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.     

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.     

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   

Models with energy penalty on interresidue rotation address insufficiencies of conventional elastic network models

In this study, I present a new elastic network model, to our knowledge, that addresses insufficiencies of two conventional models—the Gaussian network model (GNM) and the anisotropic network model (ANM). It has been shown previously that the GNM is not rotation-invariant due to its energy, which penalizes rigid-body rotation (external rotation). As a result, GNM models are found contaminated with rigid-body rotation, especially in the most collective ones. A new model (EPIRM) is proposed to remove such external component in modes. The extracted internal motions result from a potential that penalizes interresidue stretching and rotation in a protein. The new model is shown to pertinently describe crystallographic temperature factors (B-factors) and protein open↔closed transitions. Also, the capability of separating internal and external motions in GNM slow modes permits reexamining important mechanochemical properties in enzyme active sites. The results suggest that catalytic residues stay closer to rigid-body rotation axes than their immediate backbone neighbors. I show that the cumulative density of states for EPIRM and ANM follow different power laws as functions of low-mode frequencies. When using a cutoff distance of 7.5 Å, The cumulative density of states of EPIRM scales faster than that of all-atom normal mode analysis and slower than that of simple lattices.     

Temperature‐induced unfolding behavior of proteins studied by tensorial elastic network model

Motivated by single molecule experiments and recent molecular dynamics (MD) studies, we propose a simple and computationally efficient method based on a tensorial elastic network model to investigate the unfolding pathways of proteins under temperature variation. The tensorial elastic network model, which relies on the native state topology of a protein, combines the anisotropic network model, the bond bending elasticity, and the backbone twist elasticity to successfully predicts both the isotropic and anisotropic fluctuations in a manner similar to the Gaussian network model and anisotropic network model. The unfolding process is modeled by breaking the native contacts between residues one by one, and by assuming a threshold value for strain fluctuation. Using this method, we simulated the unfolding processes of four well‐characterized proteins: chymotrypsin inhibitor, barnase, ubiquitein, and adenalyate kinase. We found that this step‐wise process leads to two or more cooperative, first‐order‐like transitions between partial denaturation states. The sequence of unfolding events obtained using this method is consistent with experimental and MD studies. The results also imply that the native topology of proteins “encrypts” information regarding their unfolding process. Proteins 2016; 84:1767–1775. © 2016 Wiley Periodicals, Inc.     

Coupling of structural fluctuations to deamidation reaction in triosephosphate isomerase by Gaussian network model

We study the structural fluctuations of triosephosphate isomerase (TIM) by an elastic model, namely, the Gaussian network model (GNM), to identify a network of coupled motions in the allosteric communication between its deamidation and catalytic sites, and the promoting motions for the deamidation activity. For this, three TIM structures have been studied: one crystal structure and two model structures designed to describe different putative models for the deamidation reaction taking place at the subunit interface. The structural fluctuations have been mapped on the functional properties; then the differences in the fluctuations between the two models in relation to the deamidation reaction have been considered. The results demonstrate that the qualitative picture of the mean-square fluctuations and the correlations between the fluctuations are similar in both, but the differences may affect the observed barrier height of the deamidation reaction. The higher packing density at regions close to deamidation sites, reflected by the high-frequency fluctuating residues in the respective regions, the stronger positive correlation between the fluctuations of the deamidation sites, and enhanced positive correlation of the primary deamidation site with the extended vicinity of the catalytic region on the juxtaposed unit promote the probability of the deamidation reaction. The results in general emphasize the importance of structural fluctuations in enzyme reactions, as well as proposing the present methodology as a plausible approach for studies on the network of coupled promoting motions in protein functions.     

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.

     

Collective dynamics of EcoRI-DNA complex by elastic network model and molecular dynamics simulations

Anisotropic network model (ANM) is used to analyze the collective motions of restriction enzyme EcoRI in free form and in complex with DNA. For comparison, three independent molecular dynamics (MD) simulations, each of 1.5 ns duration, are also performed for the EcoRI-DNA complex in explicit water. Although high mobility (equilibrium fluctuations) of inner and outer loops that surround the DNA is consistent in both methods and experiments, MD runs sample different conformational subspaces from which reliable collective dynamics cannot be extracted. However, ANM employed on different conformations from MD simulations indicates very similar collective motions. The stems of the inner loops are quite immobile even in the free enzyme and form a large, almost fixed, pocket for DNA binding. As a result, the residues that make specific and non-specific interactions with the DNA exhibit very low fluctuations in the free enzyme. The vibrational entropy difference between the EcoRI complex and free protein + unkinked DNA is positive (favorable), which may partially counteract the unfavorable enthalpy difference of DNA kink formation. Dynamic domains in EcoRI complex and cross-correlations between residue fluctuations indicate possible means of communication between the distal active sites.     

Identification of specificity and promiscuity of PDZ domain interactions through their dynamic behavior

PDZ domains (PDZs), the most common interaction domain proteins, play critical roles in many cellular processes. PDZs perform their job by binding specific protein partners. However, they are very promiscuous, binding to more than one protein, yet selective at the same time. We examined the binding related dynamics of various PDZs to have insight about their specificity and promiscuity. We used full atomic normal mode analysis and a modified coarse‐grained elastic network model to compute the binding related dynamics. In the latter model, we introduced specificity for each single parameter constant and included the solvation effect implicitly. The modified model, referred to as specific‐Gaussian Network Model (s‐GNM), highlights some interesting differences in the conformational changes of PDZs upon binding to Class I or Class II type peptides. By clustering the residue fluctuation profiles of PDZs, we have shown: (i) binding selectivities can be discriminated from their dynamics, and (ii) the dynamics of different structural regions play critical roles for Class I and Class II specificity. s‐GNM is further tested on a dual‐specific PDZ which showed only Class I specificity when a point mutation exists on the βA‐βB loop. We observe that the binding dynamics change consistently in the mutated and wild type structures. In addition, we found that the binding induced fluctuation profiles can be used to discriminate the binding selectivity of homolog structures. These results indicate that s‐GNM can be a powerful method to study the changes in binding selectivities for mutant or homolog PDZs. Proteins 2009. © 2009 Wiley‐Liss, Inc.     

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.     

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.     

The performance of fine‐grained and coarse‐grained elastic network models and its dependence on various factors

In a recent work we developed a method for deriving accurate simplified models that capture the essentials of conventional all‐atom NMA and identified two best simplified models: ssNMA and eANM, both of which have a significantly higher correlation with NMA in mean square fluctuation calculations than existing elastic network models such as ANM and ANMr2, a variant of ANM that uses the inverse of the squared separation distances as spring constants. Here, we examine closely how the performance of these elastic network models depends on various factors, namely, the presence of hydrogen atoms in the model, the quality of input structures, and the effect of crystal packing. The study reveals the strengths and limitations of these models. Our results indicate that ssNMA and eANM are the best fine‐grained elastic network models but their performance is sensitive to the quality of input structures. When the quality of input structures is poor, ANMr2 is a good alternative for computing mean‐square fluctuations while ANM model is a good alternative for obtaining normal modes. Proteins 2015; 83:1273–1283. © 2015 Wiley Periodicals, Inc.     

A comparative analysis of the equilibrium dynamics of a designed protein inferred from NMR,X‐ray,and computations

A detailed analysis of high‐resolution structural data and computationally predicted dynamics was carried out for a designed sugar‐binding protein. The mean‐square deviations in the positions of residues derived from nuclear magnetic resonance (NMR) models and those inferred from X‐ray crystallographic B‐factors for two different crystal forms were compared with the predictions based on the Gaussian Network Model (GNM) and the results from molecular dynamics (MD) simulations. GNM systematically yielded a higher correlation than MD, with experimental data, suggesting that the lack of atomistic details in the coarse‐grained GNM is more than compensated for by the mathematically exact evaluation of fluctuations using the native contacts topology. Evidence is provided that particular loop motions are curtailed by intermolecular contacts in the crystal environment causing a discrepancy between theory and experiments. Interestingly, the information conveyed by X‐ray crystallography becomes more consistent with NMR models and computational predictions when ensembles of X‐ray models are considered. Less precise (broadly distributed) ensembles indeed appear to describe the accessible conformational space under native state conditions better than B‐factors. Our results highlight the importance of using multiple conformations obtained by alternative experimental methods, and analyzing results from both coarse‐grained models and atomic simulations, for accurate assessment of motions accessible to proteins under native state conditions. Proteins 2009. © 2009 Wiley‐Liss, Inc.     

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)     

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.     

The effects of rigid motions on elastic network model force constants

Elastic network models provide an efficient way to quickly calculate protein global dynamics from experimentally determined structures. The model's single parameter, its force constant, determines the physical extent of equilibrium fluctuations. The values of force constants can be calculated by fitting to experimental data, but the results depend on the type of experimental data used. Here, we investigate the differences between calculated values of force constants and data from NMR and X-ray structures. We find that X-ray B factors carry the signature of rigid-body motions, to the extent that B factors can be almost entirely accounted for by rigid motions alone. When fitting to more refined anisotropic temperature factors, the contributions of rigid motions are significantly reduced, indicating that the large contribution of rigid motions to B factors is a result of over-fitting. No correlation is found between force constants fit to NMR data and those fit to X-ray data, possibly due to the inability of NMR data to accurately capture protein dynamics.