Picosecond timescale rigid-helix and side-chain motions in deoxymyoglobin

Elastic and conformational softness of a globular protein

Flexibility, or softness, is crucial for protein function and consists of a conformational component, involving jumps between potential wells, and an elastic component, involving fluctuations within the wells. Combining molecular dynamics simulation with incoherent neutron scattering and light scattering measurements on green fluorescent protein, we reveal a relationship between the intrawell fluctuations and elastic moduli of the protein. This finding leads to a simple means of experimentally separating the conformational from the elastic atomic displacements.

Origin of slow relaxation following photoexcitation of W7 in myoglobin and the dynamics of its hydration layer

Molecular dynamics simulations are used to calculate the time-dependent Stokes shift following photoexcitation of Trp-7 (W7) in myoglobin. In agreement with experiment, a long time (approximately 60 ps) component is observed. Since the long time Stokes shift component is absent when we repeat the calculation with protein frozen at the instant of photoexcitation, we firmly establish that protein flexibility is required to observe slow Stokes shift dynamics in this case. A transition between sub-states near the middle of a 30 ns ground-state trajectory gave us an opportunity to compare solvation dynamics in two different environments. While some of the superficial features are different, we find that the underlying dynamics are shared by the two isomers. It is necessary to look beyond a decomposition of the Stokes shift into protein and water contributions and probe the underlying dynamics of protein side groups, backbone, and water dynamics to obtain a full picture of the relaxation process. We analyze water residence times, diffusion, and reorientation dynamics in the hydration layer. We find slow components in each of these quantities and critically examine their origin and how they affect the observed Stokes shift.

Hydration dynamics and time scales of coupled water-protein fluctuations

We report experimental and theoretical studies on water and protein dynamics following photoexcitation of apomyoglobin. Using site-directed mutation and with femtosecond resolution, we experimentally observed relaxation dynamics with a biphasic distribution of time scales, 5 and 87 ps, around the site Trp7. Theoretical studies using both linear response and direct nonequilibrium molecular dynamics (MD) calculations reproduced the biphasic behavior. Further constrained MD simulations with either frozen protein or frozen water revealed the molecular mechanism of slow hydration processes and elucidated the role of protein fluctuations. Observation of slow water dynamics in MD simulations requires protein flexibility, regardless of whether the slow Stokes shift component results from the water or protein contribution. The initial dynamics in a few picoseconds represents fast local motions such as reorientations and translations of hydrating water molecules, followed by slow relaxation involving strongly coupled water-protein motions. We observed a transition from one isomeric protein configuration to another after 10 ns during our 30 ns ground-state simulation. For one isomer, the surface hydration energy dominates the slow component of the total relaxation energy. For the other isomer, the slow component is dominated by protein interactions with the chromophore. In both cases, coupled water-protein motion is shown to be necessary for observation of the slow dynamics. Such biologically important water-protein motions occur on tens of picoseconds. One significant discrepancy exists between theory and experiment, the large inertial relaxation predicted by simulations but clearly absent in experiment. Further improvements required in the theoretical model are discussed.

Exploring global motions and correlations in the ribosome

We studied slower global coupled motions of the ribosome with half a microsecond of coarse-grained molecular dynamics. A low-resolution anharmonic network model that allows for the evolution of tertiary structure and long-scale sampling was developed and parameterized. Most importantly, we find that functionally important movements of L7/L12 and L1 lateral stalks are anticorrelated. Other principal directions of motions include widening of the tRNA cleft and the rotation of the small subunit which occurs as one block and is in phase with the movement of L1 stalk. The effect of the dynamical correlation pattern on the elongation process is discussed. Small fluctuations of the 3' tRNA termini and anticodon nucleotides show tight alignment of substrates for the reaction. Our model provides an efficient and reliable way to study the dynamics of large biomolecular systems composed of both proteins and nucleic acids.

High-resolution prediction of protein helix positions and orientations

We have developed a new method for predicting helix positions in globular proteins that is intended primarily for comparative modeling and other applications where high precision is required. Unlike helix packing algorithms designed for ab initio folding, we assume that knowledge is available about the qualitative placement of all helices. However, even among homologous proteins, the corresponding helices can demonstrate substantial differences in positions and orientations, and for this reason, improperly positioned helices can contribute significantly to the overall backbone root-mean-square deviation (RMSD) of comparative models. A helix packing algorithm for use in comparative modeling must obtain high precision to be useful, and for this reason we utilize an all-atom protein force field (OPLS) and a Generalized Born continuum solvent model. To reduce the computational expense associated with using a detailed, physics-based energy function, we have developed new hierarchical and multiscale algorithms for sampling the helices and flanking loops. We validate the method using a test suite of 33 cases, which are drawn from a diverse set of high-resolution crystal structures. The helix positions are reproduced with an average backbone RMSD of 0.6 A, while the average backbone RMSD of the complete loop-helix-loop region (i.e., the helix with the surrounding loops, which are also repredicted) is 1.3 A.

Building-block approach for determining low-frequency normal modes of macromolecules

Normal mode analysis of proteins of various sizes, ranging from 46 (crambin) up to 858 residues (dimeric citrate synthase) were performed, by using standard approaches, as well as a recently proposed method that rests on the hypothesis that low-frequency normal modes of proteins can be described as pure rigid-body motions of blocks of consecutive amino-acid residues. Such a hypothesis is strongly supported by our results, because we show that the latter method, named RTB, yields very accurate approximations for the low-frequency normal modes of all proteins considered. Moreover, the quality of the normal modes thus obtained depends very little on the way the polypeptidic chain is split into blocks. Noteworthy, with six amino-acids per block, the normal modes are almost as accurate as with a single amino-acid per block. In this case, for a protein of n residues and N atoms, the RTB method requires the diagonalization of an n x n matrix, whereas standard procedures require the diagonalization of a 3N x 3N matrix. Being a fast method, our approach can be useful for normal mode analyses of large systems, paving the way for further developments and applications in contexts for which the normal modes are needed frequently, as for example during molecular dynamics calculations.

A synthetic picture of intramolecular dynamics of proteins. Towards a contemporary statistical theory of biochemical processes

An increasing body of experimental evidence indicates the slow character of internal dynamics of native proteins. The important consequence of this is that theories of chemical reactions, used hitherto, appear inadequate for description of most biochemical reactions. Construction of a contemporary, truly advanced statistical theory of biochemical processes will need simple but realistic models of microscopic dynamics of biomolecules. In this review, intended to be a contribution towards this direction, three topics are considered. First, an intentionally simplified picture of dynamics of native proteins which emerges from recent investigations is presented. Fast vibrational modes of motion, of periods varying from 10(-14) to 10(-11) s, are contrasted with purely stochastic conformational transitions. Significant evidence is adduced that the relaxation time spectrum of the latter spreads in the whole range from 10(-11) to 10(5) s or longer, and up to 10(-7) s it is practically quasi-continuous. Next, the essential ideas of the theory of reaction rates based on stochastic models of intramolecular dynamics are outlined. Special attention is paid to reactions involving molecules in the initial conformational substrates confirmed to the transition state, which is realized in actual experimental situations. And finally, the two best experimentally justified classes of models of conformational transition dynamics, symbolically referred to as "protein glass" and "protein machine", are described and applied to the interpretation of a few simple biochemical processes, perhaps the most important result reported is the demonstration of the possibility of predominance of the short initial condition-dependent stage of protein involved reactions over the main stage described by the standard kinetics. This initial stage, and not the latter, is expected to be responsible for the coupling of component reactions in the complete enzymatic cycles as well as more complex processes of biological free energy transduction.

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.

Molecular dynamics of individual alpha-helices of bacteriorhodopsin in dimyristol phosphatidylocholine. I. Structure and dynamics

Understanding the role of the lipid bilayer in membrane protein structure and dynamics is needed for tertiary structure determination methods. However, the molecular details are not well understood. Molecular dynamics computer calculations can provide insight into these molecular details of protein:lipid interactions. This paper reports on 10 simulations of individual alpha-helices in explicit lipid bilayers. The 10 helices were selected from the bacteriorhodopsin structure as representative alpha-helical membrane folding components. The bilayer is constructed of dimyristoyl phosphatidylcholine molecules. The only major difference between simulations is the primary sequence of the alpha-helix. The results show dramatic differences in motional behavior between alpha-helices. For example, helix A has much smaller root-mean-squared deviations than does helix D. This can be understood in terms of the presence of aromatic residues at the interface for helix A that are not present in helix D. Additional motions are possible for the helices that contain proline side chains relative to other amino acids. The results thus provide insight into the types of motion and the average structures possible for helices within the bilayer setting and demonstrate the strength of molecular simulations in providing molecular details that are not directly visualized in experiments.

Search for rigid sub domains in DNA from molecular dynamics simulations

A strategy is presented for searching which atoms can be regrouped within rigid sub-units during the time course of Molecular Dynamics simulations of biopolymers. The root mean square fluctuations of the interatomic distances are used as a criterion. The number of rigid sub-units which are found depends on the tolerance rc for the definition of a rigid body, i.e. until which value the fluctuations can be neglected. The method is applied to two self-complementary oligonucleotides belonging to the B-form family which give identical results. With rc = 0.027 nm each nucleotide may be described as 3 rigid sub-units: the sugar ring, the base and the backbone (PO4 + C5' atoms). With rc = 0.01 nm, the same sub-units are obtained except that C5' can no more be regrouped with the PO4 atoms. It is shown that the variation of the coulombic potential owing to the deformation of the sub-units during the time course of the simulation is on the same order of magnitude as the inaccuracy due to the choice of the force field parameters.

Dynamics of hydrogen atoms in superoxide dismutase by quasielastic neutron scattering

The low energy dynamic of the enzyme Cu,Zn superoxide dismutase have been investigated by means of quasielastic neutron scattering in the temperature range 4-320 K. Below 200 K the scattering is purely elastic, while above this temperature a pronounced decrease in the elastic intensity is observed, together with the onset of a small quasielastic component. This behavior is similar to that previously observed in other more flexible globular proteins, and can be attributed to transitions between slightly different conformational substates of the protein tertiary structure. The presence of only a small quasielastic component, whose intensity is < or = 25% of the total spectrum, is related to the high structural rigidity of this protein.

Low-frequency vibrations in alpha-helices: helicoidal analysis of polyalanine and deoxymyoglobin molecular dynamics trajectories

We present an approach to the analysis of low-frequency (0-200 cm-1) alpha-helix vibrations in molecular dynamics simulations. The approach employs the P-Curves algorithm [H. Sklenar, C. Etchebest, and R. Lavery, (1989) Proteins: Structure, Function and Genetics, Vol. 6, pp. 46-60] to determine the helical axis and a set of helicoidal parameters describing the axis curvature and the position of the repeating units with respect to the axis and each other. The vibrations are analyzed in terms of time correlation functions of the fluctuations of P-Curves parameters and their Fourier transforms. Simulations of polyalanine and myoglobin are analyzed. For polyalanine, global twisting, bending, and stretching vibrations are found at 11, 20, and 40 cm-1, respectively. In myoglobin, the spectra of the global helix vibrations are qualitatively different from those of polyalanine and considerably more complicated. Local vibrations of individual amino acid units in the helix backbones are also analyzed with P-Curves and compared.

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).

Rigid-body motions of sub-units in DNA: a correlation analysis of a 200 ps molecular dynamics simulation

A 200 ps molecular dynamics simulation of the B-form double stranded self-complementary octanucleotide d(CTGATCAG) is analyzed in terms of correlated motions using the canonical analysis approach. Each nucleotide is decomposed in three sub-units corresponding to the base, the sugar ring and the backbone respectively. The correlation between the full dynamics of two sub-units was found to decrease as their mutual distance increases. The interpretation of the full dynamics of sub-units as the superimposition of rigid-body motions (translation and orientation) and deformation shows that the main source of correlation is rigid-body motions. Correlation between sub-units deformation is weak and practically vanishes for sub-units belonging to non-adjacent nucleotides. It is also shown that the correlation is much more important for sub-units of the same strand than of opposite strands. We conclude that the internal dynamics of the octanucleotide may be well described by rigid-body motions, the sub-units deformation having only local influence whereas sub-units translation and rotation have repercussion to long distances. The results presented in this study suggest how the number of degrees of freedom may be reduced for simulating long-time dynamics of oligonucleotides.

Structure and dynamics of the water around myoglobin

The interplay between simulations at various levels of hydration and experimental observables has led to a picture of the role of solvent in thermodynamics and dynamics of protein systems. One of the most studied protein-solvent systems is myoglobin, which serves as a paradigm for the development of structure-function relationships in many biophysical studies. We review here some aspects of the solvation of myoglobin and the resulting implications. In particular, recent theoretical and simulation studies unify much of the diverse set of experimental results on water near proteins.

Protein structure prediction: recognition of primary, secondary, and tertiary structural features from amino acid sequence

This review attempts a critical stock-taking of the current state of the science aimed at predicting structural features of proteins from their amino acid sequences. At the primary structure level, methods are considered for detection of remotely related sequences and for recognizing amino acid patterns to predict posttranslational modifications and binding sites. The techniques involving secondary structural features include prediction of secondary structure, membrane-spanning regions, and secondary structural class. At the tertiary structural level, methods for threading a sequence into a mainchain fold, homology modeling and assigning sequences to protein families with similar folds are discussed. A literature analysis suggests that, to date, threading techniques are not able to show their superiority over sequence pattern recognition methods. Recent progress in the state of ab initio structure calculation is reviewed in detail. The analysis shows that many structural features can be predicted from the amino acid sequence much better than just a few years ago and with attendant utility in experimental research. Best prediction can be achieved for new protein sequences that can be assigned to well-studied protein families. For single sequences without homologues, the folding problem has not yet been solved.

Protein interactions and dynamics probed by quantum chemistry, computer simulations and neutron experiments

We review some recent experiments and calculations on aspects of the structure and dynamics of proteins and related systems. The use of quantum chemical techniques to determine geometries and energies of supramolecular complexes of biological interest is illustrated, and the concomitant development of empirical energy functions for use in protein simulations outlined. We describe how simulations of crystalline peptides and amino-acids using an empirical force field can be combined with appropriate coherent and incoherent inelastic neutron scattering experiments to elucidate the characteristics of lattice vibrations and diffusive atomic motions in the crystals. The application of molecular dynamics simulations to the interpretation of incoherent neutron scattering experiments on proteins is examined and the resulting ideas on the general characteristics of protein motion discussed in terms of their functional implications.

Correlated intramolecular motions and diffuse X-ray scattering in lysozyme

Correlated motions of protein atoms are of biological significance in processes involving ligand binding, conformational change and information transmission. X-ray scattering patterns from protein crystals contain diffuse scattering that originates from correlated displacements of atoms. Here we present experimental data on diffuse X-ray scattering from lysozyme crystals. We show that the diffuse scattering is similar in form to scattering derived from molecular dynamics simulation and normal mode analysis of the isolated protein, the normal modes giving the closest agreement with experiment.

Structure and dynamics of bacteriorhodopsin. Comparison of simulation and experiment

Global features of the structure and dynamics of bacteriorhodopsin are investigated using molecular modelling, dynamical simulations and neutron scattering experiments. The simulations are performed on a model system consisting of one protein molecule plus intrinsic water molecules. The simulation-derived structure is compared with neutron diffraction data on the location of water and with the available electron microscopy structure of highest resolution. The simulated water geometry is in good accord with the neutron data. The protein structure deviates slightly but significantly from the experiment. The low-frequency vibrational frequency distribution of a low-hydration purple membrane is derived from inelastic neutron scattering data and compared with the corresponding simulation-derived quantity.