Homology modelling and molecular dynamics simulations: comparative studies of human aquaporin-1

The structures of the mammalian water transport protein Aqp1 and of its bacterial homologue GlpF enables us to test whether homology models can be used to explore relationships between structure, dynamics and function in mammalian transport proteins. Molecular dynamics simulations (totalling almost 40 ns) were performed starting from: the X-ray structure of Aqp1; a homology model of Aqp1 based on the GlpF structure; and intermediate resolution structures of Aqp1 derived from electron microscopy. Comparisons of protein RMSDs vs. time suggest that the homology models are of comparable conformational stability to the X-ray structure, whereas the intermediate resolution structures exhibit significant conformation drift. For simulations based on the X-ray structure and on homology models, the flexibility profile vs. residue number correlates well with the crystallographic B-values for each residue. In the simulations based on intermediate resolution structures, mobility of the highly conserved NPA loops is substantially higher than in the simulations based on the X-ray structure or the homology models. Pore radius profiles remained relatively constant in the X-ray and homology model simulations but showed substantial fluctuations (reflecting the higher NPA loop mobility) in the intermediate resolution simulations. The orientation of the dipoles of water molecules within the pore is of key importance in maintaining low proton permeability through Aqp1. This property seems to be quite robust to the starting model used in the simulation. These simulations suggest that homology models based on bacterial homologues may be used to derive functionally relevant information on the structural dynamics of mammalian transport proteins.     

One membrane protein,two structures and six environments: a comparative molecular dynamics simulation study of the bacterial outer membrane protein PagP

PagP is a bacterial outer membrane protein consisting of an 8 stranded transmembrane β-barrel and an N-terminal α-helix. It is an enzyme which catalyses transfer of a palmitoyl chain from a phospholipid to lipid A. Molecular dynamics simulations have been used to compare the dynamic behaviour in simulations starting from two different structures (X-ray vs. NMR) and in six different environments (detergent micelles formed by dodecyl phosphocholine and by octyl glucoside, vs. four species of phospholipid bilayer). Analysis of interactions between the protein and its environment reveals the role played by the N-terminal α-helix, which interacts with the lipid headgroups to lock the PagP molecule into the bilayer. The PagP β-barrel adopts a tilted orientation in lipid bilayers, facilitating access of lipid tails into the mouth of the central binding pocket. In simulations starting from the X-ray structure in lipid bilayer, the L1 and L2 loops move towards one another, leading to the formation of a putative active site by residues H33, D76 and S77 coming closer together.     

Combining NMR ensembles and molecular dynamics simulations provides more realistic models of protein structures in solution and leads to better chemical shift prediction

While chemical shifts are invaluable for obtaining structural information from proteins, they also offer one of the rare ways to obtain information about protein dynamics. A necessary tool in transforming chemical shifts into structural and dynamic information is chemical shift prediction. In our previous work we developed a method for 4D prediction of protein ¹H chemical shifts in which molecular motions, the 4th dimension, were modeled using molecular dynamics (MD) simulations. Although the approach clearly improved the prediction, the X-ray structures and single NMR conformers used in the model cannot be considered fully realistic models of protein in solution. In this work, NMR ensembles (NMRE) were used to expand the conformational space of proteins (e.g. side chains, flexible loops, termini), followed by MD simulations for each conformer to map the local fluctuations. Compared with the non-dynamic model, the NMRE+MD model gave 6–17% lower root-mean-square (RMS) errors for different backbone nuclei. The improved prediction indicates that NMR ensembles with MD simulations can be used to obtain a more realistic picture of protein structures in solutions and moreover underlines the importance of short and long time-scale dynamics for the prediction. The RMS errors of the NMRE+MD model were 0.24, 0.43, 0.98, 1.03, 1.16 and 2.39 ppm for ¹Hα, ¹HN, ¹³Cα, ¹³Cβ, ¹³CO and backbone ¹⁵N chemical shifts, respectively. The model is implemented in the prediction program 4DSPOT, available at .     

Motions and structural variability within toxins: implication for their use as scaffolds for protein engineering

Animal toxins are small proteins built on the basis of a few disulfide bonded frameworks. Because of their high variability in sequence and biologic function, these proteins are now used as templates for protein engineering. Here we report the extensive characterization of the structure and dynamics of two toxin folds, the "three-finger" fold and the short alpha/beta scorpion fold found in snake and scorpion venoms, respectively. These two folds have a very different architecture; the short alpha/beta scorpion fold is highly compact, whereas the "three-finger" fold is a beta structure presenting large flexible loops. First, the crystal structure of the snake toxin alpha was solved at 1.8-A resolution. Then, long molecular dynamics simulations (10 ns) in water boxes of the snake toxin alpha and the scorpion charybdotoxin were performed, starting either from the crystal or the solution structure. For both proteins, the crystal structure is stabilized by more hydrogen bonds than the solution structure, and the trajectory starting from the X-ray structure is more stable than the trajectory started from the NMR structure. The trajectories started from the X-ray structure are in agreement with the experimental NMR and X-ray data about the protein dynamics. Both proteins exhibit fast motions with an amplitude correlated to their secondary structure. In contrast, slower motions are essentially only observed in toxin alpha. The regions submitted to rare motions during the simulations are those that exhibit millisecond time-scale motions. Lastly, the structural variations within each fold family are described. The localization and the amplitude of these variations suggest that the regions presenting large-scale motions should be those tolerant to large insertions or deletions.     

4D prediction of protein <Superscript>1</Superscript>H chemical shifts

A 4D approach for protein ¹H chemical shift prediction was explored. The 4th dimension is the molecular flexibility, mapped using molecular dynamics simulations. The chemical shifts were predicted with a principal component model based on atom coordinates from a database of 40 protein structures. When compared to the corresponding non-dynamic (3D) model, the 4th dimension improved prediction by 6–7%. The prediction method achieved RMS errors of 0.29 and 0.50 ppm for Hα and HN shifts, respectively. However, for individual proteins the RMS errors were 0.17–0.34 and 0.34–0.65 ppm for the Hα and HN shifts, respectively. X-ray structures gave better predictions than the corresponding NMR structures, indicating that chemical shifts contain invaluable information about local structures. The ¹H chemical shift prediction tool 4DSPOT is available from .     

Relative stability of protein structures determined by X-ray crystallography or NMR spectroscopy: a molecular dynamics simulation study

The relative stability of protein structures determined by either X-ray crystallography or nuclear magnetic resonance (NMR) spectroscopy has been investigated by using molecular dynamics simulation techniques. Published structures of 34 proteins containing between 50 and 100 residues have been evaluated. The proteins selected represent a mixture of secondary structure types including all alpha, all beta, and alpha/beta. The proteins selected do not contain cysteine-cysteine bridges. In addition, any crystallographic waters, metal ions, cofactors, or bound ligands were removed before the systems were simulated. The stability of the structures was evaluated by simulating, under identical conditions, each of the proteins for at least 5 ns in explicit solvent. It is found that not only do NMR-derived structures have, on average, higher internal strain than structures determined by X-ray crystallography but that a significant proportion of the structures are unstable and rapidly diverge in simulations.     

Protein conformational dynamics of crambin in crystal, solution and in the trajectories of molecular dynamics simulations

Atomic displacement parameters — B factors of the eight crambin crystal structures obtained at 0.54–1.5 Å resolution and temperatures of 100–293 K have been analyzed. The comparable contributions to the B factor values are the intramolecular motions which are modeled by the harmonic vibration calculations and derived from the molecular dynamics simulation (MD) as well as rigid body changes in the position of a protein molecule as a whole. In solution for the average NMR structure of crambin the amplitudes of the backbone atomic fluctuations of the most residues of the segments with the regular backbone conformations are close to the amplitudes of the small scale harmonic vibrations. For the same residues the probability of the medium scale fluctuations fixed by the hydrogen exchange method is very low. The restricted conformational mobility of those segments is coupled with the depressed amplitudes of the fluctuation changes of the tertiary structure registered by the residue accessibility changes in an ensemble of NMR structures that forms the average NMR structure of crambin. The amplitudes of temperature fluctuations of backbone atoms and the tertiary structure raise in the segment with the irregular conformations, turn and loops. In the same segments the amplitudes of the calculated harmonic vibrations also increase, but to a lesser extent and especially in the interhelical loop with the most strong and complicated fluctuation changes of the backbone conformation. In solution for the NMR structure in this loop the conformational transitions occur between the conformational substates separated by the energy barriers, but they are not observed even in the long 100 ns trajectories from the MD simulation of crambin. These strong local fluctuation changes of the structure may play a key role in the protein functioning and modern performance improvements in the MD simulation techniques are oriented to increase the probability of protein appearance in the trajectories from the MD simulations.     

Molecular dynamics simulations of RNA kissing-loop motifs reveal structural dynamics and formation of cation-binding pockets

Explicit solvent molecular dynamics (MD) simulations were carried out for three RNA kissing–loop complexes. The theoretical structure of two base pairs (2 bp) complex of H3 stem–loop of Moloney murine leukemia virus agrees with the NMR structure with modest violations of few NMR restraints comparable to violations present in the NMR structure. In contrast to the NMR structure, however, MD shows relaxed intermolecular G-C base pairs. The core region of the kissing complex forms a cation-binding pocket with highly negative electrostatic potential. The pocket shows nanosecond-scale breathing motions coupled with oscillations of the whole molecule. Additional simulations were carried out for 6 bp kissing complexes of the DIS HIV-1 subtypes A and B. The simulated structures agree well with the X-ray data. The subtype B forms a novel four-base stack of bulged-out adenines. Both 6 bp kissing complexes have extended cation-binding pockets in their central parts. While the pocket of subtype A interacts with two hexacoordinated Mg²⁺ ions and one sodium ion, pocket of subtype B is filled with a string of three delocalized Na⁺ ions with residency times of individual cations 1–2 ns. The 6 bp complexes show breathing motions of the cation-binding pockets and loop major grooves.     

Free-energy calculations highlight differences in accuracy between X-ray and NMR structures and add value to protein structure prediction

BACKGROUND: While X-ray crystallography structures of proteins are considerably more reliable than those from NMR spectroscopy, it has been difficult to assess the inherent accuracy of NMR structures, particularly the side chains. RESULTS: For 15 small single-domain proteins, we used a molecular mechanics-/dynamics-based free-energy approach to investigate native, decoy, and fully extended alpha conformations. Decoys were all less energetically favorable than native conformations in nine of the ten X-ray structures and in none of the five NMR structures, but short 150 ps molecular dynamics simulations on the experimental structures caused them to have the lowest predicted free energy in all 15 proteins. In addition, a strong correlation exists (r(2) = 0.86) between the predicted free energy of unfolding, from native to fully extended conformations, and the number of residues. CONCLUSIONS: This work suggests that the approximate treatment of solvent used in solving NMR structures can lead NMR model conformations to be less reliable than crystal structures. This conclusion was reached because of the considerably higher calculated free energies and the extent of structural deviation during aqueous dynamics simulations of NMR models compared to those determined by X-ray crystallography. Also, the strong correlation found between protein length and predicted free energy of unfolding in this work suggests, for the first time, that a free-energy function can allow for identification of the native state based on calculations on an extended state and in the absence of an experimental structure.     

A comparison of the dynamic behavior of monomeric and dimeric insulin shows structural rearrangements in the active monomer

Molecular dynamics (MD) simulations (5-10ns in length) and normal mode analyses were performed for the monomer and dimer of native porcine insulin in aqueous solution; both starting structures were obtained from an insulin hexamer. Several simulations were done to confirm that the results obtained are meaningful. The insulin dimer is very stable during the simulation and remains very close to the starting X-ray structure; the RMS fluctuations calculated from the MD simulation agree with the experimental B-factors. Correlated motions were found within each of the two monomers; they can be explained by persistent non-bonded interactions and disulfide bridges. The correlated motions between residues B24 and B26 of the two monomers are due to non-bonded interactions between the side-chains and backbone atoms. For the isolated monomer in solution, the A chain and the helix of the B chain are found to be stable during 5ns and 10ns MD simulations. However, the N-terminal and the C-terminal parts of the B chain are very flexible. The C-terminal part of the B chain moves away from the X-ray conformation after 0.5-2.5ns and exposes the N-terminal residues of the A chain that are thought to be important for the binding of insulin to its receptor. Our results thus support the hypothesis that, when monomeric insulin is released from the hexamer (or the dimer in our study), the C-terminal end of the monomer (residues B25-B30) is rearranged to allow binding to the insulin receptor. The greater flexibility of the C-terminal part of the beta chain in the B24 (Phe-->Gly) mutant is in accord with the NMR results. The details of the backbone and side-chain motions are presented. The transition between the starting conformation and the more dynamic structure of the monomers is characterized by displacements of the backbone of Phe B25 and Tyr B26; of these, Phe B25 has been implicated in insulin activation.     

Phosphorylation-induced changes in backbone dynamics of the dematin headpiece C-terminal domain

Dematin is an actin-binding protein abundant in red blood cells and other tissues. It contains a villin-type ‘headpiece’ F-actin-binding domain at its extreme C-terminus. The isolated dematin headpiece domain (DHP) undergoes a significant conformational change upon phosphorylation. The mutation of Ser74 to Glu closely mimics the phosphorylation of DHP. We investigated motions in the backbone of DHP and its mutant DHPS74E using several complementary NMR relaxation techniques: laboratory frame ¹⁵N NMR relaxation, which is sensitive primarily to the ps–ns time scale, cross-correlated chemical shift modulation NMR relaxation detecting correlated μs–ms time scale motions of neighboring ¹³C′ and ¹⁵N nuclei, and cross-correlated relaxation of two ¹⁵N–¹H dipole–dipole interactions detecting slow motions of backbone NH vectors in successive amino acid residues. The results indicate a reduction in mobility upon the mutation in several regions of the protein. The additional salt bridge formed in DHPS74E that links the N- and C-terminal subdomains is likely to be responsible for these changes. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Molecular dynamics simulations of photoactive yellow protein (PYP) in three states of its photocycle: a comparison with X-ray and NMR data and analysis of the effects of Glu46 deprotonation and mutation

Photoactive yellow protein (PYP) is a prototype of the PAS domain superfamily of signaling proteins. The signaling process is coupled to a three-state photocycle. After the photoinduced trans-cis isomerization of the chromophore, 4-hydroxycinnamic acid (pCA), an early intermediate (pR) is formed, which proceeds to a second intermediate state (pB) on a sub-millisecond time scale. The signaling process is thought to be connected to the conformational changes upon the formation of pB and its recovery to the ground state (pG), but the exact signaling mechanism is not known. Experimental studies of PYP by solution NMR and X-ray crystallography suggest a very flexible protein backbone in the ground as well as in the signaling state. The relaxation from the pR to the pB state is accompanied by the protonation of the chromophore's phenoxyl group. This was found to be of crucial importance for the relaxation process. With the goal of gaining a better understanding of these experimental observations on an atomistic level, we performed five MD simulations on the three different states of PYP: a 1 ns simulation of PYP in its ground state [pG(MD)], a 1 ns simulation of the pR state [pR(MD)], a 2 ns simulation of the pR state with the chromophore protonated (pRprot), a 2 ns simulation of the pR state with Glu46 exchanged by Gln (pRGln) and a 2 ns simulation of PYP in its signaling state [pB(MD)]. Comparison of the pG simulation results with X-ray and NMR data, and with the results obtained for the pB simulation, confirmed the experimental observations of a rather flexible protein backbone and conformational changes during the recovery of the pG from the pB state. The conformational changes in the region around the chromophore pocket in the pR state were found to be crucially dependent on the strength of the Glu46-pCA hydrogen bond, which restricts the mobility of the chromophore in its unprotonated form considerably. Both the mutation of Glu46 with Gln and the protonation of the chromophore weaken this hydrogen bond, leading to an increased mobility of pCA and large structural changes in its surroundings. These changes, however, differ considerably during the pRGln and pRprot simulations, providing an atomistic explanation for the enhancement of the rate constant in the Gln46 mutant. Electronic supplementary material to this article is available at and is accessible for athorized users. Electronic Publication     

Backbone dynamics of the ribonuclease binase active site area using multinuclear ((15)N and (13)CO) NMR relaxation and computational molecular dynamics

The nano-pico second backbone dynamics of the ribonuclease binase, homologous to barnase, is investigated with (15)N, (13)C NMR relaxation at 11.74 and 18.78 T and with a 1.1 ns molecular dynamics simulation. The data are compared with the temperature factors reported for the X-ray structure of this enzyme. The molecular dynamics and X-ray data correspond well and predict motions in the loops 56-61 and 99-104 that contain residues that specifically recognize substrate and are catalytic (His101), respectively. In contrast, the (15)N relaxation data indicate that these loops are mostly ordered at the nano-pico second time scale. Nano-pico second motions in the recognition loop 56-61 are evident from (13)CO-(13)C cross relaxation data, but the mobility of the catalytic loop 99-104 is not detected by (13)CO cross relaxation either. From the results of this and previous work [Wang, L., Pang, Y., Holder, T., Brender, J. R., Kurochkin, A., and Zuiderweg, E. R. P. (2001) Proc. Natl. Acad. Sci. U.S.A., 98, 7684-7689], the following dynamical characterization of the active site area of binase emerges: a beta sheet, rigid at all probed time scales, supports the catalytic residue Glu 72. Both substrate-encapsulating loops are mobile on both fast and slow time scales, but the fast motions of the loop which contains the other catalytic residue, His 101, as predicted by B-factors and computational molecular dynamics is not detected by NMR relaxation. This work strongly argues for the use of several measures in the study of protein dynamics.     

Locally accessible conformations of proteins: multiple molecular dynamics simulations of crambin.

Multiple molecular dynamics (MD) simulations of crambin with different initial atomic velocities are used to sample conformations in the vicinity of the native structure. Individual trajectories of length up to 5 ns sample only a fraction of the conformational distribution generated by ten independent 120 ps trajectories at 300 K. The backbone atom conformational space distribution is analyzed using principal components analysis (PCA). Four different major conformational regions are found. In general, a trajectory samples only one region and few transitions between the regions are observed. Consequently, the averages of structural and dynamic properties over the ten trajectories differ significantly from those obtained from individual trajectories. The nature of the conformational sampling has important consequences for the utilization of MD simulations for a wide range of problems, such as comparisons with X-ray or NMR data. The overall average structure is significantly closer to the X-ray structure than any of the individual trajectory average structures. The high frequency (less than 10 ps) atomic fluctuations from the ten trajectories tend to be similar, but the lower frequency (100 ps) motions are different. To improve conformational sampling in molecular dynamics simulations of proteins, as in nucleic acids, multiple trajectories with different initial conditions should be used rather than a single long trajectory.     

β‐Hairpin folding and stability: molecular dynamics simulations of designed peptides in aqueous solution

The structural properties of a 10‐residue and a 15‐residue peptide in aqueous solution were investigated by molecular dynamics simulation. The two designed peptides, SYINSDGTWT and SESYINSDGTWTVTE, had been studied previously by NMR at 278 K and the resulting model structures were classified as 3:5 β‐hairpins with a type I + G1 β‐bulge turn. In simulations at 278 K, starting from the NMR model structure, the 3:5 β‐hairpin conformers proved to be stable over the time period evaluated (30 ns). Starting from an extended conformation, simulations of the decapeptide at 278 K, 323 K and 353 K were also performed to study folding. Over the relatively short time scales explored (30 ns at 278 K and 323 K, 56 ns at 353 K), folding to the 3:5 β‐hairpin could only be observed at 353 K. At this temperature, the collapse to β‐hairpin‐like conformations is very fast. The conformational space accessible to the peptide is entirely dominated by loop structures with different degrees of β‐hairpin character. The transitions between different types of ordered loops and β‐hairpins occur through two unstructured loop conformations stabilized by a single side‐chain interaction between Tyr2 and Trp9, which facilitates the changes of the hydrogen‐bond register. In agreement with previous experimental results, β‐hairpin formation is initially driven by the bending propensity of the turn segment. Nevertheless, the fine organization of the turn region appears to be a late event in the folding process. Copyright © 2004 European Peptide Society and John Wiley & Sons, Ltd.     

Conformational ensemble of an intrinsically flexible loop in mitochondrial import protein Tim21 studied by modeling and molecular dynamics simulations

BackgroundTim21, a subunit of a highly dynamic translocase of the inner mitochondrial membrane (TIM23) complex, translocates proteins by interacting with subunits in the translocase of the outer membrane (TOM) complex and Tim23 channel in the TIM23 complex. A loop segment in Tim21, which is in close proximity of the binding site of Tim23, has different conformations in X-ray, NMR and new crystal contact-free space (CCFS) structures. MD simulations can provide information on the structure and dynamics of the loop in solution.MethodsThe conformational ensemble of the loop was characterized using loop modeling and molecular dynamics (MD) simulations.ResultsMD simulations confirmed mobility of the loop. Multidimensional scaling and clustering were used to characterize the dynamic conformational ensemble of the loop. Free energy landscape showed that the CCFS crystal structure occupied a low energy region as compared to the conventional X-ray crystal structure. Analysis of crystal packing indicates that the CCFS provides larger conformational space for the motions of the loop.ConclusionsOur work reported the conformational ensemble of the loop in solution, which is in agreement with the structure obtained from CCFS approach. The combination of the experimental techniques and computational methods is beneficial for studying highly flexible regions of proteins.General significanceComputational methods, such as loop modeling and MD simulations, have proved to be useful for studying conformational flexibility of proteins. These methods in integration with experimental techniques such as CCFS has the potential to transform the studies on flexible regions of proteins.     

Conformational dynamics of M2 helices in KirBac channels: helix flexibility in relation to gating via molecular dynamics simulations

KirBac1.1 and 3.1 are bacterial homologues of mammalian inward rectifier K channels. We have performed extended molecular dynamics simulations (five simulations, each of >20 ns duration) of the transmembrane domain of KirBac in two membrane environments, a palmitoyl oleoyl phosphatidylcholine bilayer and an octane slab. Analysis of these simulations has focused on the conformational dynamics of the pore-lining M2 helices, which form the cytoplasmic hydrophobic gate of the channel. Principal components analysis reveals bending of M2, with a molecular hinge at the conserved glycine (Gly134 in KirBac1.1, Gly120 in KirBac3.1). More detailed analysis reveals a dimer-of-dimers type motion. The first two eigenvectors describing the motions of M2 correspond to helix kink and swivel motions. The conformational flexibility of M2 seen in these simulations correlates with differences in M2 conformation between that seen in the X-ray structures of closed channels (KcsA and KirBac) in which the helix is undistorted, and in open channels (e.g. MthK) in which the M2 helix is kinked. Thus, the simulations, albeit on a time scale substantially shorter than that required for channel gating, suggest a gating model in which the intrinsic flexibility of M2 about a molecular hinge is coupled to conformational transitions of an intracellular 'gatekeeper' domain, the latter changing conformation in response to ligand binding.     

Comparison of X‐ray and NMR structures: Is there a systematic difference in residue contacts between X‐ray‐ and NMR‐resolved protein structures?

We have compared structures of 78 proteins determined by both NMR and X-ray methods. It is shown that X-ray and NMR structures of the same protein have more differences than various X-ray structures obtained for the protein, and even more than various NMR structures of the protein. X-ray and NMR structures of 18 of these 78 proteins have obvious large-scale structural differences that seem to reflect a difference of crystal and solution structures. The other 60 pairs of structures have only small-scale differences comparable with differences between various X-ray or various NMR structures of a protein; we have analyzed these structures more attentively. One of the main differences between NMR and X-ray structures concerns the number of contacts per residue: (1) NMR structures presented in PDB have more contacts than X-ray structures at distances below 3.0 A and 4.5-6.5 A, and fewer contacts at distances of 3.0-4.5 A and 6.5-8.0 A; (2) this difference in the number of contacts is greater for internal residues than for external ones, and it is larger for beta-containing proteins than for all-alpha proteins. Another significant difference is that the main-chain hydrogen bonds identified in X-ray and NMR structures often differ. Their correlation is 69% only. However, analogous difference is found for refined and rerefined NMR structures, allowing us to suggest that the observed difference in interresidue contacts of X-ray and NMR structures of the same proteins is due mainly to a difference in mathematical treatment of experimental results.     

Principal component and normal mode analysis of proteins; a quantitative comparison using the GroEL subunit

Principal component analysis (PCA) and normal mode analysis (NMA) have emerged as two invaluable tools for studying conformational changes in proteins. To compare these approaches for studying protein dynamics, we have used a subunit of the GroEL chaperone, whose dynamics is well characterized. We first show that both PCA on trajectories from molecular dynamics (MD) simulations and NMA reveal a general dynamical behavior in agreement with what has previously been described for GroEL. We thus compare the reproducibility of PCA on independent MD runs and subsequently investigate the influence of the length of the MD simulations. We show that there is a relatively poor one-to-one correspondence between eigenvectors obtained from two independent runs and conclude that caution should be taken when analyzing principal components individually. We also observe that increasing the simulation length does not improve the agreement with the experimental structural difference. In fact, relatively short MD simulations are sufficient for this purpose. We observe a rapid convergence of the eigenvectors (after ca. 6 ns). Although there is not always a clear one-to-one correspondence, there is a qualitatively good agreement between the movements described by the first five modes obtained with the three different approaches; PCA, all-atoms NMA, and coarse-grained NMA. It is particularly interesting to relate this to the computational cost of the three methods. The results we obtain on the GroEL subunit contribute to the generalization of robust and reproducible strategies for the study of protein dynamics, using either NMA or PCA of trajectories from MD simulations.     

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.