Sequence-dependent motions of DNA: a normal mode analysis at the base-pair level

Computer simulation of the dynamic structure of DNA can be carried out at various levels of resolution. Detailed high resolution information about the motions of DNA is typically collected for the atoms in a few turns of double helix. At low resolution, by contrast, the sequence-dependence features of DNA are usually neglected and molecules with thousands of base pairs are treated as ideal elastic rods. The present normal mode analysis of DNA in terms of six base-pair "step" parameters per chain residue addresses the dynamic structure of the double helix at intermediate resolution, i.e., the mesoscopic level of a few hundred base pairs. Sequence-dependent effects are incorporated into the calculations by taking advantage of "knowledge-based" harmonic energy functions deduced from the mean values and dispersion of the base-pair "step" parameters in high-resolution DNA crystal structures. Spatial arrangements sampled along the dominant low frequency modes have end-to-end distances comparable to those of exact polymer models which incorporate all possible chain configurations. The normal mode analysis accounts for the overall bending, i.e., persistence length, of the double helix and shows how known discrepancies in the measured twisting constants of long DNA molecules could originate in the deformability of neighboring base-pair steps. The calculations also reveal how the natural coupling of local conformational variables affects the global motions of DNA. Successful correspondence of the computed stretching modulus with experimental data requires that the DNA base pairs be inclined with respect to the direction of stretching, with chain extension effected by low energy transverse motions that preserve the strong van der Waals' attractions of neighboring base-pair planes. The calculations further show how one can "engineer" the macroscopic properties of DNA in terms of dimer deformability so that polymers which are intrinsically straight in the equilibrium state exhibit the mesoscopic bending anisotropy essential to DNA curvature and loop formation.     

Interpreting genotype-by-environment interaction using redundancy analysis

Summary Methods for the interpretation of genotype-by-environment interaction in the presense of explicitly measured environmental variables can be divided into two groups. Firstly, methods that extract environmental characterizations from the data itself, which are subsequently related to measured environmental variables, e.g., regression on the mean or singular value decomposition of the matrix of residuals from additivity, followed by correlation, or regression, methods. Secondly, methods that incorporate measured environmental variables directly into the model, e.g., multiple regression of individual genotypical responses on environmental variables, or factorial regression in which a genotype-by-environment matrix is modelled in terms of concomitant variables for the environmental factor. In this paper a redundancy analysis is presented, which can be derived from the singular-value decomposition of the residuals from additivity by imposing the restriction on the environmental scores of having to be linear combinations of environmental variables. At the same time, redundancy analysis is derivable from factorial regression by rotation of the axes in the space spanned by the fitted values of the factorial regression, followed by a reduction of dimensionality through discarding the least explanatory axes. Redundancy analysis is a member of the second group of methods, and can be an important tool in the interpretation of genotype-by-environment interaction, especially with reference to concomitant environmental information. A theoretical treatise of the method is given, followed by a practical example in which the results of the method are compared to the results of the other methods mentioned.     

Domain motions and the open-to-closed conformational transition of an enzyme: a normal mode analysis of S-adenosyl-L-homocysteine hydrolase

The structure and fluctuations of the enzyme S-adenosyl-L-homocysteine hydrolase (SAHH) are analyzed in an effort to explain its biological function. Besides the previously identified open structure, characteristic of the substrate-free enzyme, we find two distinct structures in enzyme-inhibitor complexes, the closed and closed-twisted conformers. Both closed conformers differ from the open form by a hinge bending motion of two large domains within each subunit, which isolate the inhibitor bound in the active site from the bulk solvent. The closed-twisted form further differs from the closed form by a rigid body twist of the two-subunit dimers. The local structural fluctuations of SAHH are analyzed by performing block normal mode analysis of the tetrameric enzyme in its three forms. For the open form, we find that the four lowest-frequency normal modes, corresponding to the collective motions of the protein with the largest amplitudes, are essentially combinations of the hinge bending deformations of the individual subunits. Thus, the mechanical properties of the open structure of SAHH lead to the presence of structural fluctuations in the direction of the open-to-closed conformational transition. A candidate for such a motion has been observed in previous fluorescence depolarization studies of the enzyme. Both structural and normal mode analyses indicate that residues 180-190 and 350-356 form hinge regions, connecting large domains which tend to move as rigid bodies in response to interactions with substrate, intermediates, and the product of the enzymatic reactions. We propose that these hinge regions play a crucial role in the enzymatic mechanism of SAHH. In contrast to the open form, normal mode calculations for the closed conformations show strong coupling of the hinge bending motions of the individual subunits to each other and to other low-frequency vibrations. Thus, information about structural changes related to reaction progress in one active site may be mechanically transmitted to other subunits of the protein, explaining the cooperativity found in the enzyme kinetics.     

Deriving correlated motions in proteins from X-ray structure refinement by using TLS parameters

Dynamic information in proteins may provide valuable information for understanding allosteric regulation of protein complexes or long-range effects of the mutations on enzyme activity. Experimental data such as X-ray B-factors or NMR order parameters provide a convenient estimate of atomic fluctuations (or atomic auto-correlated motions) in proteins. However, it is not as straightforward to obtain atomic cross-correlated motions in proteins — one usually resorts to more sophisticated computational methods such as Molecular Dynamics, normal mode analysis or atomic network models. In this report, we show that atomic cross-correlations can be reliably obtained directly from protein structure using X-ray refinement data. We have derived an analytic form of atomic correlated motions in terms of the original TLS parameters used to refine the B-factors of X-ray structures. The correlated maps computed using this equation are well correlated with those of the method based on a mechanical model (the correlation coefficient is 0.75) for a non-homologous dataset comprising 100 structures. We have developed an approach to compute atomic cross-correlations directly from X-ray protein structure. Being in analytic form, it is fast and provides a feasible way to compute correlated motions in proteins in a high throughput way. In addition, avoiding sophisticated computational operations; it provides a quick, reliable way, especially for non-computational biologists, to obtain dynamics information directly from protein structure relevant to its function.     

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

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

Enhancing backbone sampling in Monte Carlo simulations using internal coordinates normal mode analysis

Normal mode methods are becoming a popular alternative to sample the conformational landscape of proteins. In this study, we describe the implementation of an internal coordinate normal mode analysis method and its application in exploring protein flexibility by using the Monte Carlo method PELE. This new method alternates two different stages, a perturbation of the backbone through the application of torsional normal modes, and a resampling of the side chains. We have evaluated the new approach using two test systems, ubiquitin and c-Src kinase, and the differences to the original ANM method are assessed by comparing both results to reference molecular dynamics simulations. The results suggest that the sampled phase space in the internal coordinate approach is closer to the molecular dynamics phase space than the one coming from a Cartesian coordinate anisotropic network model. In addition, the new method shows a great speedup (∼5–7×), making it a good candidate for future normal mode implementations in Monte Carlo methods.     

Predicting the functional motions of p97 using symmetric normal modes

p97 is a protein complex of the AAA+ family. Although functions of p97 are well understood, the mechanism by which p97 performs its unfolding activities remains unclear. In this work, we present a novel way of applying normal mode analysis to study this six‐fold symmetric molecular machine. By selecting normal modes that are axial symmetric and give the largest movements at D1 or D2 pore residues, we are able to predict the functional motions of p97, which are then validated by experimentally observed conformational changes. Our results shed light and provide new understandings on several key steps of the p97 functional process that were previously unclear or controversial, and thus are able to reconcile multiple previous findings. Specifically, our results reveal that (i) a venous valve‐like mechanism is used at D2 pore to ensure a one‐way exit‐only traffic of substrates; (ii) D1 pore remains shut during the functional process; (iii) the “swing‐up” motion of the N domain is closely coupled with the vertical motion of the D1 pore along the pore axis; (iv) because of the shut D1 pore and the one‐way traffic at D2 pore, it is highly likely that substrates enter the chamber through the gaps at the D1/D2 interface. The limited chamber volume inside p97 suggests that a substrate may be pulling out from D2 while at the same time being pulling in at the interface; (v) lastly, p97 uses a series of actions that alternate between twisting and pulling to remove the substrate. Proteins 2016; 84:1823–1835. © 2016 Wiley Periodicals, Inc.     

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.     

Terahertz optical measurements of correlated motions with possible allosteric function

A suggested mechanism for allosteric response is the distortion of the energy landscape with agonist binding changing the protein structure’s access to functional configurations. Intramolecular vibrations are indicative of the energy landscape and may have trajectories that enable functional conformational change. Here, we discuss the development of an optical method to measure the intramolecular vibrations in proteins, namely, crystal anisotropy terahertz microscopy, and the various approaches which can be used to identify the spectral data with specific structural motions.     

Comparative normal mode analysis of LFA-1 integrin I-domains

The conformational dynamics of the Inserted domain (I-domain) from the lymphocyte function-associated antigen-1 (LFA-1) was investigated by normal mode analysis of multiple structures of the low, intermediate, and high affinity states. LFA-1 is an integrin expressed on leukocytes and is of critical importance in adhesion reactions, like antigen-specific responses, homing, and diapedesis. The main ligand binding site of LFA-1 is the I-domain, which recognizes intercellular adhesion molecules (ICAMs), members of the immunoglobulin superfamily. From experimental crystal structures, a large-scale conformational change of, among others, the α7 helix of the I-domain has been observed leading to the proposal that these structural changes are linked to the conformational regulation of LFA-1. The results from the present calculations show that structural changes of the α7 helix consistent with those observed in the crystal structures are significantly sampled by the low frequency modes. This was found to be particularly true for the low affinity state of the I-domain, indicating that low frequency motions favor the conformational transition implicated in activation. However, beyond the simple downward shift of the helix implied by the crystal structures, the calculations further show that there is a noticeable swinging-out motion of the helix. The consequences of this motion are discussed in the context of integrin activation and inhibition. Moreover, significant changes in the atomic-level dynamics and in long-range correlated motions of the I-domain were found to occur upon binding of the natural ligand ICAM. These changes were more local upon binding of an allosteric inhibitor. The present study opens the question of how changes in dynamics may contribute to the long-range transmission of signal upon ICAM binding by the LFA-1 I-domain.     

Dynamical structure of transfer RNA studied by normal mode analysis

The internal motion of yeast phenylalanine transfer RNA is studied by normal mode analysis in extended dihedral angle space, in which the flexibility of five-membered ribose rings is treated faithfully by introducing a variable for its pseudo-rotational motion. Analysis of global molecular motions reveals that the molecule is very soft. We show that this softness comes not from the property of the “material” comprising the molecule but from its slender shape. Analysis of thermal distance fluctuations reveals that this molecule can be regarded as consisting dynamically of three blocks. Thermal fluctuations of the mainchain dihedral angles show rigidity of the anticodon region. They also show flexibility of regions around nonstacking bases. Base-stacking interactions cause suppression of the correlated functions of mainchain dihedral angles beyond a ribose ring. We analyze the thermal fluctuation of parameters describing the positions of two adjacent bases. Fluctuations of relative translational parameters in the anticodon and acceptor stem regions are found to be larger than those in other stem regions. The relative translational motions cause the two stem regions to undergo global twisting and bending motions. We show that the role of pseudo-rotational motion of sugars is important in regions around bases which are involved in nonregular interactions. Received: 29 October 1998 / Revised version: 8 February 1999 / Accepted: 11 February 1999     

Normal mode analysis of the horseradish peroxidase collective motions: correlation with spectroscopically observed heme distortions

Horseradish peroxidase C is a class III peroxidase whose structure is stabilized by the presence of two endogenous calcium atoms. Calcium removal has been shown to decrease the enzymatic activity of the enzyme and significantly affect the spectroscopically detectable properties of the heme, such as the spin state of the iron, heme normal modes, and distortions from planarity. In this work, we report on normal mode analysis (NMA) performed on models subjected to 2 ns of molecular dynamics simulations to describe the effect of calcium removal on protein collective motions and to investigate the correlation between active site (heme) and protein matrix fluctuations. We show that in the native peroxidase model, heme fluctuations are correlated to matrix fluctuations while they are not in the calcium-depleted model.     

Dynamic structure of subtilisin-eglin c complex studied by normal mode analysis

Normal mode analysis of subtilisin-eglin c complex was performed to investigate the dynamics at the interface between the enzyme and the inhibitor. The internal motions of the complex calculated from the normal modes were divided into three parts: the internal motions changing the shape of each molecule, the external rigid-body motions changing their mutual dispositions, and the coupling between the internal and external motions. From the results of the analysis, the following characteristic features were found in the dynamics at the interface regions: 1) negative correlation between the internal and external motions within each molecule, and 2) positive correlation between the external motions of the two molecules. The former decreases the apparent amplitudes of motions at the interface. The latter minimizes the interference between individual motions of the two molecules. These dynamic characteristics allow the enzyme and the inhibitor to move as freely as possible. This finding suggests that the experimental evidence of the large entropy gain on binding should be attributed not only to strong hydrophobic interactions, but also to the dynamic structure of the complex, which is found to minimize an unavoidable loss of the conformational entropy on binding. Proteins 32:324–333, 1998. © 1998 Wiley-Liss, Inc.     

Interpreting the protein language using proteomics

Post-translational modifications define the functional and structural plasticity of proteins in archaea, prokaryotes and eukaryotes. Multi-site protein modification modulates protein activity and macromolecular interactions and is involved in a range of fundamental molecular processes. Combining state-of-the-art technologies in molecular cell biology, protein mass spectrometry and bioinformatics, it is now feasible to discover and study the structural and functional roles of distinct protein post-translational modifications.     

Harmonicity and anharmonicity in protein dynamics: A normal mode analysis and principal component analysis

A comparison of a normal mode analysis and principal component analysis of a 200-ps molecular dynamics trajectory of bovine pancreatic trypsin inhibitor in vacuum has been made in order to further elucidate the harmonic and anharmonic aspects in the dynamics of proteins. An anharmonicity factor is defined which measures the degree of anharmonicity in the modes, be they principal modes or normal modes, and it is shown that the principal mode system naturally divides into anharmonic modes with peak frequencies below 80 cm^?1, and harmonic modes with frequencies above this value. In general the larger the mean-square fluctuation of a principal mode, the greater the degree of anharmonicity in its motion. The anharmonic modes represent only 12% of the total number of variables, but account for 98% of the total mean-square fluctuation. The transitional nature of the anharmonic motion is demonstrated. The results strongly suggest that in a large subspace, the free energy surface, as probed by the simulation, is approximated by a multi-dimensional parabola which is just a resealed version of the parabola corresponding to the harmonic approximation to the conformational energy surface at a single minimum. After 200 ps, the resealing factor, termed the “normal mode resealing factor,” has apparently converged to a value whereby the mean-square fluctuation within the subspace is about twice that predicted by the normal mode analysis. © 1995 Wiley-Liss, Inc.     

Insights into correlated motions and long-range interactions in CheY derived from molecular dynamics simulations

CheY is a response regulator protein involved in bacterial chemotaxis. Much is known about its active and inactive conformations, but little is known about the mechanisms underlying long-range interactions or correlated motions. To investigate these events, molecular dynamics simulations were performed on the unphosphorylated, inactive structure from Salmonella typhimurium and the CheY-BeF(3)(-) active mimic structure (with BeF(3)(-) removed) from Escherichia coli. Simulations utilized both sequences in each conformation to discriminate sequence- and structure-specific behavior. The previously identified conformational differences between the inactive and active conformations of the strand-4-helix-4 loop, which are present in these simulations, arise from the structural, and not the sequence, differences. The simulations identify previously unreported structure-specific flexibility features in this loop and sequence-specific flexibility features in other regions of the protein. Both structure- and sequence-specific long-range interactions are observed in the active and inactive ensembles. In the inactive ensemble, two distinct mechanisms based on Thr-87 or Ile-95 rotameric forms, are observed for the previously identified g+ and g- rotamer sampling by Tyr-106. These molecular dynamics simulations have thus identified both sequence- and structure-specific differences in flexibility, long-range interactions, and rotameric form of key residues. Potential biological consequences of differential flexibility and long-range correlated motion are discussed.