How long does DNA keep the memory of its conformation? A time-dependent canonical correlation analysis of molecular dynamics simulation

The time dependence of the correlation between motions of different parts of DNA is analyzed from a 200 ps molecular dynamics simulation of the double-stranded self-complementary d(CTGATCAG) in the B form. Each nucleotide is decomposed into three subunits corresponding to the furanose ring (SU), the base (BA), and the backbone (SK). The motion of each subunit is considered as the superimposition of rigid body translation, rigid body rotation, and internal deformation. Canonical time-dependent correlation functions calculated with coordinates describing the different components of the subunits motion are defined and computed. This allows us to probe how long a particular type of motion of one subunit influences the other types of motions of other subunits (cross correlation functions) or how long a particular subunit keeps the memory of its own conformation or location (autocorrelation functions). From auto-correlation analysis it is found that deformation decorrelates within a few tenths of picoseconds, rotational correlation times are on the order of 8 ps, while translational motions are long-time correlated. The deformation of a subunit is not correlated to the deformation of another one (at the 200 ps time scale of our simulation), but influences slightly their translation and orientation as time increases. © 1996 John Wiley & Sons, Inc.     

Comparison of tRNA motions in the free and ribosomal bound structures

A general method is presented that allows the separation of the rigid body motions from the nonrigid body motions of structural subunits when bound in a complex. The application presented considers the motions of the tRNAs: free, bound to the ribosome and to a synthase. We observe that both the rigid body and nonrigid body motions of the structural subunits are highly controlled by the large ribosomal assembly and are important for the functional motions of the assembly. For the intact ribosome, its major parts, the 30S and the 50S subunits, are found to have counterrotational motions in the first few slowest modes, which are consistent with the experimentally observed ratchet motion. The tRNAs are found to have on average approximately 72-75% rigid body motions and principally translational motions within the first 100 slow modes of the complex. Although the three tRNAs exhibit different apparent total motions, after the rigid body motions are removed, the remaining internal motions of all three tRNAs are essentially the same. The direction of the translational motions of the tRNAs are in the same direction as the requisite translocation step, especially in the first slowest mode. Surprisingly the small intrinsically flexible mRNA has all of its internal motions completely inhibited and shows mainly a rigid-body translation in the slow modes of the ribosome complex. On the other hand, the required nonrigid body motions of the tRNA during translocation reveal that the anticodon-stem-loop, as well as the acceptor arm, of the tRNA enjoy a large mobility but act as rigid structural units. In summary, the ribosome exerts its control by enforcing rigidity in the functional parts of the tRNAs as well as in the mRNA.     

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.     

Prediction of protein motions from amino acid sequence and its application to protein-protein interaction

Background  

Structural flexibility is an important characteristic of proteins because it is often associated with their function. The movement of a polypeptide segment in a protein can be broken down into two types of motions: internal and external ones. The former is deformation of the segment itself, but the latter involves only rotational and translational motions as a rigid body. Normal Model Analysis (NMA) can derive these two motions, but its application remains limited because it necessitates the gathering of complete structural information.     

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.     

hdANM: a new comprehensive dynamics model for protein hinges

Hinge motions are essential for many protein functions, and their dynamics are important to understand underlying biological mechanisms. The ways that these motions are represented by various computational methods differ significantly. By focusing on a specific class of motion, we have developed a new hinge-domain anisotropic network model (hdANM) that is based on the prior identification of flexible hinges and rigid domains in the protein structure and the subsequent generation of global hinge motions. This yields a set of motions in which the relative translations and rotations of the rigid domains are modulated and controlled by the deformation of the flexible hinges, leading to a more restricted, specific view of these motions. hdANM is the first model, to our knowledge, that combines information about protein hinges and domains to model the characteristic hinge motions of a protein. The motions predicted with this new elastic network model provide important conceptual advantages for understanding the underlying biological mechanisms. As a matter of fact, the generated hinge movements are found to resemble the expected mechanisms required for the biological functions of diverse proteins. Another advantage of this model is that the domain-level coarse graining makes it significantly more computationally efficient, enabling the generation of hinge motions within even the largest molecular assemblies, such as those from cryo-electron microscopy. hdANM is also comprehensive as it can perform in the same way as the well-known protein dynamics models (anisotropic network model, rotations-translations of blocks, and nonlinear rigid block normal mode analysis), depending on the definition of flexible and rigid parts in the protein structure and on whether the motions are extrapolated in a linear or nonlinear fashion. Furthermore, our results indicate that hdANM produces more realistic motions as compared to the anisotropic network model. hdANM is an open-source software, freely available, and hosted on a user-friendly website.     

Normal‐mode‐based modeling of allosteric couplings that underlie cyclic conformational transition in F1 ATPase

F₁ ATPase, a rotary motor comprised of a central stalk ( γ subunit) enclosed by three α and β subunits alternately arranged in a hexamer, features highly cooperative binding and hydrolysis of ATP. Despite steady progress in biophysical, biochemical, and computational studies of this fascinating motor, the structural basis for cooperative ATPase involving its three catalytic sites remains not fully understood. To illuminate this key mechanistic puzzle, we have employed a coarse‐grained elastic network model to probe the allosteric couplings underlying the cyclic conformational transition in F₁ ATPase at a residue level of detail. We will elucidate how ATP binding and product (ADP and phosphate) release at two catalytic sites are coupled with the rotation of γ subunit via various domain motions in α ₃ β ₃ hexamer (including intrasubunit hinge‐bending motions in β subunits and intersubunit rigid‐body rotations between adjacent α and β subunits). To this end, we have used a normal‐mode‐based correlation analysis to quantify the allosteric couplings of these domain motions to local motions at catalytic sites and the rotation of γ subunit. We have then identified key amino acid residues involved in the above couplings, some of which have been validated against past studies of mutated and γ ‐truncated F₁ ATPase. Our finding strongly supports a binding change mechanism where ATP binding to the empty catalytic site triggers a series of intra‐ and intersubunit domain motions leading to ATP hydrolysis and product release at the other two closed catalytic sites. Proteins 2009. © 2009 Wiley‐Liss, Inc.     

Nucleotide dependent motion and mechanism of action of p97/VCP

The AAA (ATPases associated with a variety of cellular activities) family of proteins bind, hydrolyze, and release ATP to effect conformational changes, assembly, or disassembly upon their binding partners and substrate molecules. One of the members of this family, the hexameric p97/valosin-containing protein p97/VCP, is essential for the dislocation of misfolded membrane proteins from the endoplasmic reticulum. Here, we observe large motions and dynamic changes of p97/VCP as it proceeds through the ATP hydrolysis cycle. The analysis is based on crystal structures of four representative ATP hydrolysis states: APO, AMP-PNP, hydrolysis transition state ADP x AlF3, and ADP bound. Two of the structures presented herein, ADP and AMP-PNP bound, are new structures, and the ADP x AlF3 structure was re-refined to higher resolution. The largest motions occur at two stages during the hydrolysis cycle: after, but not upon, nucleotide binding and then following nucleotide release. The motions occur primarily in the D2 domain, the D1 alpha-helical domain, and the N-terminal domain, relative to the relatively stationary and invariant D1alpha/beta domain. In addition to the motions, we observed a transition from a rigid state to a flexible state upon loss of the gamma-phosphate group, and a further increase in flexibility within the D2 domains upon nucleotide release. The domains within each protomer of the hexameric p97/VCP deviate from strict 6-fold symmetry, with the more flexible ADP state exhibiting greater asymmetry compared to the relatively rigid ADP x AlF3 state, suggesting a mechanism of action in which hydrolysis and conformational changes move about the hexamer in a processive fashion.     

Picosecond dynamics of tyrosine side chains in proteins.

To probe the details of small amplitude motions in proteins, a dynamical analysis of the orientation fluctuations of two tyrosine side chains in the bovine pancreatic trypsin inhibitor is presented. Detailed results are given for the time history and correlation functions obtained for the ring motion from a molecular dynamics simulation of the entire protein. It is shown that even on a picosecond time scale orientational fluctuations of +/-30 degrees from the average position occur for the tyrosine rings in the interior of the protein. It is found that the Langevin equation is applicable to the ring torsional motion, which corresponds to that of an angular harmonic oscillator with near-critical damping. Two possible microscopic models for the observed damping effects are outlined. One of these, analogous to liquid behavior, is based on kinetic theory and takes account of the collisions which occur between atoms of the protein; the other, more analogous to solid behavior, involves the coupling among a large number of harmonic oscillators. The collisional model with parameters obtained from theoretical estimates leads to good agreement with the correlation functions from the dynamic simulation. However, the dephasing of harmonic oscillations can yield similar short-time results so that a distinction between the two models is difficult. The importance of damping effects on the motions involved in conformational transitions and enzymatic reactions is discussed.     

Multiscale modeling of macromolecular conformational changes combining concepts from rigidity and elastic network theory

The development of a two-step approach for multiscale modeling of macromolecular conformational changes is based on recent developments in rigidity and elastic network theory. In the first step, static properties of the macromolecule are determined by decomposing the molecule into rigid clusters by using the graph-theoretical approach FIRST and an all-atom representation of the protein. In this way, rigid clusters are not limited to consist of residues adjacent in sequence or secondary structure elements as in previous studies. Furthermore, flexible links between rigid clusters are identified and can be modeled as such subsequently. In the second step, dynamical properties of the molecule are revealed by the rotations-translations of blocks approach (RTB) using an elastic network model representation of the coarse-grained protein. In this step, only rigid body motions are allowed for rigid clusters, whereas links between them are treated as fully flexible. The approach was tested on a data set of 10 proteins that showed conformational changes on ligand binding. For efficiency, coarse-graining the protein results in a remarkable reduction of memory requirements and computational times by factors of 9 and 27 on average and up to 25 and 125, respectively. For accuracy, directions and magnitudes of motions predicted by our approach agree well with experimentally determined ones, despite embracing in extreme cases >50% of the protein into one rigid cluster. In fact, the results of our method are in general comparable with when no or a uniform coarse-graining is applied; and the results are superior if the movement is dominated by loop or fragment motions. This finding indicates that explicitly distinguishing between flexible and rigid regions is advantageous when using a simplified protein representation in the second step. Finally, motions of atoms in rigid clusters are also well predicted by our approach, which points to the need to consider mobile protein regions in addition to flexible ones when modeling correlated motions.     

New modification of model-free approach to analysis of nuclear magnetic relaxation data in proteins

A formal approach to the analysis of 13C magnetic relaxation data in proteins has been developed. It is based on the concepts of one of the authors on the internal motions in solid polymers (Fedotov, V.D., Pulse NMR in bulk polymers, Doctoral dissertation, Kazan, USSR, 1981). According to this approach the intermolecular motions in proteins are considered as anisotropic ones and described in terms of a spectrum of correlation times. To characterize the motions a set of formal microdynamic parameters has been introduced. They are: the anisotropy parameter (a measure of spatial restriction of motion), the most probable correlation time, the parameter of the correlation time distribution width. The analysis of protonated carbon relaxation in globular proteins (bovine pancreatic trypsin inhibitor and ribonuclease S) and polymers has been carried out by the model-free approach. Microdynamic parameters of CH3-, CH2-, aromatic CH-groups have been considered within the framework of the diffusional rotation-oscillation models. To explain the backbone CH-group relaxation the model of the defect diffusion has been applied. The distinctive feature of the results obtained is the broad correlation time distribution for all groups of any type. The causes of nonexponential correlation function of local motion have been discussed. To elucidate the nature of the correlation time the carbon magnetization decays in the wide range of microdynamic parameter values imitating various experimental conditions have been calculated.     

Normal modes of vibration in bovine pancreatic trypsin inhibitor and its mechanical property

The normal mode analysis of conformational fluctuation is carried out for a small globular protein, bovine pancreatic trypsin inhibitor. Results are analyzed mainly to reveal the mechanical construction of the protein molecule. We take dihedral angles, including peptide omega angles, as independent variables for the normal mode analysis. There are 306 such angles in this molecule. Motions in modes with frequencies lower than 120 cm-1 are shown to involve atoms in the whole protein molecule, and spatial change of displacement vectors is continuous, i.e., those of atoms near in space are similar. To quantitate the observation of the continuity, a correlation function of direction vectors of atomic displacements is calculated. From this function we define a quantity that is interpreted as the wave length of an equivalent elastic plane wave. From this quantity we deduce effective Young's modulus for each mode. For the mode with the lowest frequency 4.4 cm-1, it turned out to be 0.8 x 10(9) dyn cm-2, the value two orders of magnitude softer than, for instance, alpha-helices. Prompted by this observation, the four lowest frequency modes and also the harmonic motions in the thermal equilibrium are analyzed further mainly to detect relatively rigid structural elements in the molecule. From this analysis emerges a mechanical picture of the protein molecule that is made up of relatively rigid elements held together by very soft parts.     

Variations on a theme by Debye and Waller: From simple crystals to proteins

Debye and Waller showed how to adjust scattering intensities in diffraction experiments for harmonic motions of atoms about an average, static reference configuration. However, many motions, particularly in biological molecules as compared to simple crystals, are far from harmonic. We show how, using a variety of simple anharmonic, multiconformational models, it is possible to construct a variety of Generalized Debye-Waller Factors, and understand their meaning. A central result for these cases is that, in principle, intensity factors cannot be obtained from true total mean square displacements of the atoms. We make the distinction between the intensity factors for unimodal quasiharmonic motions and those for the anharmonic, multimodal (valley hopping) motions. Only the former affect the conventional B factors. Proteins 29:153–160, 1997. Published 1997 Wiley-Liss, Inc.

1 This article is a US Government work and, as such, is in the public domain in the United States of America.

     

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.     

The influence of interdomain interactions on the intradomain motions in yeast phosphoglycerate kinase: a molecular dynamics study

A 3-ns molecular dynamics simulation in explicit solvent was performed to examine the inter- and intradomain motions of the two-domain enzyme yeast phosphoglycerate kinase without the presence of substrates. To elucidate contributions from individual domains, simulations were carried out on the complete enzyme as well as on each isolated domain. The enzyme is known to undergo a hinge-bending type of motion as it cycles from an open to a closed conformation to allow the phosphoryl transfer occur. Analysis of the correlation of atomic movements during the simulations confirms hinge bending in the nanosecond timescale: the two domains of the complete enzyme exhibit rigid body motions anticorrelated with respect to each other. The correlation of the intradomain motions of both domains converges, yielding a distinct correlation map in the enzyme. In the isolated domain simulations—in which interdomain interactions cannot occur—the correlation of domain motions no longer converges and shows a very small correlation during the same simulation time. This result points to the importance of interdomain contacts in the overall dynamics of the protein. The secondary structure elements responsible for interdomain contacts are also discussed.     

A method for the analysis of domain movements in large biomolecular complexes

A new method for the analysis of domain movements in large, multichain, biomolecular complexes is presented. The method is applicable to any molecule for which two atomic structures are available that represent a conformational change indicating a possible domain movement. The method is blind to atomic bonding and atom type and can, therefore, be applied to biomolecular complexes containing different constituent molecules such as protein, RNA, or DNA. At the heart of the method is the use of blocks located at grid points spanning the whole molecule. The rotation vector for the rotation of atoms from each block between the two conformations is calculated. Treating components of these vectors as coordinates means that each block is associated with a point in a “rotation space” and that blocks with atoms that rotate together, perhaps as part of the same rigid domain, will have colocated points. Thus a domain can be identified from the clustering of points from blocks that span it. Domain pairs are accepted for analysis of their relative movements in terms of screw axes based upon a set of reasonable criteria. Here, we report on the application of the method to biomolecules covering a considerable size range: hemoglobin, liver alcohol dehydrogenase, S‐Adenosylhomocysteine hydrolase, aspartate transcarbamylase, and the 70S ribosome. The results provide a depiction of the conformational change within each molecule that is easily understood, giving a perspective that is expected to lead to new insights. Of particular interest is the allosteric mechanism in some of these molecules. Results indicate that common boundaries between subunits and domains are good regions to focus on as movement in one subunit can be transmitted to another subunit through such interfaces. Proteins 2009. © 2008 Wiley‐Liss, Inc.     

A normal mode analysis of structural plasticity in the biomolecular motor F(1)-ATPase

Normal modes have been used to explore the inherent flexibility of the alpha, beta and gamma subunits of F(1)-ATPase in isolation and as part of the alpha(3)beta(3)gamma complex. It was found that the structural plasticity of the gamma and beta subunits, in particular, correlates with their functions. The N and C-terminal helices forming the coiled-coil domain of the gamma subunit are highly flexible in the isolated subunit, but more rigid in the alpha(3)beta(3)gamma complex due to interactions with other subunits. The globular domain of the gamma subunit is structurally relatively rigid when isolated and in the alpha(3)beta(3)gamma complex; this is important for its functional role in coupling the F(0) and F(1) complex of ATP synthase and in inducing the conformational changes of the beta subunits in synthesis. Most important, the character of the lowest-frequency modes of the beta(E) subunit is highly correlated with the large beta(E) --> beta(TP) transition. This holds for the C-terminal domain and the nucleotide-binding domain, which undergo significant conformational transitions in the functional cycle of F(1)-ATPase. This is most evident in the ligand-free beta(E) subunit; the flexibility in the nucleotide-binding domain is reduced somewhat in the beta(TP) subunit in the presence of Mg(2+).ATP. The low-frequency modes of the alpha(3)beta(3)gamma complex show that the motions of the globular domain of the gamma subunit and of the C-terminal and nucleotide binding domains of the beta(E) subunits are coupled, in accord with their function. Overall, the normal mode analysis reveals that F(1)-ATPase, like other macromolecular assemblies, has the intrinsic structural flexibility required for its function encoded in its sequence and three-dimensional structure. This inherent plasticity is an essential aspect of assuring a small free energy cost for the large-scale conformational transition that occurs in molecular motors.     

Normal mode analysis as a method to derive protein dynamics information from the Protein Data Bank

Normal mode analysis (NMA) can facilitate quick and systematic investigation of protein dynamics using data from the Protein Data Bank (PDB). We developed an elastic network model-based NMA program using dihedral angles as independent variables. Compared to the NMA programs that use Cartesian coordinates as independent variables, key attributes of the proposed program are as follows: (1) chain connectivity related to the folding pattern of a polypeptide chain is naturally embedded in the model; (2) the full-atom system is acceptable, and owing to a considerably smaller number of independent variables, the PDB data can be used without further manipulation; (3) the number of variables can be easily reduced by some of the rotatable dihedral angles; (4) the PDB data for any molecule besides proteins can be considered without coarse-graining; and (5) individual motions of constituent subunits and ligand molecules can be easily decomposed into external and internal motions to examine their mutual and intrinsic motions. Its performance is illustrated with an example of a DNA-binding allosteric protein, a catabolite activator protein. In particular, the focus is on the conformational change upon cAMP and DNA binding, and on the communication between their binding sites remotely located from each other. In this illustration, NMA creates a vivid picture of the protein dynamics at various levels of the structures, i.e., atoms, residues, secondary structures, domains, subunits, and the complete system, including DNA and cAMP. Comparative studies of the specific protein in different states, e.g., apo- and holo-conformations, and free and complexed configurations, provide useful information for studying structurally and functionally important aspects of the protein.