Insights into Equilibrium Dynamics of Proteins from Comparison of NMR and X-Ray Data with Computational Predictions (original) (raw)
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Solid-state NMR can provide atomic-resolution information about protein motions occurring on a vast range of time scales under similar conditions to those of Xray diffraction studies and therefore offers a highly complementary approach to characterizing the dynamic fluctuations occurring in the crystal. We compare experimentally determined dynamic parameters, spin relaxation, chemical shifts, and dipolar couplings, to values calculated from a 200 ns MD simulation of protein GB1 in its crystalline form, providing insight into the nature of structural dynamics occurring within the crystalline lattice. This simulation allows us to test the accuracy of commonly applied procedures for the interpretation of experimental solid-state relaxation data in terms of dynamic modes and time scales. We discover that the potential complexity of relaxationactive motion can lead to significant under-or overestimation of dynamic amplitudes if different components are not taken into consideration. SECTION: Biophysical Chemistry and Biomolecules
vGNM: A Better Model for Understanding the Dynamics of Proteins in Crystals
Journal of Molecular Biology, 2007
The dynamics of proteins are important for understanding their functions. In recent years, the simple coarse-grained Gaussian Network Model (GNM) has been fairly successful in interpreting crystallographic B-factors. However, the model clearly ignores the contribution of the rigid body motions and the effect of crystal packing. The model cannot explain the fact that the same protein may have significantly different B-factors under different crystal packing conditions. In this work, we propose a new Gaussian network model, called vGNM, which takes into account both the contribution of the rigid body motions and the effect of crystal packing, by allowing the amplitude of the internal modes to be variables. It hypothesizes that the effect of crystal packing should cause some modes to be amplified, and others to become less feasible. In doing so, vGNM is able to resolve the apparent discrepancy in experimental B-factors among structures of the same protein but with different crystal packing conditions, which GNM cannot explain. With a small number of parameters, vGNM is able to reproduce experimental B-factors for a large set of proteins with significantly better correlations (having a mean value of 0.81 as compared to 0.59 by GNM). The results of applying vGNM also show that the rigid body motions account for nearly 60% of the total fluctuations, in good agreement with previous findings.
Proteins: Structure, Function, and Bioinformatics, 2003
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 ␣, all , and ␣/. 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 NMRderived 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. Proteins 2003;53:111-120.
On the relationship between the protein structure and protein dynamics
Proteins-structure Function and Bioinformatics, 2008
Recently, we have developed a method (Shih et al., Proteins: Structure, Function, and Bioinformatics 2007;68: 34–38) to compute correlation of fluctuations of proteins. This method, referred to as the protein fixed-point (PFP) model, is based on the positional vectors of atoms issuing from the fixed point, which is the point of the least fluctuations in proteins. One corollary from this model is that atoms lying on the same shell centered at the fixed point will have the same thermal fluctuations. In practice, this model provides a convenient way to compute the average dynamical properties of proteins directly from the geometrical shapes of proteins without the need of any mechanical models, and hence no trajectory integration or sophisticated matrix operations are needed. As a result, it is more efficient than molecular dynamics simulation or normal mode analysis. Though in the previous study the PFP model has been successfully applied to a number of proteins of various folds, it is not clear to what extent this model will be applied. In this article, we have carried out the comprehensive analysis of the PFP model for a dataset comprising 972 high-resolution X-ray structures with pairwise sequence identity ≤25%. We found that in most cases the PFP model works well. However, in case of proteins comprising multiple domains, each domain should be treated separately as an independent dynamical module with its own fixed point; and in case of the protein complex comprising a number of subunits, if functioning as a biological unit, the whole complex should be considered as one single dynamical module with one fixed point. Under such considerations, the resultant correlation coefficient between the computed and the X-ray structural B-factors for the data set is 0.59 and 75% (727/972) of proteins with a correlation coefficient ≥0.5. Our result shows that the fixed-point model is indeed quite general and will be a useful tool for high throughput analysis of dynamical properties of proteins. Proteins 2008. © 2008 Wiley-Liss, Inc.
Optimization and Evaluation of a Coarse-Grained Model of Protein Motion Using X-Ray Crystal Data
Biophysical Journal, 2006
Simple coarse-grained models, such as the Gaussian network model, have been shown to capture some of the features of equilibrium protein dynamics. We extend this model by using atomic contacts to define residue interactions and introducing more than one interaction parameter between residues. We use B-factors from 98 ultra-high resolution (#1.0 Å) x-ray crystal structures to optimize the interaction parameters. The average correlation between Gaussian network-model fluctuation predictions and the B-factors is 0.64 for the data set, consistent with a previous large-scale study. By separating residue interactions into covalent and noncovalent, we achieve an average correlation of 0.74, and addition of ligands and cofactors further improves the correlation to 0.75. However, further separating the noncovalent interactions into nonpolar, polar, and mixed yields no significant improvement. The addition of simple chemical information results in better prediction quality without increasing the size of the coarse-grained model.
The Journal of Physical Chemistry A, 2006
15 N-1 H spin relaxation is a powerful method for deriving information on protein dynamics. The traditional method of data analysis is model-free (MF), where the global and local N-H motions are independent and the local geometry is simplified. The common MF analysis consists of fitting singlefield data. The results are typically field-dependent, and multi-field data cannot be fit with standard fitting schemes. Cases where known functional dynamics has not been detected by MF were identified by us and others. Recently we applied to spin relaxation in proteins the Slowly Relaxing Local Structure (SRLS) approach which accounts rigorously for mode-mixing and general features of local geometry. SRLS was shown to yield MF in appropriate asymptotic limits. We found that the experimental spectral density corresponds quite well to the SRLS spectral density. The MF formulae are often used outside of their validity ranges, allowing small data sets to be force-fitted with good statistics but inaccurate best-fit parameters. This paper focuses on the mechanism of force-fitting and its implications. It is shown that MF force-fits the experimental data because mode-mixing, the rhombic symmetry of the local ordering and general features of local geometry are not accounted for. Combined multi-field multi-temperature data analyzed by MF may lead to the detection of incorrect phenomena, while conformational entropy derived from MF order parameters may be highly inaccurate. On the other hand, fitting to more appropriate models can yield consistent physically insightful information. This requires that the complexity of the theoretical spectral densities matches the integrity of the experimental data. As shown herein, the SRLS densities comply with this requirement. Manuscript 22,25,37 We summarize below key aspects. The various reference frames, which define the SRLS model, and their relation to N-H sites in proteins, are shown in . A segment of the protein backbone comprising the atoms C α i , N i , HN i , C′ i-1 , O i-1 and C α i-1 , the equilibrium positions of which are traditionally taken to lie within the peptide plane defined by N i , HN i , C ′ i-1 and O i-1 , is illustrated in . The orientation of the N-H bond with respect to the magnetic field is modulated by its local motions and by the global motion of the protein. Thus, in the SRLS model we are dealing with at least two dynamic modes which we can represent by two bodies (N-H bond and protein) whose motions are coupled or mixed. For each motion two frames need to be introduced. The first is the local ordering/local diffusion frame, M, which is fixed in body 1 (in this case the N-H bond) and is usually determined by its geometric shape in the context of its motionally restricting environment. The second is the director frame, C′, whose axes represent the preferred orientation of the N-H bond and which is fixed within the protein framework. The motion of body 1 is coupled to, or mixed with, the motion of body 2 (in this case the protein) by a local coupling or orienting potential which seeks to bring the N-H bond into alignment with the director frame. There are no limitations on the relative rates of motion of the two bodies, or the symmetry and strength of the coupling potential.
Global Dynamics of Proteins: Bridging Between Structure and Function
Annual Review of Biophysics, 2010
Biomolecular systems possess unique, structure-encoded dynamic properties that underlie their biological functions. Recent studies indicate that these dynamic properties are determined to a large extent by the topology of native contacts. In recent years, elastic network models used in conjunction with normal mode analyses have proven to be useful for elucidating the collective dynamics intrinsically accessible under native state conditions, including in particular the global modes of motions that are robustly defined by the overall architecture. With increasing availability of structural data for well-studied proteins in different forms (liganded, complexed, or free), there is increasing evidence in support of the correspondence between functional changes in structures observed in experiments and the global motions predicted by these coarse-grained analyses. These observed correlations suggest that computational methods may be advantageously employed for assessing functional change...
Synergistic use of NMR and MD simulations to study the structural heterogeneity of proteins
Wiley Interdisciplinary Reviews: Computational Molecular Science, 2012
ABSTRACT Nuclear magnetic resonance spectroscopy (NMR) and molecular dynamics (MD) simulations are powerful techniques for the structural characterization of macromolecules. NMR is unique in its ability to provide experimental information at atomic level on the structure as well as on the amplitude and rate of structural fluctuations. MD provides physically sound models and potential mechanisms that connect conformations in time. Nevertheless, none of these techniques allow yet obtaining experimentally validated movies of protein motions at atomic resolution. Instead, it is their complementarity and synergy which offer a unique opportunity toward this end. Here, we overview recent examples that illustrate how much these two techniques benefit from each other, both passively and actively, for the characterization of the structural heterogeneity in proteins. © 2012 John Wiley & Sons, Ltd.