allosteric regulation are discussed.

Computational challenges for macromolecular structure determination by X-ray crystallography and solution NMR-spectroscopy

Macromolecular structure determination by X-ray crystallography and solution NMR spectroscopy has experienced unprecedented growth during the past decade.

Mutational studies of protein structures and their stabilities

The fundamental relationship between structure and function has served to guide investigations into the workings of living systems at all levels - from the whole organism to individual cells on down to individual molecules. When X-ray crystallography began to reveal the three-dimensional structures of proteins like myoglobin, lysozyme and RNase A, protein chemists were well prepared to draw inferences about functional mechanisms from the precise positioning of amino acid residues they could see. The close proximity between an amino acid side chain and a chemical group on a bound ligand strongly suggests a functional role for that side chain in binding affinity and specificity. Likewise, the nearly universal finding of large clusters of hydrophobic side chains buried in the core of proteins strongly supports a major functional role of hydrophobic interactions in protein folding and stability. Even though eminently plausible hypotheses like these, grounded in the most fundamental principles of chemistry and the logic of structure–function relationships, become widely accepted and make their way into textbooks, protein chemists have felt compelled to search for ways to test them and put them on a more quantitative basis.

Flexibility in crystalline insulins

Comparisons of atomic models for chemically identical protein molecules solved in differing crystal environments provide information on flexibility in the protein structure. The structures of five T4 lysozyme proteins in differing crystal environments showed large relative displacements of the two domains with conserved backbone conformations that are connected by a flexible hinge (H. R. Faber and B. W. Matthews. 1990. Nature (Lond.). 348:263-266). In contrast, my comparison of the positions of all the atoms in two crystal forms of insulin shows that the structural changes caused by the differing crystal contacts are contained within nearby amino acids and are not propagated through the core of the insulin molecule. Groups of atoms that are most significantly displaced are not shifted in large rigid units but are repacked into new and distinct conformations. The transmission of displacements through the single domain insulin molecule is, like the movements due to thermal vibrations (D. L. D. Caspar, J. Clarage, D. M. Salunke, M. S. Clarage. 1988. Nature (Lond.). 332:659-662), characterized by short-range interactions between small atomic groups.

Correlations of atomic movements in lysozyme crystals

Diffuse scattering data have been collected on two crystal forms of lysozyme, tetragonal and triclinic, using synchrotron radiation. The observed diffraction patterns were simulated using an exact theory for simple model crystals which relates the diffuse scattering intensity distribution to the amplitudes and correlations of atomic movements. Although the mean square displacements in the tetragonal form are twice that in the triclinic crystal, the predominant component of atomic movement in both crystals is accounted for by short-range coupled motions where displacement correlations decay exponentially as a function of atomic separation, with a relaxation distance of approximately 6 A. Lattice coupled movements with a correlation distance approximately 50 A account for only about 5-10% of the total atomic mean square displacements in the protein crystals. The results contradict various presumptions that the disorder in protein crystals can be modeled predominantly by elastic vibrations or rigid body movements.

Normal modes of symmetric protein assemblies. Application to the tobacco mosaic virus protein disk

We use group theoretical methods to study the molecular dynamics of symmetric protein multimers in the harmonic or quasiharmonic approximation. The method explicitly includes the long-range correlations between protein subunits. It can thus address collective dynamic effects, such as cooperativity between subunits. The n lowest-frequency normal modes of each individual subunit are combined into symmetry coordinates for the entire multimer. The Hessian of the potential energy is thereby reduced to a series of blocks of order n or 2n. In the quasiharmonic approximation, the covariance matrix of the atomic oscillations is reduced to the same block structure by an analogous set of symmetry coordinates. The method is applied to one layer of the tobacco mosaic virus protein disk in vacuo, to gain insight into the role of conformational fluctuations and electrostatics in tobacco mosaic virus assembly. The system has 78,000 classical, positional, degrees of freedom, yet the calculation is reduced by symmetry to a problem of order 4,600. Normal modes in the 0-100 cm-1 range were calculated. The calculated correlations extend mainly from each subunit to its nearest neighbors. The network of core helices has weak correlations with the rest of the structure. Similarly, the inner loops 90-108 are uncorrelated with the rest of the structure. Thus, the model predicts that the dielectric response in the RNA-binding region is mainly due to the loops alone.

Free R value: a novel statistical quantity for assessing the accuracy of crystal structures

The determination of macromolecular structure by crystallography involves fitting atomic models to the observed diffraction data. The traditional measure of the quality of this fit, and presumably the accuracy of the model, is the R value. Despite stereochemical restraints, it is possible to overfit or 'misfit' the diffraction data: an incorrect model can be refined to fairly good R values as several recent examples have shown. Here I propose a reliable and unbiased indicator of the accuracy of such models. By analogy with the cross-validation method of testing statistical models I define a statistical quantity (R(free) (T) that measures the agreement between observed and computed structure factor amplitudes for a 'test' set of reflections that is omitted in the modelling and refinement process. As examples show, there is a high correlation between R(free) (T) and the accuracy of the atomic model phases. This is useful because experimental phase information is usually inaccurate, incomplete or unavailable. I expect that R(free) (T) will provide a measure of the information content of recently proposed models of thermal motion and disorder, time-averaging and bulk solvent.

Exploration of disorder in protein structures by X-ray restrained molecular dynamics

Conformational disorder in crystal structures of ribonuclease-A and crambin is studied by including two independent structures in least-squares optimizations against X-ray data. The optimizations are carried out by X-ray restrained molecular dynamics (simulated annealing refinement) and by conventional least-squares optimization. Starting from two identical structures, the optimizations against X-ray data lead to significant deviations between the two, with rms backbone displacements of 0.45 A for refinement of ribonuclease at 1.53 A resolution, and 0.31 A for crambin at 0.945 A. More than 15 independent X-ray restrained molecular dynamics runs have been carried out for ribonuclease, and the displacements between the resulting structures are highly reproducible for most atoms. These include residues with two or more conformations with significant dihedral angle differences and alternative hydrogen bonding, as well as groups of residues that undergo displacements that are suggestive of rigid-body librations. The crystallographic R-values obtained are approximately 13%, as compared to 15.3% for a comparable refinement with a single structure. Least-squares optimization without an intervening restrained molecular dynamics stage is sufficient to reproduce most of the observed displacements. Similar results are obtained for crambin, where the higher resolution of the X-ray data allows for refinement of unconstrained individual anisotropic temperature factors. These are shown to be correlated with the displacements in the two-structure refinements.