Dynamics of proteins predicted by molecular dynamics simulations and analytical approaches: application to alpha-amylase inhibitor

The dynamics of alpha-amylase inhibitors has been investigated using molecular dynamics (MD) simulations and two analytical approaches, the Gaussian network model (GNM) and anisotropic network model (ANM). MD simulations use a full atomic approach with empirical force fields, while the analytical approaches are based on a coarse-grained single-site-per-residue model with a single-parameter harmonic potential between sufficiently close (r 相似文献   

Escherichia coli adenylate kinase dynamics: comparison of elastic network model modes with mode-coupling (15)N-NMR relaxation data

The dynamics of adenylate kinase of Escherichia coli (AKeco) and its complex with the inhibitor AP(5)A, are characterized by correlating the theoretical results obtained with the Gaussian Network Model (GNM) and the anisotropic network model (ANM) with the order parameters and correlation times obtained with Slowly Relaxing Local Structure (SRLS) analysis of (15)N-NMR relaxation data. The AMPbd and LID domains of AKeco execute in solution large amplitude motions associated with the catalytic reaction Mg(+2)*ATP + AMP --> Mg(+2)*ADP + ADP. Two sets of correlation times and order parameters were determined by NMR/SRLS for AKeco, attributed to slow (nanoseconds) motions with correlation time tau( perpendicular) and low order parameters, and fast (picoseconds) motions with correlation time tau( parallel) and high order parameters. The structural connotation of these patterns is examined herein by subjecting AKeco and AKeco*AP(5)A to GNM analysis, which yields the dynamic spectrum in terms of slow and fast modes. The low/high NMR order parameters correlate with the slow/fast modes of the backbone elucidated with GNM. Likewise, tau( parallel) and tau( perpendicular) are associated with fast and slow GNM modes, respectively. Catalysis-related domain motion of AMPbd and LID in AKeco, occurring per NMR with correlation time tau( perpendicular), is associated with the first and second collective slow (global) GNM modes. The ANM-predicted deformations of the unliganded enzyme conform to the functional reconfiguration induced by ligand-binding, indicating the structural disposition (or potential) of the enzyme to bind its substrates. It is shown that NMR/SRLS and GNM/ANM analyses can be advantageously synthesized to provide insights into the molecular mechanisms that control biological function.     

Tensorial elastic network model for protein dynamics: Integration of the anisotropic network model with bond‐bending and twist elasticities

We present a tensorial elastic network model (TNM) to describe the equilibrium fluctuations of proteins near their native fold structure. The model combines the anisotropic network model (ANM), bond bending elasticity, and backbone twist elasticity, and can predict both the isotropic fluctuations, similar to the Gaussian network model (GNM), and anisotropic fluctuations, similar to the ANM. TNM performs equally well for B‐factor predictions as GNM and predicts the anisotropy of B‐factors better than ANM. The model also outperforms the ANM in its predictability of the complete anisotropic displacement parameters. Proteins 2012; © 2012 Wiley Periodicals, Inc.     

vGNM: a better model for understanding the dynamics of proteins in crystals

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 GNM, 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 important. 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.     

Generalized spring tensor models for protein fluctuation dynamics and conformation changes

Background

In the last decade, various coarse-grained elastic network models have been developed to study the large-scale motions of proteins and protein complexes where computer simulations using detailed all-atom models are not feasible. Among these models, the Gaussian Network Model (GNM) and Anisotropic Network Model (ANM) have been widely used. Both models have strengths and limitations. GNM can predict the relative magnitudes of protein fluctuations well, but due to its isotropy assumption, it can not be applied to predict the directions of the fluctuations. In contrast, ANM adds the ability to do the latter, but loses a significant amount of precision in the prediction of the magnitudes.

Results

In this article, we develop a single model, called generalized spring tensor model (STeM), that is able to predict well both the magnitudes and the directions of the fluctuations. Specifically, STeM performs equally well in B-factor predictions as GNM and has the ability to predict the directions of fluctuations as ANM. This is achieved by employing a physically more realistic potential, the Gō-like potential. The potential, which is more sophisticated than that of either GNM or ANM, though adds complexity to the derivation process of the Hessian matrix (which fortunately has been done once for all and the MATLAB code is freely available electronically at http://www.cs.iastate.edu/~gsong/STeM), causes virtually no performance slowdown.

Conclusions

Derived from a physically more realistic potential, STeM proves to be a natural solution in which advantages that used to exist in two separate models, namely GNM and ANM, are achieved in one single model. It thus lightens the burden to work with two separate models and to relate the modes of GNM with those of ANM at times. By examining the contributions of different interaction terms in the Gō potential to the fluctuation dynamics, STeM reveals, (i) a physical explanation for why the distance-dependent, inverse distance square (i.e., Open image in new window ) spring constants perform better than the uniform ones, and (ii), the importance of three-body and four-body interactions to properly modeling protein dynamics.

     

Global ribosome motions revealed with elastic network model

The motions of large systems such as the ribosome are not fully accessible with conventional molecular simulations. A coarse-grained, less-than-atomic-detail model such as the anisotropic network model (ANM) is a convenient informative tool to study the cooperative motions of the ribosome. The motions of the small 30S subunit, the larger 50S subunit, and the entire 70S assembly of the two subunits have been analyzed using ANM. The lowest frequency collective modes predicted by ANM show that the 50S subunit and 30S subunit are strongly anti-correlated in the motion of the 70S assembly. A ratchet-like motion is observed that corresponds well to the experimentally reported ratchet motion. Other slow modes are also examined because of their potential links to the translocation steps in the ribosome. We identify several modes that may facilitate the E-tRNA exiting from the assembly. The A-site t-RNA and P-site t-RNA are found to be strongly coupled and positively correlated in these slow modes, suggesting that the translocations of these two t-RNAs occur simultaneously, while the motions of the E-site t-RNA are less correlated, and thus less likely to occur simultaneously. Overall the t-RNAs exhibit relatively large deformations. Animations of these slow modes of motion can be viewed at.     

Network models reveal stability and structural rearrangement of signal recognition particle

The signal recognition particle (SRP) and its receptors (SR) mediate the cotranslational targeting of the membrane and secretory proteins in all cells. In Escherichia coli, SRP is composed of the Ffh protein and the 4.5S SRP RNA. Ffh is a multidomain protein comprising a methionine-rich (M) domain, a helical N domain, and a Ras-like guanine triphosphatase (GTPase) (G) domain. The N and G domains are commonly referred to as one structural unit, the NG domain. In this article, the complex structure of SRP and SR is investigated with the Gaussian network model (GNM) and anisotropic network model (ANM). GNM provides the information of structure stability. It is found that the intermolecular interactions between SRP and SR can obviously decrease the fluctuation of NG domains. Nevertheless, the large structural rearrangement will take place during the cotranslational protein targeting cycle. Hence, the moving directions of fluctuation regions are further ascertained by using cross-correlation analysis and the ANM. The NG domain of Ffh undergoes a clockwise rotation around the GM linker and the M domain of Ffh shows an opposite direction to the NG domain. These functional movements will facilitate the SRP structure to transform into the free form and the sequence-bound form. These simple coarse-grained analyses can be used as a general and quick method for the mechanism studies of protein assembly and supramolecular systems.     

Network models reveal stability and structural rearrangement of signal recognition particle

The signal recognition particle (SRP) and its receptors (SR) mediate the cotranslational targeting of the membrane and secretory proteins in all cells. In Escherichia coli, SRP is composed of the Ffh protein and the 4.5S SRP RNA. Ffh is a multidomain protein comprising a methionine-rich (M) domain, a helical N domain, and a Ras-like guanine triphosphatase (GTPase) (G) domain. The N and G domains are commonly referred to as one structural unit, the NG domain. In this article, the complex structure of SRP and SR is investigated with the Gaussian network model (GNM) and anisotropic network model (ANM). GNM provides the information of structure stability. It is found that the intermolecular interactions between SRP and SR can obviously decrease the fluctuation of NG domains. Nevertheless, the large structural rearrangement will take place during the cotranslational protein targeting cycle. Hence, the moving directions of fluctuation regions are further ascertained by using cross-correlation analysis and the ANM. The NG domain of Ffh undergoes a clockwise rotation around the GM linker and the M domain of Ffh shows an opposite direction to the NG domain. These functional movements will facilitate the SRP structure to transform into the free form and the sequence-bound form. These simple coarse-grained analyses can be used as a general and quick method for the mechanism studies of protein assembly and supramolecular systems.     

Insights into equilibrium dynamics of proteins from comparison of NMR and X-ray data with computational predictions

For a representative set of 64 nonhomologous proteins, each containing a structure solved by NMR and X-ray crystallography, we analyzed the variations in atomic coordinates between NMR models, the temperature (B) factors measured by X-ray crystallography, and the fluctuation dynamics predicted by the Gaussian network model (GNM). The NMR and X-ray data exhibited a correlation of 0.49. The GNM results, on the other hand, yielded a correlation of 0.59 with X-ray data and a distinctively better correlation (0.75) with NMR data. The higher correlation between GNM and NMR data, compared to that between GNM and X-ray B factors, is shown to arise from the differences in the spectrum of modes accessible in solution and in the crystal environment. Mainly, large-amplitude motions sampled in solution are restricted, if not inaccessible, in the crystalline environment of X-rays. Combined GNM and NMR analysis emerges as a useful tool for assessing protein dynamics.     

An analysis of the influence of protein intrinsic dynamical properties on its thermal unfolding behavior

The influence of the protein topology-encoded dynamical properties on its thermal unfolding motions was studied in the present work. The intrinsic dynamics of protein topology was obtained by the anisotropic network model (ANM). The ANM has been largely used to investigate protein collective functional motions, but it is not well elucidated if this model can also reveal the preferred large-scale motions during protein unfolding. A small protein barnase is used as a typical case study to explore the relationship between protein topology-encoded dynamics and its unfolding motions. Three thermal unfolding simulations at 500 K were performed for barnase and the entire unfolding trajectories were sampled and partitioned into several windows. For each window, the preferred unfolding motions were investigated by essential dynamics analysis, and then associated with the intrinsic dynamical properties of the starting conformation in this window, which is detected by ANM. The results show that only a few slow normal modes imposed by protein structure are sufficient to give a significant overlap with the preferred unfolding motions. Especially, the large amplitude unfolding movements, which imply that the protein jumps out of a local energy basin, can be well described by a single or several ANM slow modes. Besides the global motions, it is also found that the local residual fluctuations encoded in protein structure are highly correlated with those in the protein unfolding process. Furthermore, we also investigated the relationship between protein intrinsic flexibility and its unfolding events. The results show that the intrinsic flexible regions tend to unfold early. Several early unfolding events can be predicted by analysis of protein structural flexibility. These results imply that protein structure-encoded dynamical properties have significant influences on protein unfolding motions.     

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.     

Substrate Recognition and Motion Mode Analyses of PFV Integrase in Complex with Viral DNA via Coarse-Grained Models

HIV-1 integrase (IN) is an important target in the development of drugs against the AIDS virus. Drug design based on the structure of IN was markedly hampered due to the lack of three-dimensional structure information of HIV-1 IN-viral DNA complex. The prototype foamy virus (PFV) IN has a highly functional and structural homology with HIV-1 IN. Recently, the X-ray crystal complex structure of PFV IN with its cognate viral DNA has been obtained. In this study, both Gaussian network model (GNM) and anisotropy network model (ANM) have been applied to comparatively investigate the motion modes of PFV DNA-free and DNA-bound IN. The results show that the motion mode of PFV IN has only a slight change after binding with DNA. The motion of this enzyme is in favor of association with DNA, and the binding ability is determined by its intrinsic structural topology. Molecular docking experiments were performed to gain the binding modes of a series of diketo acid (DKA) inhibitors with PFV IN obtained from ANM, from which the dependability of PFV IN-DNA used in the drug screen for strand transfer (ST) inhibitors was confirmed. It is also found that the functional groups of keto-enol, bis-diketo, tetrazole and azido play a key role in aiding the recognition of viral DNA, and thus finally increase the inhibition capability for the corresponding DKA inhibitor. Our study provides some theoretical information and helps to design anti-AIDS drug based on the structure of IN.     

Anisotropic network model: systematic evaluation and a new web interface

MOTIVATION: The Anisotropic Network Model (ANM) is a simple yet powerful model for normal mode analysis of proteins. Despite its broad use for exploring biomolecular collective motions, ANM has not been systematically evaluated to date. A lack of a convenient interface has been an additional obstacle for easy usage. RESULTS: ANM has been evaluated on a large set of proteins to establish the optimal model parameters that achieve the highest correlation with experimental data and its limits of accuracy and applicability. Residue fluctuations in globular proteins are shown to be more accurately predicted than those in nonglobular proteins, and core residues are more accurately described than solvent-exposed ones. Significant improvement in agreement with experiments is observed with increase in the resolution of the examined structure. A new server for ANM calculations is presented, which offers flexible options for controlling model parameters and output formats, interactive animation of collective modes and advanced graphical features. AVAILABILITY: ANM server (http://www.ccbb.pitt.edu/anm)     

Dynamics of proteins in crystals: comparison of experiment with simple models

The dynamic behavior of proteins in crystals is examined by comparing theory and experiments. The Gaussian network model (GNM) and a simplified version of the crystallographic translation libration screw (TLS) model are used to calculate mean square fluctuations of C(alpha) atoms for a set of 113 proteins whose structures have been determined by x-ray crystallography. Correlation coefficients between the theoretical estimations and experiment are calculated and compared. The GNM method gives better correlation with experimental data than the rigid-body libration model and has the added benefit of being able to calculate correlations between the fluctuations of pairs of atoms. By incorporating the effect of neighboring molecules in the crystal the correlation is further improved.     

Large‐scale analysis of the dynamics of enzymes

Protein enzymes enable the cell to execute chemical reactions in short time by accelerating the rate of the reactions in a selective manner. The motions or dynamics of the enzymes are essential for their function. Comparison of the dynamics of a set of 1247 nonhomologous enzymes was performed. For each enzyme, the slowest modes of motion are calculated using the Gaussian network model (GNM) and they are globally aligned. Alignment is done using the dynamic programming algorithm of Needleman and Wunsch, commonly used for sequence alignment. Only 96 pairs of proteins were identified to have three similar GNM slow modes with 63 of them having a similar structure. The most frequent slowest mode of motion describes a two domains anticorrelated motion that characterizes at least 23% of the enzymes. Therefore, dynamics uniqueness cannot be accounted for by the slowest mode itself but rather by the combination of several slow modes. Different quaternary structure packing can restrain the motion of enzyme subunits differently and may serve as another mechanism that increases the dynamics uniqueness. Proteins 2013; 81:1910–1918. © 2013 Wiley Periodicals, Inc.     

Fluctuation dynamics analysis of gp120 envelope protein reveals a topologically based communication network

Human Immunodeficiency Virus (HIV) infection is initiated by binding of the viral glycoprotein gp120, to the cellular receptor CD4. On CD4 binding, gp120 undergoes conformational change, permitting binding to the chemokine receptor. Crystal structures of gp120 ternary complex reveal the CD4 bound conformation of gp120. We report here the application of the Gaussian network model (GNM) to the crystal structures of gp120 bound to CD4 or CD4 mimic and 17b, to study the collective motions of the gp120 core and determine the communication propensities of the residue network. The GNM fluctuation profiles identify residues in the inner domain and outer domain that may facilitate conformational change or stability, respectively. Communication propensities delineate a residue network that is topologically suited for signal propagation from the Phe43 cavity throughout the gp120 outer domain. These results provide a new context for interpreting gp120 core envelope structure–function relationships. Proteins 2010. © 2010 Wiley‐Liss, Inc.     

Evaluating elastic network models of crystalline biological molecules with temperature factors, correlated motions, and diffuse x-ray scattering

In this study, the variance-covariance matrix of protein motions is used to compare several elastic network models within the theoretical framework of x-ray scattering from crystals. A set of 33 ultra-high resolution structures is used to characterize the average scaling behavior of the vibrational density of states and make comparisons between experimental and theoretical temperature factors. Detailed investigations of the vibrational density of states, correlations, and predicted diffuse x-ray scatter are carried out for crystalline Staphylococcal nuclease; correlations and diffuse x-ray scatter are also compared to predictions from the translation, libration, screw model and a liquid-like dynamics model. We show that elastic network models developed to best predict temperature factors without regard for the crystal environment have relatively strong long-range interactions that yield very short-ranged atom-atom correlations. Further, we find that the low-frequency modes dominate the variance-covariance matrix only for those models with a physically reasonable vibrational density of states, and the fraction of modes required to converge the correlations is higher than that typically used for elastic network model studies. The practical implications are explored using computed diffuse x-ray scatter, which can be measured experimentally.