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.     

Structure and internal mobility of proteins: a molecular dynamics study of hen egg white lysozyme

The structure and internal motions of the protein hen egg white lysozyme are studied by analysis of simulation and experimental data. A molecular dynamics simulation and an energy minimization of the protein in vacuum have been made and the results compared with high-resolution structures and temperature factors of hen egg white lysozyme in two different crystal forms and of the homologous protein human lysozyme. The structures obtained from molecular dynamics and energy minimization have root-mean-square deviations for backbone atoms of 2.3 Å and 1.1–1.3 Å, respectively, relative to the crystal structures; the different crystal structures have root-mean-square deviations of 0.73–0.81 Å for the backbone atoms. In comparing the backbone dihedral angles, the difference between the dynamics and the crystal structure on which it is based is the same as that between any two crystal structures. The internal fluctuations of atomic positions calculated from the molecular dynamics trajectory agree well with the temperature factors from the three structures. Simulation and crystal results both show that there are large motions for residues involved in exposed turns of the backbone chain, relatively smaller motions for residues involved in the middle of helices or β-sheet structures, and relatively small motions of residues near disulfide bridges. Also, both the simulation and crystal data show that side-chain atoms have larger fluctuations than main-chain atoms. Moreover, the regions that have large deviations among the x-ray crystal structures, which indicates flexibility, are found to have large fluctuations in the simulation.     

Molecular dynamics simulations of a bacterial autotransporter: NalP from Neisseria meningitidis

NalP is an autotransporter secretory protein found in the outer membrane of Neisseria meningitidis. The crystal structure of the NalP translocator domain revealed a transmembrane beta-barrel containing a central alpha-helix. The role of this alpha-helix, and of the conformational dynamics of the beta-barrel pore have been studied via atomistic molecular dynamics simulations. Three simulations, each of 10 ns duration, of NalP embedded within a solvated DMPC bilayer were performed. The helix was removed from the barrel interior in one simulation. The conformational stability of the protein is similar to that of other outer membrane proteins, e.g., OmpA, in comparable simulations. The transmembrane beta-barrel is stable even in the absence of the alpha-helix. Removal of the helix results in an influx of water into the pore region, suggesting the helix acts as a 'plug'. Water molecules entering the resultant pore form hydrogen bonds with the barrel lining that compensate for the loss of helix-barrel hydrogen bonds. The dimensions of the pore fluctuate over the course of the simulation revealing it to be flexible, but only wide enough to allow transport of the passenger domain in an unfolded or extended conformation. The simulations help us to understand the role of the central helix in plugging the pore and in maintaining the width of the barrel, and show that the NalP monomer is sufficient for the transport of the passenger domain in an unfolded or extended conformation.     

Collective motions in proteins: a covariance analysis of atomic fluctuations in molecular dynamics and normal mode simulations.

A method is described for identifying collective motions in proteins from molecular dynamics trajectories or normal mode simulations. The method makes use of the covariances of atomic positional fluctuations. It is illustrated by an analysis of the bovine pancreatic trypsin inhibitor. Comparison of the covariance and cross-correlation matrices shows that the relative motions have many similar features in the different simulations. Many regions of the protein, especially regions of secondary structure, move in a correlated manner. Anharmonic effects, which are included in the molecular dynamics simulations but not in the normal analysis, are of some importance in determining the larger scale collective motions, but not the more local fluctuations. Comparisons of molecular dynamics simulations in the present and absence of solvent indicate that the environment is of significance for the long-range motions.     

Energetic approach to the folding of alpha/beta barrels

The folding of a polypeptide into a parallel (alpha/beta)8 barrel (which is also called a circularly permuted beta 8 alpha 8 barrel) has been investigated in terms of energy minimization. According to the arrangement of hydrogen bonds between two neighboring beta-strands of the central barrel therein, such an alpha/beta barrel structure can be folded into six different types: (1) left-tilted, left-handed crossover; (2) left-tilted, right-handed crossover; (3) nontilted, left-handed crossover; (4) nontilted, right-handed crossover; (5) right-tilted, left-handed crossover; and (6) right-tilted, right-handed crossover. Here "tilt" refers to the orientational relation of the beta-strands to the axis of the central beta-barrel, and "crossover" to the beta alpha beta folding connection feature of the parallel beta-barrel. It has been found that the right-tilted, right-handed crossover alpha/beta barrel possesses much lower energy than the other five types of alpha/beta barrels, elucidating why the observed alpha/beta barrels in proteins always assume the form of right tilt and right-handed crossover connection. As observed, the beta-strands in the energy-minimized right-tilted, right-handed crossover (alpha/beta)8-barrel are of strong right-handed twist. The value of root-mean-square fits also indicates that the central barrel contained in the lowest energy (alpha/beta)8 structure thus found coincides very well with the observed 8-stranded parallel beta-barrel in triose phosphate isomerase (TIM). Furthermore, an energetic analysis has been made demonstrating why the right-tilt, right-handed crossover barrel is the most stable structure. Our calculations and analysis support the principle that it is possible to account for the main features of frequently occurring folding patterns in proteins by means of conformational energy calculations even for very complicated structures such as (alpha/beta)8 barrels.     

Combination of Neutron Scattering and Molecular Dynamics to Determine Internal Motions in Biomolecules

Abstract

The forms and frequencies of atomic dynamics on the pico- and nanosecond timescales are accessible experimentally using incoherent neutron scattering. Molecular dynamics simulations cover the same space and time domains and neutron scattering intensities can be calculated from the simulations for direct comparison with experiment. To illustrate the complementarity of neutron scattering and molecular dynamics we examine measured and simulation-derived elastic incoherent scattering profiles from myoglobin and from the crystalline alanine dipeptide. Elastic incoherent scattering gives information on the geometry of the volume accessible to the atoms in the samples. The simulation-derived dipeptide elastic scattering profiles are in reasonable accord with experiment, deviations being due to the sampling limitations in the simulations and experimental detector normalisation procedures. The simulated dynamics is decomposed, revealing characteristic profiles due to rotational diffusional and translational vibrational motions of the methyl groups. In myoglobin, for which the timescale of the simulation matches more closely that accessible to the experiment, good agreement is seen for the elastic incoherent structure factor. This indicates that the space sampled by the hydrogen atoms in the protein on the timescale <100 ps is well represented by the simulation. Part of the helix atom fluctuations can be described in terms of rigid helix motions.     

Molecular dynamics simulations of hemoglobin A in different states and bound to DPG: effector-linked perturbation of tertiary conformations and HbA concerted dynamics

Recent functional studies reported on human adult hemoglobin (HbA) show that heterotropic effector-linked tertiary structural changes are primarily responsible for modulating the oxygen affinity of hemoglobin. We present the results of 6-ns molecular dynamics simulations performed to gain insights into the dynamical and structural details of these effector-linked tertiary changes. All-atom simulations were carried out on a series of models generated for T- and R-state HbA, and for 2,3-diphosphoglycerate-bound models. Cross-correlation analyses identify both intra- and intersubunit correlated motions that are perturbed by the presence of the effector. Principal components analysis was used to decompose the covariance matrix extracted from the simulations and reconstruct the trajectories along the principal coordinates representative of functionally important collective motions. It is found that HbA in both quaternary states exists as ensembles of tertiary conformations that introduce dynamic heterogeneity in the protein. 2,3-Diphosphoglycerate induces significant perturbations in the fluctuations of both HbA states that translate into the protein visiting different tertiary conformations within each quaternary state. The analysis reveals that the presence of the effector affects the most important components of HbA motions and that heterotropic effectors modify the overall dynamics of the quaternary equilibrium via tertiary changes occurring in regions where conserved functionally significant residues are located, namely in the loop regions between helices C and E, E and F, and F and G, and in concerted helix motions. The changes are not apparent when comparing the available x-ray crystal structures in the presence and absence of effector, but are striking when comparing the respective dynamic tertiary conformations of the R and T tetramers.     

A molecular dynamics simulation of bacteriophage T4 lysozyme.

An analysis of a 400 ps molecular dynamics simulation of the 164 amino acid enzyme T4 lysozyme is presented. The simulation was carried out with all hydrogen atoms modeled explicitly, the inclusion of all 152 crystallographic waters and at a temperature of 300 K. Temporal analysis of the trajectory versus energy, hydrogen bond stability, r.m.s. deviation from the starting crystal structure and radius of gyration, demonstrates that the simulation was both stable and representative of the average experimental structure. Average structural properties were calculated from the enzyme trajectory and compared with the crystal structure. The mean value of the C alpha displacements of the average simulated structure from the X-ray structure was 1.1 +/- 0.1 A; differences of the backbone phi and psi angles between the average simulated structure and the crystal structure were also examined. Thermal-B factors were calculated from the simulation for heavy and backbone atoms and both were in good agreement with experimental values. Relationships between protein secondary structure elements and internal motions were studied by examining the positional fluctuations of individual helix, sheet and turn structures. The structural integrity in the secondary structure units was preserved throughout the simulation; however, the A helix did show some unusually high atomic fluctuations. The largest backbone atom r.m.s. fluctuations were found in non-secondary structure regions; similar results were observed for r.m.s. fluctuations of non-secondary structure phi and psi angles. In general, the calculated values of r.m.s. fluctuations were quite small for the secondary structure elements. In contrast, surface loops and turns exhibited much larger values, being able to sample larger regions of conformational space. The C alpha difference distance matrix and super-positioning analyses comparing the X-ray structure with the average dynamics structure suggest that a 'hinge-bending' motion occurs between the N- and C-terminal domains.     

Modelling the dynamics of an antigenic peptide using NMR relaxation data.

The internal dynamics of a cyclic peptide which was designed to mimic an antigenic loop of the haemagglutinin, is studied through heteronuclear relaxation along the 13C alpha-1H alpha vectors and through homonuclear relaxation along the 1H alpha-1HN and 1H beta-1H beta' vectors. Order parameters are extracted from the longitudinal and cross-relaxation data. Molecular dynamics simulations are performed and the order parameters are calculated in different ways from the trajectories. The simulation, which is performed in vacuo, gives smaller order parameters (vector motions of larger amplitude) than the experimental results. However, the general features of the experimental order parameters are reproduced by the molecular dynamics simulation. The flexibility of the molecule can then be investigated from the results of the molecular dynamics. It shows that the mobility observed through the order parameters is due to motions in flanking regions, remote from the observed vectors.     

A molecular dynamics study of the C-terminal fragment of the L7/L12 ribosomal protein. Secondary structure motion in a 150 picosecond trajectory

A 150 picosecond molecular dynamics computer simulation of the C-terminal fragment of the L7/L12 ribosomal protein from Escherichia coli is reported. The molecular dynamics results are compared with the available high-resolution X-ray data in terms of atomic positions, distances and positional fluctuations. Good agreement is found between the molecular dynamics results and the X-ray data. The form and parameters of the interaction potential energy function and the procedures for deriving it are discussed. Some current misunderstandings concerning the ways of evaluating the efficiency of molecular dynamics algorithms and of application of bond-length constraints in protein simulations are cleared up. The 150 picosecond trajectory has been scanned in a search for correlated motions within and between secondary structure elements. The beta-strands have diffusional stretching modes, and uncorrelated transversal displacements. The dynamic analysis of alpha-helices shows a variety of features. The atomic fluctuations differ between the helix ends; this effect reflects long time-scale motions. Two alpha-helices, alpha A and alpha C, show diffusive longitudinal stretching modes. The third helix, alpha B, has a correlated asymmetric longitudinal stretching; the N-terminal part dominates this behaviour. Furthermore, alpha B presents a librational motion with respect to the other parts of the molecule with a frequency of approximately 5 cm-1. This motion is coupled to helix stretching. Interestingly, the regions of highly conserved residues contain the most mobile parts of the molecule.     

The crystal structure of human muscle aldolase at 3.0 A resolution

The three-dimensional structure of fructose-1,6-bisphosphate aldolase from human muscle has been determined at 3.0 A resolution by X-ray crystallography. The active protein is a tetramer of 4 identical subunits each of which is composed of an eight-stranded alpha/beta-barrel structure. The lysine residue responsible for Schiff base formation with the substrate is located near the centre of the barrel in the middle of the sixth beta-strand. While the overall topology of the alpha/beta-barrel is very similar to those found in several other enzymes, the distribution of charged residues inside the core of the barrel seems distinct. The quaternary fold of human muscle aldolase uses interfacial regions also involved in the subunit association of other alpha/beta-barrel proteins found in glycolysis, but exploits these regions in a manner not seen previously.     

In meso crystal structure and docking simulations suggest an alternative proteoglycan binding site in the OpcA outer membrane adhesin

OpcA is an integral outer membrane adhesin protein from Neisseria meningitidis, the causative agent of meningococcal meningitis and septicemia. It binds to sialic acid (SA)-containing polysaccharides on the surface of epithelial cells. The crystal structure of OpcA showed that the protein adopts a 10-stranded beta-barrel structure, with five extensive loop regions on the extracellular side of the membrane. These form a crevice structure, lined with basic residues, which was hypothesized to act as the binding site for polysaccharide ligands. In the current study, a distinctly different OpcA structure has been obtained using crystals grown from a lipidic mesophase. Comparison of the two structures shows that the largest loop (L2), which closes over the end of the beta-barrel in the original crystal form, adopts a much more extended structure by reaching outward and away from the protein. The difference in conformation may be attributable to the absence of zinc ions from the crystallization conditions for the in meso crystal form: in the original structure, two zinc ions were bound to the external loops. Molecular dynamics (MD) simulations performed on the two OpcA models in a lipid bilayer environment demonstrated pronounced loop mobility. These observations support the view that the loop regions of OpcA are capable of a high degree of conformational flexibility. The original binding site for polysaccharide is not present in the in meso crystal form, and is disrupted during MD simulations. Docking analysis suggests a putative alternative location for the SA ligand in the new crystal form of OpcA.     

Anisotropy and anharmonicity of atomic fluctuations in proteins: analysis of a molecular dynamics simulation

Positional probability density functions (pdf) for the atomic fluctuations are determined from a molecular dynamics simulation for hen egg-white lysozyme. Most atoms are found to have motions that are highly anisotropic but only slightly anharmonic. The largest deviations from harmonic motion are in the direction of the largest rms fluctuations in the local principal axis frame. Backbone atoms tend to be more nearly harmonic than sidechain atoms. The atoms with the largest anharmonicities tend to have pdfs with multiple peaks, each of which is close to harmonic. Several model pdfs are evaluated on the basis of how well they fit probability densities from the dynamics simulations when parameterized in terms of the moments of the distribution. Gram-Charlier and Edgeworth perturbation expansions, which have been successful in describing the motions of small molecules in crystals, are shown to be inadequate for the distributions found in the dynamics of proteins. Multipeaked distribution functions are found to be more appropriate.     

OmpA: a pore or not a pore? Simulation and modeling studies

The bacterial outer membrane protein OmpA is composed of an N-terminal 171-residue beta-barrel domain (OmpA(171)) that spans the bilayer and a periplasmic, C-terminal domain of unknown structure. OmpA has been suggested to primarily serve a structural role, as no continuous pore through the center of the barrel can be discerned in the crystal structure of OmpA(171). However, several groups have recorded ionic conductances for bilayer-reconstituted OmpA(171). To resolve this apparent paradox we have used molecular dynamics (MD) simulations on OmpA(171) to explore the conformational dynamics of the protein, in particular the possibility of transient formation of a central pore. A total of 19 ns of MD simulations of OmpA(171) have been run, and the results were analyzed in terms of 1) comparative behavior of OmpA(171) in different bilayer and bilayer-mimetic environments, 2) solvation states of OmpA(171), and 3) pore characteristics in different MD simulations. Significant mobility was observed for residues and water molecules within the beta-barrel. A simulation in which putative gate region side chains of the barrel interior were held in a non-native conformation led to an open pore, with a predicted conductance similar to experimental measurements. The OmpA(171) pore has been shown to be somewhat more dynamic than suggested by the crystal structure. A gating mechanism is proposed to explain its documented channel properties, involving a flickering isomerization of Arg138, forming alternate salt bridges with Glu52 (closed state) and Glu128 (open state).     

Molecular dynamics simulations of the holo and apo forms of retinol binding protein. Structural and dynamical changes induced by retinol removal

The effects of removing retinol from the X-ray structure of holo-retinol binding protein are studied using the molecular dynamics technique. Structural and dynamical properties emerging from an 80 ps simulation of the apo form, for which no crystallographic structure is available, are compared with the results of a 70 ps trajectory of the holo-protein. Dynamical stationarity is attained after roughly 30 ps, and the resulting average structure is proposed as a reasonable model of the apo-protein. Conformational changes are observed for the loops at the beta-barrel entrance during the non-equilibrium part of the apo-trajectory. Tryptophan labelling experiments and retinoid reconstitution experiments point towards this part of the molecule as being involved in prealbumin binding. Structural changes in this region may therefore explain the differences in prealbumin affinity between the apo and holo forms. Furthermore, a change in the position of the alpha-helix, corresponding to a pivot around its C terminus, is observed for the apo-protein. The resulting conformation of the alpha-helix is found to be similar to that in apo-beta-lactoglobulin, which also can bind retinol and for which a crystal structure exists. The results from the holo simulation are compared to the crystallographic data and show good agreement. The dynamics of the secondary and tertiary structural elements are analysed and compared for the two forms. The beta-barrel is found to be extremely cooperative in its atomic motions in both simulations, and the top and bottom beta-sheets perform collective fluctuations with respect to each other in the low-frequency limit of the simulations. The dynamics of the alpha-helical region presents clear differences between the two forms; while the holo-protein has a well-defined spectrum for the longitudinal stretching mode, the apo form displays a fairly large bending of the alpha-helix at several points of the trajectory.     

Alpha7 helix plays an important role in the conformational stability of PTP1B

The C-terminus of Protein Tyrosine Phosphatase 1B (PTP1B) includes an α-helix α7), which forms an allosteric binding site 20 ? away from the active site. This helix is specific to PTP1B and its truncation decreases the catalytic activity significantly. Here, molecular dynamics (MD) simulations in the presence and absence of α7 were performed to investigate the role played by α7. The highly mobile α7 was found to maintain its contacts with loop 11 (L11)α3 helix throughout the simulations. The interactions of Tyr152 on L11, Tyr176, Thr177 on the catalytically important WPD loop and Ser190 on α3 are important for the conformational stability and the concerted motions of the regions surrounding the WPD loop. In the absence of α7, L11 and WPD loop move away from their crystal structure conformations, resulting in the loss of the interactions in this region, and a decrease in the residue displacement correlations in the vicinity of WPD loop. Therefore, we suggest that one of the functionally important roles of α7 may be to limit the L11 and α3 motions, and, facilitate the WPD loop motions. Truncation of α7 in PTP1B is found to affect distant regions as well, such as the substrate recognition site and the phosphate binding-loop (P-loop), changing the conformations of these regions significantly. Our results show that the PTP1B specific α7 is important for the conformation and dynamics of the WPD loop, and also may play a role in ligand binding.     

Characterization of the Conformational Fluctuations in the Josephin Domain of Ataxin-3

As for a variety of other molecular recognition processes, conformational fluctuations play an important role in the cleavage of polyubiquitin chains by the Josephin domain of ataxin-3. The interaction between Josephin and ubiquitin appears to be mediated by the motions of α-helical hairpin that is unusual among deubiquitinating enzymes. Here, we characterized the conformational fluctuations of the helical hairpin by incorporating NMR measurements as replica-averaged restraints in molecular dynamics simulations, and by validating the results by small-angle x-ray scattering measurements. This approach allowed us to define the extent of the helical hairpin motions and suggest a role of such motions in the recognition of ubiquitin.     

Motions and structural variability within toxins: implication for their use as scaffolds for protein engineering

Animal toxins are small proteins built on the basis of a few disulfide bonded frameworks. Because of their high variability in sequence and biologic function, these proteins are now used as templates for protein engineering. Here we report the extensive characterization of the structure and dynamics of two toxin folds, the "three-finger" fold and the short alpha/beta scorpion fold found in snake and scorpion venoms, respectively. These two folds have a very different architecture; the short alpha/beta scorpion fold is highly compact, whereas the "three-finger" fold is a beta structure presenting large flexible loops. First, the crystal structure of the snake toxin alpha was solved at 1.8-A resolution. Then, long molecular dynamics simulations (10 ns) in water boxes of the snake toxin alpha and the scorpion charybdotoxin were performed, starting either from the crystal or the solution structure. For both proteins, the crystal structure is stabilized by more hydrogen bonds than the solution structure, and the trajectory starting from the X-ray structure is more stable than the trajectory started from the NMR structure. The trajectories started from the X-ray structure are in agreement with the experimental NMR and X-ray data about the protein dynamics. Both proteins exhibit fast motions with an amplitude correlated to their secondary structure. In contrast, slower motions are essentially only observed in toxin alpha. The regions submitted to rare motions during the simulations are those that exhibit millisecond time-scale motions. Lastly, the structural variations within each fold family are described. The localization and the amplitude of these variations suggest that the regions presenting large-scale motions should be those tolerant to large insertions or deletions.