Two- and Higher Point Correlation Functions in Proteins

Abstract

A method is presented for a more efficient sampling of the configurational space of proteins as compared to conventional sampling techniques such as molecular dynamics. The method is based on the large conformational changes in proteins revealed by the “essential dynamics” analysis. A form of constrained dynamics is performed, forcing the system to move along some of the essential coordinates. This results in a broader sampling of the essential subspace than in a comparable conventional molecular dynamics simulation without constraints. The new sampling method (essential dynamics sampling) was applied to the histidine-containing phosphocarrier protein HPr. The results indicate that the essential dynamics sampling method produces physically allowed structures, as estimated by the evaluation of many geometrical properties. In addition, a study of the motions in the essential subspace reveals a diffusion-like behavior.     

Insight Derived from Molecular Dynamics Simulation into Substrate-Induced Changes in Protein Motions of Proteinase K

Abstract

Because of the significant industrial, agricultural and biotechnological importance of serine protease proteinase K, it has been extensively investigated using experimental approaches such as X-ray crystallography, site-directed mutagenesis and kinetic measurement. However, detailed aspects of enzymatic mechanism such as substrate binding, release and relevant regulation remain unstudied. Molecular dynamics (MD) simulations of the proteinase K alone and in complex with the peptide substrate AAPA were performed to investigate the effect of substrate binding on the dynamics/molecular motions of proteinase K. The results indicate that during simulations the substrate-complexed proteinase K adopt a more compact and stable conformation than the substrate-free form. Further essential dynamics (ED) analysis reveals that the major internal motions are confined within a subspace of very small dimension. Upon substrate binding, the overall flexibility of the protease is reduced; and the noticeable displacements are observed not only in substrate-binding regions but also in regions opposite the substrate-binding groove/pockets. The dynamic pockets caused by the large concerted motions are proposed to be linked to the substrate recognition, binding, orientation and product release; and the significant displacements in regions opposite the binding groove/pockets are considered to play a role in modulating the dynamics of enzyme-substrate interaction. Our simulation results complement the biochemical and structural studies, highlighting the dynamic mechanism of the functional properties of proteinase K.     

Molecular Dynamics of Phenylalanine Transfer RNA

Abstract

The atomic motions of yeast phenylalanine transfer RNA have been simulated using the molecular dynamics algorithm. Two simulations were carried out for a period of 12 picoseconds, one with a normal Van der Waals potential and the other with a modified Van der Waals potential intended to mimic the effect of solvent. An analysis of large scale motions, surface exposure, root mean square displacements, helical oscillations and relaxation mechanisms reveals the maintenance of stability in the simulated structures and the general similarity of the various dynamic features of the two simulations. The regions of conformational flexibility and rigidity for tRNA^Phe have been shown in a quantitative measure through this approach.     

Direct Measurement of Hydration-Related Dynamic Changes in Lysozyme using Inelastic Neutron Scattering Spectroscopy

Abstract

Inelastic neutron scattering spectroscopy is used to investigate dynamic changes in lysozyme powder at two different low D,0 hydrations (0.07g D²,O/g protein and 0,20 g D²,O/g protein). In the higher hydration sample, the inelastic scattering between 0.8 and 4.0 cm^?1 energy transfer is increased and the elastic scattering is decreased. The decreased elastic scattering suggests increased atomic amplitudes of motion and the increased 0.8 to 4.0 cm^?1 scattering suggests increased motions in this frequency range. Comparison with normal mode models of lysozyme dynamics shows that the inelastic difference occurs in the frequency region predicted for the lowest frequency, largest amplitude, global modes of the molccule[M. Levitt, C. Sanderand P. S. Stern, J. Mol. Biol. 181. 423 (1985). B.Brooks and M.Karplus.Prot. Natl Acad. Sci (U.S.A) 82. 4995 (1985), R.E. Bruccoleri, M. Karplus and J.A. McCammon, Biopolymers 25 1767 (1986)]. Our results are consistent with a model in which an increased number of low frequency global modes are present in the higher hydrated sample.     

Comparison of normal mode analyses on a small globular protein in dihedral angle space and Cartesian coordinate space

Normal mode analyses on the protein, bovine pancreatic trypsin inhibitor, in dihedral angle space and Cartesian coordinate space are compared. In Cartesian coordinate space it is found that modes of frequencies lower than 30 cm(-1) contribute 80% of the total mean-square fluctuation and are represented almost completely by motions in the dihedral angles. Bond angle and length fluctuations dominate in modes above 200 cm(-1), but contribute less than 2% to the total mean-square fluctuation. In the low-frequency modes a good correspondence between patterns of atomic displacements was found, but on average the root-mean-square fluctuations of the Cartesian coordinate modes are 13% greater than their dihedral angle counterparts. The main effect of fluctuations in the bond angles and lengths, therefore, is to allow the dihedral angles to become more flexible. As the important subspaces determined from the two methods overlap considerably, dihedral angle space analysis can be applied to proteins too large for Cartesian coordinate space analysis.     

Analysis of conformational motions and related key residue interactions responsible for a specific function of proteins with elastic network model

Protein collective motions play a critical role in many biochemical processes. How to predict the functional motions and the related key residue interactions in proteins is important for our understanding in the mechanism of the biochemical processes. Normal mode analysis (NMA) of the elastic network model (ENM) is one of the effective approaches to investigate the structure-encoded motions in proteins. However, the motion modes revealed by the conventional NMA approach do not necessarily correspond to a specific function of protein. In the present work, a new analysis method was proposed to identify the motion modes responsible for a specific function of proteins and then predict the key residue interactions involved in the functional motions by using a perturbation approach. In our method, an internal coordinate that accounts for the specific function was introduced, and the Cartesian coordinate space was transformed into the internal/Cartesian space by using linear approximation, where the introduced internal coordinate serves as one of the axes of the coordinate space. NMA of ENM in this internal/Cartesian space was performed and the function-relevant motion modes were identified according to their contributions to the specific function of proteins. Then the key residue interactions important for the functional motions of the protein were predicted as the interactions whose perturbation largely influences the fluctuation along the internal coordinate. Using our proposed methods, the maltose transporter (MalFGK₂) from E. Coli was studied. The functional motions and the key residue interactions that are related to the channel-gating function of this protein were successfully identified.     

Atomic mean-square displacements in proteins by molecular dynamics: a case for analysis of variance

Information on protein internal motions is usually obtained through the analysis of atomic mean-square displacements, which are a measure of variability of the atomic positions distribution functions. We report a statistical approach to analyze molecular dynamics data on these displacements that is based on probability distribution functions. Using a technique inspired by the analysis of variance, we compute unbiased, reliable mean-square displacements of the atoms and analyze them statistically. We applied this procedure to characterize protein thermostability by comparing the results for a thermophilic enzyme and a mesophilic homolog. In agreement with previous experimental observations, our analysis suggests that the proteins surface regions can play a role in the different thermal behavior.     

On the Atomic Velocities in Molecular and Langevin Dynamics Simulations of Soft-Sphere Systems

Abstract

Time dependent probability distributions of the changes of direction of atomic velocities are considered in order to examine in detail the shape of the trajectories obtained through molecular simulations. We have analysed the atomic motions obtained from molecular dynamics simulations of soft-sphere systems at three very different states, i.e. a dilute fluid, a liquid at high density, and a solid. The methodology has also been used to check the reliability of the velocity evolution obtained when it is assumed that a single particle obeys the generalized Langevin equation and the effect of the other particles is represented by friction and random forces.     

Protein dynamics in solution and powder measured by incoherent elastic neutron scattering: the influence of Q-range and energy resolution

Incoherent elastic neutron scattering (IENS) has been widely used to measure intramolecular atomic mean square displacements (MSDs) of proteins in powder and in solution. The instrumental energy resolution and the wave vector transfer (Q-range) determine, respectively, the time and length scales of observable motions. In order to investigate contributions of diffusive motions to MSDs measured by this method, we calculated the elastic intensity for several simple scattering functions. We showed that continuous translational diffusion contributes to MSDs in a Q-range where the energy width of the scattering function is of the order of the instrumental energy resolution. We discuss the choice of instruments adapted to focus on intramolecular motions in the presence of solvent or global macromolecular diffusion. The concepts developed are applied to interpret experimental data from H₂O- and D₂O-hydrated proteins. Finally, analogies between the Gaussian approximation in IENS and the Guinier approximation in small-angle scattering are discussed.     

New Methodology for Computer-Aided Modelling of Biomolecular Structure and Dynamics 1. Non-Cyclic Structures

Abstract

A general methodology is proposed for the conformational modelling of biomolecular systems. The approach allows one: (i) to describe the system under investigation by an arbitrary set of internal variables, i.e., torsion angles, bond angles, and bond lengths; it offers a possibility to pass from the free structure to a completely fixed one with the number of variables from 3N to zero, respectively, where N is the number of atoms; (ii) to consider both, a single molecule and a complex of many molecules, (e.g., proteins, water, ligands, etc.) in terms of one universal model; (iii) to study the dynamics of the system using explicit analytical Lagrangian equations of motion, thus opening up possibilities for investigations of slow concerted motions such as domain oscillations in proteins etc.; (iv) to calculate the partial derivatives of various functions of conformation, e.g., the conformatinal energy or external constraints imposed, using a standard efficient procedure regardless of the variables and the structure of the system. The approach is meant to be used in various investigations concerning the conformations and dynamics of biomacromolecules.     

Model-free methods of analyzing domain motions in proteins from simulation: A comparison of normal mode analysis and molecular dynamics simulation of lysozyme

Model-free methods are introduced to determine quantities pertaining to protein domain motions from normal mode analyses and molecular dynamics simulations. For the normal mode analysis, the methods are based on the assumption that in low frequency modes, domain motions can be well approximated by modes of motion external to the domains. To analyze the molecular dynamics trajectory, a principal component analysis tailored specifically to analyze interdomain motions is applied. A method based on the curl of the atomic displacements is described, which yields a sharp discrimination of domains, and which defines a unique interdomain screw-axis. Hinge axes are defined and classified as twist or closure axes depending on their direction. The methods have been tested on lysozyme. A remarkable correspondence was found between the first normal mode axis and the first principal mode axis, with both axes passing within 3 Å of the alpha-carbon atoms of residues 2, 39, and 56 of human lysozyme, and near the interdomain helix. The axes of the first modes are overwhelmingly closure axes. A lesser degree of correspondence is found for the second modes, but in both cases they are more twist axes than closure axes. Both analyses reveal that the interdomain connections allow only these two degrees of freedom, one more than provided by a pure mechanical hinge. Proteins 27:425–437, 1997. © 1997 Wiley-Liss, Inc.     

Molecular Dynamics Simulations of NaCl-type Solid Solution Crystals: The First Application of Molecular Dynamics to Solid Solutions

Abstract

Solid solution crystals appear widely in the fields of earth sciences and inorganic material sciences. The physical properties of solid solutions may vary continuously with chemical composition. Sometimes, linear relationships of the properties with composition are assumed. However, this approximation is not always applicable (e.g., [1], [2], [3]). In order to elucidate the properties of solid solutions, studies on the relation between the macroscopic properties and the atomic configurations (microscopic property) in the crystal are desirable. One of the most effective approaches to the subject is molecular dynamics (MD). However, as far as the authors are aware there have been no molecular dynamics studies on solid solution crystals.     

Energy landscape of a native protein: Jumping-among-minima model

We have investigated energy landscape of human lysozyme in its native state by using principal component analysis and a model, jumping-among-minima (JAM) model. These analyses are applied to 1 nsec molecular dynamics trajectory of the protein in water. An assumption embodied in the JAM model allows us to divide protein motions into intra-substate and inter-substate motions. By examining intra-substate motions, it is shown that energy surfaces of individual conformational substates are nearly harmonic and mutually similar. As a result of principal component analysis and JAM model analysis, protein motions are shown to consist of three types of collective modes, multiply hierarchical modes, singly hierarchical modes, and harmonic modes. Multiply hierarchical modes, the number of which accounts only for 0.5% of all modes, dominate contributions to total mean-square atomic fluctuation. Inter-substate motions are observed only in a small-dimensional subspace spanned by the axes of multiplyhierarchical and singly hierarchical modes. Inter-substate motions have two notable time components: faster component seen within 200 psec and slower component. The former involves transitions among the conformational substates of the low-level hierarchy, whereas the latter involves transitions of the higher level substates observed along the first four multiply hierarchical modes. We also discuss dependence of the subspace, which contains conformational substates, on time duration of simulation. Proteins 33:496–517, 1998. © 1998 Wiley-Liss, Inc.     

Investigation of Domain Motions in Bacteriophage T4 Lysozyme

Abstract

Hinge-bending in T4 lysozyme has been inferred from single amino acid mutant crystalline allomorphs by Matthews and coworkers. This raises an important question: are the different conformers in the unit cell artifacts of crystal packing forces, or do they represent different solution state structures? The objective of this theoretical study is to determine whether domain motions and hinge-bending could be simulated in T4 lysozyme using molecular dynamics. An analysis of a 400 ps molecular dynamics simulation of the 164 amino acid enzyme T4 lysozyme is presented. Molecular dynamics calculations were computed using the Discover software package (Biosym Technologies). All hydrogen atoms were modeled explicitly with the inclusion of all 152 crystallographic waters at a temperature of 300 K. The native T4 lysozyme molecular dynamics simulation demonstrated hinge-bending in the protein. Relative domain motions between the N-terminal and C-terminal domains were evident. The enzyme hinge bending sites resulted from small changes in backbone atom conformations over several residues rather than rotation about a single bound. Two hinge loci were found in the simulation. One locus comprises residues 8–14 near the C-terminal of the A helix; the other site, residues 77–83 near the C-terminal of the C helix. Comparison of several snapshot structures from the dynamics trajectory clearly illustrates domain motions between the two lysozyme lobes. Time correlated atomic motions in the protein were analyzed using a dynamical cross-correlation map. We found a high degree of correlated atomic motions in each of the domains and, to a lesser extent, anticorrelated motions between the two domains. We also found that the hairpin loop in the N-terminal lobe (residues 19–24) acted as a mobile ‘flap’ and exhibited highly correlated dynamic motions across the cleft of the active site, especially with residue 142.     

Proteins will Fold Anyway!!

Abstract

In order to investigate the environmental conditions of amino acid residues in protein molecules, four kinds of packing studies (atomic, geometric, hydrophobic and hydration) were formulated and tested on two proteins; bovine pancreatic trypsin inhibitor (BPTI) and bovine pancreatic ribonuclease S (RNase S). The inter-relationship of these packings on the fluctuations of amino acid residues was analysed by comparing the packing results with the dynamical studies, such as the root-mean-square-deviation values of atomic displacements obtained from the trajectories of molecular dynamics simulation, temperature factor information from crystal structures and residue fluctuations in proteins from continuum model. These analyses yield information about the most fluctuating and most stabilizing residue sites. Comparison of the results obtained by these methods indicate a good agreement, specifying an inverse correlation between the residue packing and fluctuations. This kind of study is helpful in identifying the specific residue sites such as nucleation, receptor binding and antigenic determining sites which in a way indirectly correlates with the functional residues in protein molecules.     

Concerted motions in copper plastocyanin and azurin: an essential dynamics study

Essential dynamics analysis of molecular dynamics simulation trajectories (1.1 ns) of two copper containing electron transfer proteins, plastocyanin and azurin, has been performed. The protein essential modes have been analysed in order to identify large concerted motions which could be relevant for the electron transfer function exerted by these proteins. The analysis, conducted for temporal windows of different lengths along the protein trajectories, shows a rapid convergence and indicates that for both the proteins the predominant internal motions occur in a subspace of only a few degrees of freedom. Moreover, it is found that for both the proteins the likely binding sites (i.e. the hydrophobic and negative patches) with the reaction partners move in a concerted fashion with a few structural regions far from the active site. Such results are discussed in connection with the possible involvement of large concerted motions in the recognition and binding interaction with physiological electron transfer partners.     

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

The contribution of rigidbody motions to the atomic trajectories in a 100 ps molecular dynamics simulation of deoxymyoglobin is examined. Two typesof rigid-body motions are considered: one in which the helices are rigid units and one in which the side-chains are rigid units. Using a quaternionbased algorithm, fits of the rigid reference structures are made to each time frame of the simulation to derive trajectories of the rigid-body motions. The fitted trajectories are analysed in terms of atomic position fluctuations, mean-square displacements as a function of time, velocity autocorrelation functions and densities of states. The results are compared with the corresponding quantities calculated from the full trajectory. The relative contribution of the rigid helix motions to the helix atom dynamics depends on which quantity is examined and on which subset of atoms is chosen: rigid-helix motions contribute 86% of the rms helix backbone atomic position fluctuations, but 30% of the helix,: atom (backbone and side-chain) mean square displacements and only 1.1% of total kinetic energy. Only very low-frequency motions contribute to the rigid-helix dynamics; the rigid-body analysis allows characteristic rigid-helix vibrations to be identified and described. Treating the side-chains as rigid bodies is foundto be an excellent approximation to both their diffusive and vibrationalmean-square displacements: 96% of side-chain atom mean-square displacements originate from rigid side-Chain motions. However, the errors in theside-chain atomic positional fits are not always small. An analysis is madeof factors contributing to the positional error for different types of side-chain. © Wiley-Liss, Inc.     

ProMode: a database of normal mode analyses on protein molecules with a full-atom model

MOTIVATION: Although information from protein dynamics simulation is important to understand principles of architecture of a protein structure and its function, simulations such as molecular dynamics and Monte Carlo are very CPU-intensive. Although the ability of normal mode analysis (NMA) is limited because of the need for a harmonic approximation on which NMA is based, NMA is adequate to carry out routine analyses on many proteins to compute aspects of the collective motions essential to protein dynamics and function. Furthermore, it is hoped that realistic animations of the protein dynamics can be observed easily without expensive software and hardware, and that the dynamic properties for various proteins can be compared with each other. RESULTS: ProMode, a database collecting NMA results on protein molecules, was constructed. The NMA calculations are performed with a full-atom model, by using dihedral angles as independent variables, faster and more efficiently than the calculations using Cartesian coordinates. In ProMode, an animation of the normal mode vibration is played with a free plug-in, Chime (MDL Information Systems, Inc.). With the full-atom model, the realistic three-dimensional motions at an atomic level are displayed with Chime. The dynamic domains and their mutual screw motions defined from the NMA results are also displayed. Properties for each normal mode vibration and their time averages, e.g. fluctuations of atom positions, fluctuations of dihedral angles and correlations between the atomic motions, are also presented graphically for characterizing the collective motions in more detail. AVAILABILITY: http://promode.socs.waseda.ac.jp