Temperature dependence of dynamics of hydrated myoglobin. Comparison of force field calculations with neutron scattering data

Molecular dynamics is used to probe the atomic motions of the carboxy-myoglobin protein as a function of temperature. Simulations of 150 picoseconds in length are carried out on the protein at 20, 60, 100, 180, 220, 240, 260, 280, 300, 320 and 340 K. The simulations attempt to mimic neutron scattering experiments very closely by including a partial hydration shell around the protein. Theoretical elastic, quasielastic and inelastic neutron scattering data are derived from the trajectories and directly compared with experiment. Compared to experiment, the simulation-derived elastic scattering curves show a decrease in intensity as a function of the scattering wavevector, q2. The inelastic and quasielastic spectra show that the inelastic peak is shifted to lower frequency than the experimental value, while quasielastic behavior is in good agreement with experiment. This suggests that the theoretical model is too flexible in the harmonic limit (low temperature), but accurately reproduces high-temperature behavior. Time correlation functions of the intermediate scattering function are determined. At low temperature there is one fast decay process, and at high temperatures there is an additional slow relaxation process that is due to quasielastic scattering. The average atomic fluctuations show that the protein behaves harmonically at low temperatures. At approximately 210 K, a glass-like transition in atomic fluctuations is seen. Above the transition temperature, the atomic fluctuations exhibit both harmonic and anharmonic behavior. Comparison of protein mobility behavior with experiment indicate the fluctuations derived from simulations are larger in the harmonic region. However, the anharmonic region agrees very well with experiment. The anharmonicity is large at all temperatures, with a gradual monotonic increase from 0.5 at 20 K to greater than 0.7 at 340 K without a noticeable change at the glass transition temperature. Heavy-atom dihedral transitions are monitored as a function of temperature. Trends in the type of dihedral transitions that occur with temperature are clearly visible. Dihedral transitions involving backbone atoms occur only above the glass transition temperature. The overall protein behavior results suggest that at low temperatures there is purely vibrational motion with one fast decay process, and above the glass transition temperature there is more anharmonic motion with a fast and a slower relaxation process occurring simultaneously.(ABSTRACT TRUNCATED AT 400 WORDS)     

Extensibility of the Extended Tail Domain of Processive and Nonprocessive Myosin V Molecules

Myosin V is a single-molecule motor that moves organelles along actin. When myosin V pulls loads inside the cell in a highly viscous environment, the force on the motor is unlikely to be constant. We propose that the tether between the single-molecule motor and the cargo (i.e., the extended tail domain of the molecule) must be able to absorb the sudden mechanical motions of the motor and allow smooth relaxation of the motion of the cargo to a new position. To test this hypothesis, we compared the elastic properties of the extended tail domains of processive (mouse myosin Va) and nonprocessive (Drosophila myosin V) molecular motors. The extended tail domain of these myosins consists of mechanically strong coiled-coil regions interspersed with flexible loops. In this work we explored the mechanical properties of coiled-coil regions using atomic force microscopy. We found that the processive and nonprocessive coiled-coil fragments display different unfolding patterns. The unfolding of coiled-coil structures occurs much later during the atomic force microscopy stretch cycle for processive myosin Va than for nonprocessive Drosophila myosin V, suggesting that this elastic tether between the cargo and motor may play an important role in sustaining the processive motions of this single-molecule motor.     

Loop motions of triosephosphate isomerase observed with elastic networks

The internal dynamics of triosephosphate isomerase have been investigated with elastic networks, with and without a substrate bound. The slowest modes of motion involve large domain motions but also a loop motion that conforms to the changes observed between the crystal structures and . Our computations confirm that the different motions of this loop are important in several of the computed slowest modes. We have shown that elastic network computations on this protein system can combine atoms for the functional parts of the structure with coarse-grained (cg) representations of the remainder of the structure in several different ways. Similar loop motions are seen with elastic network models for atomistic and mixed cg models. The loop motions are reproduced with an overlap of 0.75-0.79 by combining the four slowest modes of motion for the free and complex forms of the enzyme.     

Incoherent elastic and quasi-elastic neutron scattering investigation of hemoglobin dynamics

In this work we investigate the dynamic properties of hemoglobin in glycerolD(8)/D(2)O solution using incoherent elastic (ENS) and quasi-elastic (QENS) neutron scattering. Taking advantage of complementary energy resolutions of backscattering spectrometers at ILL (Grenoble), we explore motions in a large space-time window, up to 1 ns and 14 A; moreover, in order to cover the harmonic and anharmonic protein dynamics regimes, the elastic experiments have been performed over the wide temperature interval of 20-300 K. To study the dependence of the measured dynamics upon the protein quaternary structure, both deoxyhemoglobin (in T quaternary conformation) and carbonmonoxyhemoglobin (in R quaternary conformation) have been investigated. From the ENS data the mean square displacements of the non-exchangeable hydrogen atoms of the protein and their temperature dependence are obtained. In agreement with previous results on hydrated powders, a dynamical transition at about 220 K is detected. The results show interesting differences between the two hemoglobin quaternary conformations, the T-state protein appearing more rigid and performing faster motions than the R-state one; however, these differences involve motions occurring in the nanosecond time scale and are not detected when only faster atomic motions in the time scale up to 100 ps are investigated. The QENS results put in evidence a relevant Lorentzian quasi-elastic contribution. Analysis of the dependence of the Elastic Incoherent Structure Factor (EISF) and of the Lorentzian halfwidth upon the momentum transfer suggests that the above quasi-elastic contribution arises from the diffusion inside a confined space, values of confinement radius and local diffusion coefficient being compatible with motions of hydrogen atoms of the amino acid side chains. When averaged over the whole range of momentum transfer the QENS data put in evidence differences between deoxy and carbonmonoxy hemoglobin and confirm the quaternary structure dependence of the protein dynamics in the nanosecond time scale.     

Global ribosome motions revealed with elastic network model

The motions of large systems such as the ribosome are not fully accessible with conventional molecular simulations. A coarse-grained, less-than-atomic-detail model such as the anisotropic network model (ANM) is a convenient informative tool to study the cooperative motions of the ribosome. The motions of the small 30S subunit, the larger 50S subunit, and the entire 70S assembly of the two subunits have been analyzed using ANM. The lowest frequency collective modes predicted by ANM show that the 50S subunit and 30S subunit are strongly anti-correlated in the motion of the 70S assembly. A ratchet-like motion is observed that corresponds well to the experimentally reported ratchet motion. Other slow modes are also examined because of their potential links to the translocation steps in the ribosome. We identify several modes that may facilitate the E-tRNA exiting from the assembly. The A-site t-RNA and P-site t-RNA are found to be strongly coupled and positively correlated in these slow modes, suggesting that the translocations of these two t-RNAs occur simultaneously, while the motions of the E-site t-RNA are less correlated, and thus less likely to occur simultaneously. Overall the t-RNAs exhibit relatively large deformations. Animations of these slow modes of motion can be viewed at.     

Direct measurement of hydration-related dynamic changes in lysozyme using inelastic neutron scattering spectroscopy

Inelastic neutron scattering spectroscopy is used to investigate dynamic changes in lysozyme powder at two different low D2O hydrations (0.07g D2O/g protein and 0.20 g D2O/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 molecular [M. Levitt, C. Sander and P.S. Stern, J. Mol. Biol. 181, 423 (1985). B. Brooks and M. Karplus, Proc. 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.     

冷冻透射电镜:从分子到系统

单颗粒电镜结合其他方法能够在(近)原子水平提供结构模型,已经成为一种研究大蛋白复合物的有效方法。该文将以两个大的蛋白裂解复合物——tripeptidyl peptidaseII(6MDa)和26S蛋白酶体(2.5MDa)举例说明。低温电子层析能进行非重复的超分子结构分析,如多核糖体和全细胞;能够为超分子组织提供前所未有的信息(可视化蛋白质组学)。     

Immunoglobulin structure exhibits control over CDR motion

Motions of the IgG structure are evaluated using normal mode analysis of an elastic network model to detect hinges, the dominance of low frequency modes, and the most important internal motions. One question we seek to answer is whether or not IgG hinge motions facilitate antigen binding. We also evaluate the protein crystal and packing effects on the experimental temperature factors and disorder predictions. We find that the effects of the protein environment on the crystallographic temperature factors may be misleading for evaluating specific functional motions of IgG. The extent of motion of the antigen binding domains is computed to show their large spatial sampling. We conclude that the IgG structure is specifically designed to facilitate large excursions of the antigen binding domains. Normal modes are shown as capable of computationally evaluating the hinge motions and the spatial sampling by the structure. The antigen binding loops and the major hinge appear to behave similarly to the rest of the structure when we consider the dominance of the low frequency modes and the extent of internal motion. The full IgG structure has a lower spectral dimension than individual F(ab) domains, pointing to more efficient information transfer through the antibody than through each domain. This supports the claim that the IgG structure is specifically constructed to facilitate antigen binding by coupling motion of the antigen binding loops with the large scale hinge motions.     

Probing the structural dynamics of the SNARE recycling machine based on coarse‐grained modeling

Membrane fusion in eukaryotes is driven by the formation of a four‐helix bundle by three SNARE proteins. To recycle the SNARE proteins, they must be disassembled by the ATPase NSF and four SNAP proteins which together form a 20S supercomplex. Recently, the first high‐resolution structures of the NSF (in both ATP and ADP state) and 20S (in four distinct states termed I, II, IIIa, and IIIb) were solved by cryo‐electron microscopy (cryo‐EM), which have paved the way for structure‐driven studies of the SNARE recycling mechanism. To probe the structural dynamics of SNARE disassembly at amino‐acid level of details, a systematic coarse‐grained modeling based on an elastic network model and related analyses were performed. Our normal mode analysis of NSF, SNARE, and 20S predicted key modes of collective motions that partially account for the observed structural changes, and illuminated how the SNARE complex can be effectively destabilized by untwisting and bending motions of the SNARE complex driven by the amino‐terminal domains of NSF in state II. Our flexibility analysis identified regions with high/low flexibility that coincide with key functional sites (such as the NSF‐SNAPs‐SNARE binding sites). A subset of hotspot residues that control the above collective motions, which will make promising targets for future mutagenesis studies were also identified. Finally, the conformational changes in 20S as induced by the transition of NSF from ATP to ADP state were modeled, and a concerted untwisting motion of SNARE/SNAPs and a sideway flip of two amino‐terminal domains were observed. In sum, the findings have offered new structural and dynamic details relevant to the SNARE disassembly mechanism, and will guide future functional studies of the SNARE recycling machinery. Proteins 2016; 84:1055–1066. © 2016 Wiley Periodicals, Inc.     

Rigid‐body motions of interacting proteins dominate multispecific binding of ubiquitin in a shape‐dependent manner

To understand the dynamic aspects of multispecificity of ubiquitin, we studied nine ubiquitin–ligand (partner protein) complexes by normal mode analysis based on an elastic network model. The coupling between ubiquitin and ligand motions was analyzed by decomposing it into rigid‐body (external) and vibrational (internal) motions of each subunit. We observed that in total the external motions in one of the subunits largely dominated the coupling. The combination of external motions of ubiquitin and the ligands showed general trends of rotations and translations. Moreover, we observed that the rotational motions of ubiquitin were correlated to the ligand orientations. We also identified ubiquitin atomic vibrations that differentiated the orientation of the ligand molecule. We observed that the extents of coupling were correlated to the shapes of the ligands, and this trend was more pronounced when the coupling involved vibrational motions of the ligand. In conclusion, an intricate interplay between internal and external motions of ubiquitin and the ligands help understand the dynamics of multispecificity, which is mostly guided by the shapes of the ligands and the complex. Proteins 2014; 82:77–89. © 2013 Wiley Periodicals, Inc.     

Crystallographic evaluation of internal motion of human alpha-lactalbumin refined by full-matrix least-squares method

The low temperature form of human alpha-lactalbumin (HAL) was crystallized from a 2H2O solution and its structure was refined to the R value of 0.119 at 1.15 A resolution by the full-matrix least-squares method. Average estimated standard deviations of atomic parameters for non-hydrogen atoms were 0.038 A for coordinates and 0.044 A2 for anisotropic temperature factors (Uij). The magnitude of equivalent isotropic temperature factors (Ueqv) was highly correlated with the distance from the molecular centroid and fitted to a quadratic equation as a function of atomic coordinates. The atomic thermal motion was rather isotropic in the core region and the anisotropy increased towards the molecular surface. The statistical analysis revealed the out-of-plane motion of main-chain oxygen atoms, indicating that peptide groups are in rotational vibration around a Calpha.Calpha axis. The TLS model, which describes the rigid-body motion in terms of translation, libration, and screw motions, was adopted for the evaluation of the molecular motion and the TLS parameters were determined by the least-squares fit to Uij. The reproduced Ueqvcal from the TLS parameters was in fair agreement with observed Ueqv, but differences were found in regions of residues, 5-22, 44-48, 70-75, and 121-123, where Ueqv was larger than Ueqvcal because of large local motions. To evaluate the internal motion of HAL, the contribution of the rigid-body motion was determined to be 42.4 % of Ueqv in magnitude, which was the highest estimation to satisfy the condition that the Uijint tensors of the internal motion have positive eigen values. The internal motion represented with atomic thermal ellipsoids clearly showed local motions different from those observed in chicken-type lysozymes which have a backbone structure very similar to HAL. The result indicates that the internal motion is closely related to biological function of proteins.     

Large‐scale comparison of protein essential dynamics from molecular dynamics simulations and coarse‐grained normal mode analyses

A large‐scale comparison of essential dynamics (ED) modes from molecular dynamic simulations and normal modes from coarse‐grained normal mode methods (CGNM) was performed on a dataset of 335 proteins. As CGNM methods, the elastic network model (ENM) and the rigid cluster normal mode analysis (RCNMA) were used. Low‐frequency normal modes from ENM correlate very well with ED modes in terms of directions of motions and relative amplitudes of motions. Notably, a similar performance was found if normal modes from RCNMA were used, despite a higher level of coarse graining. On average, the space spanned by the first quarter of ENM modes describes 84% of the space spanned by the five ED modes. Furthermore, no prominent differences for ED and CGNM modes among different protein structure classes (CATH classification) were found. This demonstrates the general potential of CGNM approaches for describing intrinsic motions of proteins with little computational cost. For selected cases, CGNM modes were found to be more robust among proteins that have the same topology or are of the same homologous superfamily than ED modes. In view of recent evidence regarding evolutionary conservation of vibrational dynamics, this suggests that ED modes, in some cases, might not be representative of the underlying dynamics that are characteristic of a whole family, probably due to insufficient sampling of some of the family members by MD. Proteins 2010. © 2010 Wiley‐Liss, Inc.     

Viral capsid equilibrium dynamics reveals nonuniform elastic properties

The long wavelength, low-frequency modes of motion are the relevant motions for understanding the continuum mechanical properties of biomolecules. By examining these low-frequency modes, in the context of a spherical harmonic basis set, we identify four elastic moduli that are required to describe the two-dimensional elastic behavior of capsids. This is in contrast to previous modeling and theoretical studies on elastic shells, which use only the two-dimensional Young's modulus (Y) and the bending modulus (κ) to describe the system. Presumably, the heterogeneity of the structure and the anisotropy of the biomolecular interactions lead to a deviation from the homogeneous, isotropic, linear elastic shell theory. We assign functional relevance of the various moduli governing different deformation modes, including a mode primarily sensed in atomic force microscopy nanoindentation experiments. We have performed our analysis on the T = 3 cowpea chlorotic mottle virus and our estimate for the nanoindentation modulus is in accord with experimental measurements.     

A coarse-grained normal mode approach for macromolecules: an efficient implementation and application to Ca(2+)-ATPase

A block normal mode (BNM) algorithm, originally proposed by Tama et al., (Proteins Struct. Func. Genet. 41:1-7, 2000) was implemented into the simulation program CHARMM. The BNM approach projects the hessian matrix into local translation/rotation basis vectors and, therefore, dramatically reduces the size of the matrix involved in diagonalization. In the current work, by constructing the atomic hessian elements required in the projection operation on the fly, the memory requirement for the BNM approach has been significantly reduced from that of standard normal mode analysis and previous implementation of BNM. As a result, low frequency modes, which are of interest in large-scale conformational changes of large proteins or protein-nucleic acid complexes, can be readily obtained. Comparison of the BNM results with standard normal mode analysis for a number of small proteins and nucleic acids indicates that many properties dominated by low frequency motions are well reproduced by BNM; these include atomic fluctuations, the displacement covariance matrix, vibrational entropies, and involvement coefficients for conformational transitions. Preliminary application to a fairly large system, Ca(2+)-ATPase (994 residues), is described as an example. The structural flexibility of the cytoplasmic domains (especially domain N), correlated motions among residues on domain interfaces and displacement patterns for the transmembrane helices observed in the BNM results are discussed in relation to the function of Ca(2+)-ATPase. The current implementation of the BNM approach has paved the way for developing efficient sampling algorithms with molecular dynamics or Monte Carlo for studying long-time scale dynamics of macromolecules.     

Dynamic and elastic properties of F-actin: a normal-modes analysis.

We examine the dynamic, elastic, and mechanical consequences of the proposed atomic models of F-actin, using a normal mode analysis. This initial analysis is done in vacuo and assumes that all monomers are rigid and equivalent. Our computation proceeds from the atomic level and, relying on a single fitting parameter, reproduces various experimental results, including persistence lengths, elastic moduli, and contact energies. The computations reveal modes of motion characteristic to all polymers, such as longitudinal pressure waves, torsional waves, and bending, as well as motions unique to F-actin. Motions typical to actin include a "groove-swinging" motion of the two long-pitch helices, as well as an axial slipping motion of the two strands. We prepare snapshots of thermally activated filaments and quantify the accumulation of azimuthal angular "disorder," variations in cross-over lengths, and various other fluctuations. We find that the orientation of a small number of select residues has a surprisingly large effect on the filament flexibility and elasticity characteristics.     

Coherent Neutron Scattering and Collective Dynamics in the Protein,GFP

Collective dynamics are considered to be one of the major properties of soft materials, including biological macromolecules. We present coherent neutron scattering studies of the low-frequency vibrations, the so-called boson peak, in fully deuterated green fluorescent protein (GFP). Our analysis revealed unexpectedly low coherence of the atomic motions in GFP. This result implies a low amount of in-phase collective motion of the secondary structural units contributing to the boson peak vibrations and fast conformational fluctuations on the picosecond timescale. These observations are in contrast to earlier studies of polymers and glass-forming systems, and suggest that random or out-of-phase motions of the β-strands contribute greater than two-thirds of the intensity to the low-frequency vibrational spectra of GFP.     

Coherent Neutron Scattering and Collective Dynamics in the Protein,GFP

Collective dynamics are considered to be one of the major properties of soft materials, including biological macromolecules. We present coherent neutron scattering studies of the low-frequency vibrations, the so-called boson peak, in fully deuterated green fluorescent protein (GFP). Our analysis revealed unexpectedly low coherence of the atomic motions in GFP. This result implies a low amount of in-phase collective motion of the secondary structural units contributing to the boson peak vibrations and fast conformational fluctuations on the picosecond timescale. These observations are in contrast to earlier studies of polymers and glass-forming systems, and suggest that random or out-of-phase motions of the β-strands contribute greater than two-thirds of the intensity to the low-frequency vibrational spectra of GFP.     

Molecular dynamics of ferrocytochrome c: Time dependence of the atomic displacements

The thermal motions of the atoms in a dynamical simulation of ferrocytochrome c are geometrically decomposed into local and highly collective components, and the contributions of these components to the net motion are determined for different intervals of time. It is found that the atomic displacement magnitudes and anisotropies are governed by local motions for times <10^?12s, but that the highly collective motions tend to be dominant at longer times. Variations in this behavior are noted among different groups of atoms. Orientational correlations between the preferred directions of atomic displacement and elements of the protein structure are analyzed as a function of time scale. Finally, several sinificant implications of these results with respect to protein structure and function are considered.     

Counterbalance of ligand‐ and self‐coupled motions characterizes multispecificity of ubiquitin

Date hub proteins are a type of proteins that show multispecificity in a time‐dependent manner. To understand dynamic aspects of such multispecificity we studied Ubiquitin as a typical example of a date hub protein. Here we analyzed 9 biologically relevant Ubiquitin‐protein (ligand) heterodimer structures by using normal mode analysis based on an elastic network model. Our result showed that the self‐coupled motion of Ubiquitin in the complex, rather than its ligand‐coupled motion, is similar to the motion of Ubiquitin in the unbound condition. The ligand‐coupled motions are correlated to the conformational change between the unbound and bound conditions of Ubiquitin. Moreover, ligand‐coupled motions favor the formation of the bound states, due to its in‐phase movements of the contacting atoms at the interface. The self‐coupled motions at the interface indicated loss of conformational entropy due to binding. Therefore, such motions disfavor the formation of the bound state. We observed that the ligand‐coupled motions are embedded in the motions of unbound Ubiquitin. In conclusion, multispecificity of Ubiquitin can be characterized by an intricate balance of the ligand‐ and self‐coupled motions, both of which are embedded in the motions of the unbound form.     

Exploring global distortions of biological macromolecules and assemblies from low-resolution structural information and elastic network theory

A theory of elastic normal modes is described for the exploration of global distortions of biological structures and their assemblies based upon low-resolution image data. Structural information at low resolution, e.g. from density maps measured by cryogenic electron microscopy (cryo-EM), is used to construct discrete multi-resolution models for the electron density using the techniques of vector quantization. The elastic normal modes computed based on these discretized low-resolution models are found to compare well with the normal modes obtained at atomic resolution. The quality of the normal modes describing global displacements of the molecular system is found to depend on the resolution of the synthetic EM data and the extent of reductionism in the discretized representation. However, models that reproduce the functional rearrangements of our test set of molecules are achieved for realistic values of experimental resolution. Thus large conformational changes as occur during the functioning of biological macromolecules and assemblies can be elucidated directly from low-resolution structural data through the application of elastic normal mode theory and vector quantization.