Subpicosecond dynamics in nucleotides measured by spontaneous Raman spectroscopy

The band widths in Raman spectra are sensitive to dynamics active on a time scale from 0.1 to 10 ps. The band widths of nucleotide vibrations and their dependence on temperature, concentration, and structure are reported. From the experimental band widths and second moments, it is derived that the adenine vibrations at 725, 1336, 1480, and 1575 cm⁻¹, and the uracil vibration at 787 cm⁻¹, are in the fast modulation limit. The correlation times of the perturbations are faster than 0.4 ps. Thermal melting of the helical structure in polynucleotides results in larger band widths, due to an increase in vibrational dephasing and energy relaxation as a consequence of the increased interaction of the base moieties with the solvent molecules. The band width of the 725 cm⁻¹ adenine vibration is dependent on the type and structure of the backbone. It is found to be perturbed by movements of the sugar-phosphate moiety relative to the base. The band width of the 1575 cm⁻¹ adenine vibration is found to be sensitive to the base-pairing interaction. From a comparison of the band widths in polynucleotides with a different base sequence (homopolymer vs alternating purine-pyrimidine sequence), it is concluded that resonant vibrational energy transfer between the base molecules is not important as a relaxation process for the vibrational band widths of nucleotides. Several theoretical models for the interpretation of band widths are discussed. The theory does not take into account the strong hydrogen-bonding nature water and hence fails to describe the observations in nucleotide-water systems. The bands of the carbonyl stretching vibrations are inhomogeneously broadened. The carbonyl groups have a strong dipolar interaction with the polar water molecules and are therefore strongly perturbed by coupling to the heatbath via hydrogen bonds. © 1997 John Wiley & Sons, Inc. Biopoly 41: 751–763, 1997     

Accuracy and precision of NMR relaxation experiments and MD simulations for characterizing protein dynamics

Model-free parameters obtained from nuclear magnetic resonance (NMR) relaxation experiments and molecular dynamics (MD) simulations commonly are used to describe the intramolecular dynamical properties of proteins. To assess the relative accuracy and precision of experimental and simulated model-free parameters, three independent data sets derived from backbone ¹⁵N NMR relaxation experiments and two independent data sets derived from MD simulations of Escherichia coli ribonuclease HI are compared. The widths of the distributions of the differences between the order parameters for pairs of NMR data sets are congruent with the uncertainties derived from statistical analyses of individual data sets; thus, current protocols for analyzing NMR data encapsulate random uncertainties appropriately. Large differences in order parameters for certain residues are attributed to systematic differences between samples for intralaboratory comparisons and unknown, possibly magnetic field-dependent, experimental effects for interlaboratory comparisons. The widths of distributions of the differences between the order parameters for two NMR sets are similar to widths of distributions for an NMR and an MD set or for two MD sets. The linear correlations between the order parameters for an MD set and an NMR set are within the range of correlations observed between pairs of NMR sets. These comparisons suggest that the NMR and MD generalized order parameters for the backbone amide N—H bond vectors are of comparable accuracy for residues exhibiting motions on a fast time scale (<100 ps). Large discrepancies between NMR and MD order parameters for certain residues are attributed to the occurrence of “rare” motional events over the simulation trajectories, the disruption of an element of secondary structure in one of the simulations, and lack of consensus among the experimental data sets. Consequently, (easily detectable) severe distortions of local protein structure and infrequent motional events in MD simulations appear to be the most serious artifacts affecting the accuracy and precision, respectively, of MD order parameters relative to NMR values. In addition, MD order parameters for motions on a fast (<100 ps) timescale are more precisely determined than their NMR counterparts, thereby permitting more detailed dynamic characterization of biologically important residues by MD simulation than is sometimes possible by experimental methods. Proteins 28:481–493, 1997. © 1997 Wiley-Liss, Inc.     

Simulation and experiment conspire to reveal cryptic intermediates and a slide from the nucleation-condensation to framework mechanism of folding

There is a change from three-state to two-state kinetics of folding across the homeodomain superfamily of proteins as the mechanism slides from framework to nucleation-condensation. The tendency for framework folding in this family correlates with inherent helical propensity. The cellular myeloblastis protein (c-Myb) falls in the mechanistic transition region. An earlier, preliminary report of protein engineering experiments and molecular dynamics simulations (MD) showed that the folding mechanism for this protein has aspects of both the nucleation-condensation and framework models. In the more in-depth analysis of the MD trajectories presented here, we find that folding may be attributed to both of these mechanisms in different regions of the protein. The folding of the loop, middle helix, and turn is best described by nucleation-condensation, whereas folding of the N and C-terminal helices may be described by the framework model. Experimentally, c-Myb folds by apparent two-state kinetics, but the MD simulations predict that the kinetics hide a high-energy intermediate. We stabilized this hypothetical folding intermediate by deleting a residue (P174) in the loop between its second and third helices, and the mutant intermediate is long-lived in the simulations. Equilibrium and kinetic experiments demonstrate that folding of the DeltaP174 mutant is indeed three-state. The presence and shape of the intermediate observed in the simulations were confirmed by small angle X-ray scattering experiments.     

A molecular dynamics simulation study of segment B1 of protein G

The immunoglobulin binding protein, segment B1 of protein G, has been studied experimentally as a paradigm for protein folding. This protein consists of 56 residues, includes both β sheet and α helix and contains neither disulfide bonds nor proline residues. We report an all-atom molecular dynamics study of the native manifold of the protein in explicit solvent. A 2-ns simulation starting from the nuclear magnetic resonance (NMR) structure and a 1-ns control simulation starting from the x-ray structure were performed. The difference between average structures calculated over the equilibrium portion of trajectories is smaller than the difference between their starting conformations. These simulation averages are structurally similar to the x-ray structure and differ in systematic ways from the NMR-determined structure. Partitioning of the fluctuations into fast (<20 ps) and slow (<20 ps) components indicates that the β sheet displays greater long-time mobility than does the α helix. Clore and Gronenborn [J. Mol. Biol. 223:853–856, 1992] detected two long-residence water molecules by NMR in a solution structure of segment B1 of protein G. Both molecules were found in the fully exposed regions and were proposed to be stabilized by bifurcated hydrogen bonds to the protein backbone. One of these long-residence water molecules, found near an exposed loop region, is identified in both of our simulations, and is seen to be involved in the formation of a stable water-mediated hydrogen bond bridge. The second water molecule, located near the middle of the α helix, is not seen with an exceptional residence time in either as a result of the conformation being closer to the x-ray structure in this region of the protein. Proteins 29:193–202, 1997. © 1997 Wiley-Liss, Inc.     

Accurate geometries for “Mountain pass” regions of the Ramachandran plot using quantum chemical calculations

Unusual local arrangements of protein in Ramachandran space are not well represented by standard geometry tools used in either protein structure refinement using simple harmonic geometry restraints or in protein simulations using molecular mechanics force fields. In contrast, quantum chemical computations using small poly‐peptide molecular models can predict accurate geometries for any well‐defined backbone Ramachandran orientation. For conformations along transition regions—ϕ from −60 to 60°—a very good agreement with representative high‐resolution experimental X‐ray (≤1.5 Å) protein structures is obtained for both backbone C⁻¹‐N‐C_α angle and the nonbonded O⁻¹…C distance, while “standard geometry” leads to the “clashing” of O…C atoms and Amber FF99SB predicts distances too large by about 0.15 Å. These results confirm that quantum chemistry computations add valuable support for detailed analysis of local structural arrangements in proteins, providing improved or missing data for less understood high‐energy or unusual regions.     

Dimerization of the p53 oligomerization domain: identification of a folding nucleus by molecular dynamics simulations

Dimerization of the p53 oligomerization domain involves coupled folding and binding of monomers. To examine the dimerization, we have performed molecular dynamics (MD) simulations of dimer folding from the rate-limiting transition state ensemble (TSE). Among 799 putative transition state structures that were selected from a large ensemble of high-temperature unfolding trajectories, 129 were identified as members of the TSE via calculation of a 50% transmission coefficient from at least 20 room-temperature simulations. This study is the first to examine the refolding of a protein dimer using MD simulations in explicit water, revealing a folding nucleus for dimerization. Our atomistic simulations are consistent with experiment and offer insight that was previously unobtainable.     

FF12MC: A revised AMBER forcefield and new protein simulation protocol

Specialized to simulate proteins in molecular dynamics (MD) simulations with explicit solvation, FF12MC is a combination of a new protein simulation protocol employing uniformly reduced atomic masses by tenfold and a revised AMBER forcefield FF99 with (i) shortened C? H bonds, (ii) removal of torsions involving a nonperipheral sp³ atom, and (iii) reduced 1–4 interaction scaling factors of torsions ? and ψ. This article reports that in multiple, distinct, independent, unrestricted, unbiased, isobaric–isothermal, and classical MD simulations FF12MC can (i) simulate the experimentally observed flipping between left‐ and right‐handed configurations for C14–C38 of BPTI in solution, (ii) autonomously fold chignolin, CLN025, and Trp‐cage with folding times that agree with the experimental values, (iii) simulate subsequent unfolding and refolding of these miniproteins, and (iv) achieve a robust Z score of 1.33 for refining protein models TMR01, TMR04, and TMR07. By comparison, the latest general‐purpose AMBER forcefield FF14SB locks the C14–C38 bond to the right‐handed configuration in solution under the same protein simulation conditions. Statistical survival analysis shows that FF12MC folds chignolin and CLN025 in isobaric–isothermal MD simulations 2–4 times faster than FF14SB under the same protein simulation conditions. These results suggest that FF12MC may be used for protein simulations to study kinetics and thermodynamics of miniprotein folding as well as protein structure and dynamics. Proteins 2016; 84:1490–1516. © 2016 The Authors Proteins: Structure, Function, and Bioinformatics Published by Wiley Periodicals, Inc.     

Conformational sampling by NMR solution structures calculated with the program DIANA evaluated by comparison with long-time molecular dynamics calculations in explicit water

The NMR solution structure of bovine pancreatic trypsin inhibitor (BPTI) obtained by distance geometry calculations with the program DIANA is compared with groups of conformers generated by molecular dynamics (MD) simulations in explicit water at ambient temperature and pressure. The MD simulations started from a single conformer and were free or restrained either by the experimental NOE distance restraints or by time-averaged restraints; the groups of conformers were collected either in 10 ps intervals during 200 ps periods of simulation, or in 50 ps intervals during a 1 ns period of simulation. Overall, these comparisons show that the standard protein structure determination protocol with the program DIANA provides a picture of the protein structure that is in agreement with MD simulations using “realistic” potential functions over a nanosecond timescale. For well-constrained molecular regions there is a trend in the free MD simulation of duration 1 ns that the sampling of the conformation space is slightly increased relative to the DIANA calculations. In contrast, for surface-exposed side-chains that are less extensively constrained by the NMR data, the DIANA conformers tend to sample larger regions of conformational space than conformers selected from any of the MD trajectories. Additional insights into the behavior of surface side-chains come from comparison of the MD runs of 200 ps or 1 ns duration. In this time range the sampling of conformation space by the protein surface depends strongly on the length of the simulation, which indicates that significant side-chain transitions occur on the nanosecond timescale and that much longer simulations will be needed to obtain statistically significant data on side-chain dynamics.     

Picosecond dynamical changes on denaturation of yeast phosphoglycerate kinase revealed by quasielastic neutron scattering

Quasielastic neutron scattering experiments performed on yeast phosphoglycerate kinase in the native form and denatured in 1.5 M guanidinium chloride reveal a change in the fast (picosecond time scale) diffusive internal dynamics of the protein. The momentum and energy transfer dependences of the scattering for both states are fitted by an analytical model in which, on the experimentally accessible picosecond time scale and angstrom length scale, the dynamics of a fraction of the nonexchangeable hydrogens in the protein is described as a superposition of vibrations with uniform diffusion in a sphere, the rest of the hydrogens undergoing only vibrational motion. The fraction diffusing changes, from ≈60% in the native protein to ≈82% in the denatured protein. The radius of the sphere also changes slightly, from ≈1.8 Å in the native protein to ≈2.2 Å in the denatured protein. Possible implications of these results for the general protein folding problem are discussed. Proteins 28:380–387, 1997 © 1997 Wiley-Liss, Inc.     

Physics and biophysics of solvent induced forces: hydrophobic interactions and context-dependent hydration

Solvent induced forces (SIFs) among solutes derive from solvent structural modification due to solutes, and consequent thermodynamic drive towards minimization of related free energy costs. The role of SIFs in biomolecular conformation and function is appreciated by observing that typical SIF values fall within the 20–200 pN interval, and that proteins are stable by only a few kcal mol^–1 (1 kcal mol^–1 corresponds to 70 pN Å). Here we study SIFs, in systems of increasing complexity, using Molecular Dynamics (MD) simulations which give time- and space-resolved details on the biologically significant scale of single protein residues and sidechains. Of particular biological relevance among our results are a strong modulability of hydrophobic SIFs by electric charges and the dependence of this modulability upon charge sign. More generally, the present results extend our understanding of the recently reported strong context-dependence of SIFs and the related potential of mean force (PMF). This context-dependence can be strong enough to propagate (by relay action) along a composite solute, and to reverse SIFs acting on a given element, relative to expectations based on its specific character (hydrophobic/ philic, charged). High specificity such as that of SIFs highlighted by the present results is of course central to biological function. Biological implications of the present results cover issues such as biomolecular functional interactions and folding (including chaperoning and pathological conformational changes), coagulation, molecular recognition, effects of phosphorylation and more.     

Dramatic differences in the motions of the mouth of open and closed cytochrome P450BM-3 by molecular dynamics simulations

Molecular dynamics trajectories were calculated separately for each of the two molecules in the asymmetric unit of the crystal structure of the hemoprotein domain of cytochrome P450BM-3. Each simulation was 200 ps in length and included a 10 Å layer of explicit solvent. The simulated time-average structure of each P450BM-3 molecule is closer to its crystal structure than the two molecular dynamics time-averaged structures are to each other. In the crystal structure, molecule 2 has a more accessible substrate binding pocket than molecule 1, and this difference is maintained throughout the simulations presented here. In particular, the substrate docking regions of molecule 1 and molecule 2 diverge in the solution state simulations. The mouth of the substrate binding pocket is significantly more mobile in the simulation of molecule 2 than in the simulation of molecule 1. For molecule 1, the width of the mouth is only slightly larger than its X-ray value of 8.7 Å and undergoes fluctuations of about 1 Å. However, in molecule 2, the mouth of the substrate binding pocket is dramatically more open in the time-average molecular dynamics structure (14.7 Å) than in the X-ray structure (10.9 Å). Furthermore, this region of the protein undergoes large amplitude motions during the trajectory that are not seen in the trajectory of molecule 1, repeatedly opening and closing up to 7 Å. Presumably, the binding of different substrates will induce the mouth region to adopt different conformations from within the wide range of structures that are accessible. © 1995 Wiley-Liss, Inc.     

Kinetic definition of protein folding transition state ensembles and reaction coordinates

Using distributed molecular dynamics simulations we located four distinct folding transitions for a 39-residue betabetaalphabeta protein fold. To characterize the nature of each room temperature transition, we calculated the probability of transmission for 500 points along each free energy barrier. We introduced a method for determining transition states by employing the transmission probability, Ptrans, and determined which conformations were transition state ensemble members (Ptrans approximately 0.5). The transmission probability may be used to characterize the barrier in several ways. For example, we ran simulations at 82 degrees C, determined the change in Ptrans with temperature for all 2,000 conformations, and quantified Hammond behavior directly using Ptrans correlation. Additionally, we propose that diffusion along Ptrans may provide the configurational diffusion rate at the top of the barrier. Specifically, given a transition state conformation x0 with estimated Ptrans=0.5, we selected a large set of subsequent conformations from independent trajectories, each exactly a small time deltat after x0 (250 ps). Calculating Ptrans for the new trial conformations, we generated the P(Ptrans|deltat=250 ps) distribution that reflected diffusion. This approach provides a novel perspective on the diffusive nature of a protein folding transition and provides a framework for a quantitative study of activated relaxation kinetics.     

The influence of Mg2+ coordination on 13C and 15N chemical shifts in CKI1RD protein domain from experiment and molecular dynamics/density functional theory calculations

Sequence dependence of ¹³C and ¹⁵N chemical shifts in the receiver domain of CKI1 protein from Arabidopsis thaliana, CKI1_RD, and its complexed form, CKI1_RD?Mg²⁺, was studied by means of MD/DFT calculations. MD simulations of a 20–ns production run length were performed. Nine explicitly hydrated structures of increasing complexity were explored, up to a 40‐amino‐acid structure. The size of the model necessary depended on the type of nucleus, the type of amino acid and its sequence neighbors, other spatially close amino acids, and the orientation of amino acid NH groups and their surface/interior position. Using models covering a 10 and a 15 Å environment of Mg²⁺, a semi‐quantitative agreement has been obtained between experiment and theory for the V67?I73 sequence. The influence of Mg²⁺ binding was described better by the 15 Å as compared to the 10 Å model. Thirteen chemical shifts were analyzed in terms of the effect of Mg²⁺ insertion and geometry preparation. The effect of geometry was significant and opposite in sign to the effect of Mg²⁺ binding. The strongest individual effects were found for ¹⁵N of D70, S74, and V68, where the electrostatics dominated; for ¹³Cβ of D69 and ¹⁵N of K76, where the influences were equal, and for ¹³Cα of F72 and ¹³Cβ of K76, where the geometry adjustment dominated. A partial correlation between dominant geometry influence and torsion angle shifts upon the coordination has been observed. Proteins 2016; 84:686–699. © 2016 Wiley Periodicals, Inc.     

Protein conformational landscapes: Energy minimization and clustering of a long molecular dynamics trajectory

Using energy minimization and cluster analysis, we have analyzed a 1020 ps molecular dynamics trajectory of solvated bovine pancreatic trypsin inhibitor. Elucidation of conformational sub states in this way both illustrates the degree of conformational convergence in the simulation and reduces the structural data to a tractable subset. The relative movement of structures upon energy minimization was used to estimate the sizes of features on the protein potential energy surface. The structures were analyzed using their pairwise root-mean-square C_α deviations, which gave a global measure of conformational changes that would not be apparent by monitoring single degrees of freedom. At time scales of 0.1 ps, energy minimization detected sharp transitions between energy minima separated by 0.1 Å rms deviation. Larger conformational clusters containing these smaller minima and separated by 0.25 Å were seen at 1 ps time scales. Both of these small features of the conformational landscape were characterized by movements in loop regions associated with small, correlated backbone dihedral angle shifts. On a nanosecond time scale, the main features of the protein energy landscape were clusters separated by over 0.7 Å rms deviation, with only seven of these sub states visited over the 1 ns trajectory. These substates, discernible both before and after energy minimization, differ mainly in a monotonic pivot of the loop residues 11–18 over the course of the simulation. This loop contains lysine 17, which specifically binds to trypsin in the active site. The trajectory did not return to previously visited clusters, indicating that this trajectory has not been shown to have completely sampled the conformational substates available to it. Because the apparent convergence to a single region of conformation space depends on both the time scale of observation and the size of the conformational features examined, convergence must be operationally defined within the context of the simulation. © 1995 Wiley-Liss, Inc.     

Comparative study of stability and transport of molecules through cyclic peptide nanotube and aquaporin: a molecular dynamics simulation approach

Abstract

The structural stability and transport properties of the cyclic peptide nanotube (CPN) 8?×?[Cys–Gly–Met–Gly]₂ in different phospholipid bilayers such as POPA (1-palmitoyl-2-oleoyl-sn-glycero-3-phosphatidic acid), POPE (1-palmitoyl-2-oleoyl-sn-glycero-3-phosphoethanolamine), POPC (1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine), POPG (1-palmitoyl-2-oleoyl-sn-glycero-3-phosphoglycerol) and POPS (1-palmitoyl-2-oleoyl-sn-glycero-3-phosphoserine) with water have been investigated using molecular dynamics (MD) simulation. The hydrogen bonds and non-bonded interaction energies were calculated to study the stability in different bilayers. One µs MD simulation in POPA lipid membrane reveals the stability of the cyclic peptide nanotube, and the simulations at various temperatures manifest the higher stability of 8?×?[Cys–Gly–Met–Gly]₂. We demonstrated that the presence of sulphur-containing amino acids in CPN enhances the stability through disulphide bonds between the adjacent rings. Further, the water permeation coefficient of the CPN is calculated and compared with human aquaporin-2 (AQP2) channel protein. It is found that the coefficients are highly comparable to the AQP2 channel though the mechanism of water transport is not similar to AQP 2; the flow of water in the CPN is taking place as a two-line 1–2–1–2 file fashion. In addition to that, the transport behavior of Na⁺ and K⁺ ions, single water molecule, urea and anti-cancer drug fluorouracil were investigated using pulling simulation and potential of mean force calculation. The above transport behavior shows that Na⁺ is trapped in CPN for a longer time than other molecules. Also, the interactions of the ions and molecules in Cα and mid-Cα plane were studied to understand the transport behavior of the CPN. Abbreviations AQP2 Aquaporin-2

CPN Cyclic peptide nanotube

MD Molecular dynamics

POPA 1-Palmitoyl-2-oleoyl-sn-glycero-3-phosphatidic acid

POPE 1-Palmitoyl-2-oleoyl-sn-glycero-3-phosphoethanolamine

POPG 1-Palmitoyl-2-oleoyl-sn-glycero-3-phosphoglycerol

POPS 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphoserine

Communicated by Ramaswamy H. Sarma     

Probing the interaction between cHAVc3 peptide and the EC1 domain of E-cadherin using NMR and molecular dynamics simulations

The goal of this work is to probe the interaction between cyclic cHAVc3 peptide and the EC1 domain of human E-cadherin protein. Cyclic cHAVc3 peptide (cyclo(1,6)Ac-CSHAVC-NH₂) binds to the EC1 domain as shown by chemical shift perturbations in the 2D ¹H,-¹⁵N-HSQC NMR spectrum. The molecular dynamics (MD) simulations of the EC1 domain showed folding of the C-terminal tail region into the main head region of the EC1 domain. For cHAVc3 peptide, replica exchange molecular dynamics (REMD) simulations generated five structural clusters of cHAVc3 peptide. Representative structures of cHAVc3 and the EC1 structure from MD simulations were used in molecular docking experiments with NMR constraints to determine the binding site of the peptide on EC1. The results suggest that cHAVc3 binds to EC1 around residues Y36, S37, I38, I53, F77, S78, H79, and I94. The dissociation constants (K_d values) of cHAVc3 peptide to EC1 were estimated using the NMR chemical shifts data and the estimated K_ds are in the range of .5 × 10^?5–7.0 × 10^?5 M.     

Distance restraints from crosslinking mass spectrometry: Mining a molecular dynamics simulation database to evaluate lysine–lysine distances

Integrative structural biology attempts to model the structures of protein complexes that are challenging or intractable by classical structural methods (due to size, dynamics, or heterogeneity) by combining computational structural modeling with data from experimental methods. One such experimental method is chemical crosslinking mass spectrometry (XL‐MS), in which protein complexes are crosslinked and characterized using liquid chromatography‐mass spectrometry to pinpoint specific amino acid residues in close structural proximity. The commonly used lysine‐reactive N‐hydroxysuccinimide ester reagents disuccinimidylsuberate (DSS) and bis(sulfosuccinimidyl)suberate (BS³) have a linker arm that is 11.4 Å long when fully extended, allowing C_α (alpha carbon of protein backbone) atoms of crosslinked lysine residues to be up to ～24 Å apart. However, XL‐MS studies on proteins of known structure frequently report crosslinks that exceed this distance. Typically, a tolerance of ～3 Å is added to the theoretical maximum to account for this observation, with limited justification for the chosen value. We used the Dynameomics database, a repository of high‐quality molecular dynamics simulations of 807 proteins representative of diverse protein folds, to investigate the relationship between lysine–lysine distances in experimental starting structures and in simulation ensembles. We conclude that for DSS/BS³, a distance constraint of 26–30 Å between C_α atoms is appropriate. This analysis provides a theoretical basis for the widespread practice of adding a tolerance to the crosslinker length when comparing XL‐MS results to structures or in modeling. We also discuss the comparison of XL‐MS results to MD simulations and known structures as a means to test and validate experimental XL‐MS methods.     

Structural features that predict real-value fluctuations of globular proteins

It is crucial to consider dynamics for understanding the biological function of proteins. We used a large number of molecular dynamics (MD) trajectories of nonhomologous proteins as references and examined static structural features of proteins that are most relevant to fluctuations. We examined correlation of individual structural features with fluctuations and further investigated effective combinations of features for predicting the real value of residue fluctuations using the support vector regression (SVR). It was found that some structural features have higher correlation than crystallographic B‐factors with fluctuations observed in MD trajectories. Moreover, SVR that uses combinations of static structural features showed accurate prediction of fluctuations with an average Pearson's correlation coefficient of 0.669 and a root mean square error of 1.04 Å. This correlation coefficient is higher than the one observed in predictions by the Gaussian network model (GNM). An advantage of the developed method over the GNMs is that the former predicts the real value of fluctuation. The results help improve our understanding of relationships between protein structure and fluctuation. Furthermore, the developed method provides a convienient practial way to predict fluctuations of proteins using easily computed static structural features of proteins. Proteins 2012; © 2012 Wiley Periodicals, Inc.