Gaussian Network Model Research Articles

Cooperativity in Thermal and Force-Induced Protein Unfolding: Integration of Crack Propagation and Network Elasticity Models

We investigate force-induced and temperature-induced unfolding of proteins using the combination of a gaussian network model and a crack propagation model based on "bond"-breaking independent events. We assume the existence of threshold values for the mean strain and strain fluctuations that dictate bond rupture. Surprisingly, we find that this stepwise process usually leads to a few cooperative, first-order-like, transitions in which several bonds break simultaneously, reminiscent of the "avalanches" seen in disordered networks.

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.

Coarse Grained Normal Mode Analysis vs. Refined Gaussian Network Model for Protein Residue-Level Structural Fluctuations

We investigate several approaches to coarse grained normal mode analysis on protein residual-level structural fluctuations by choosing different ways of representing the residues and the forces among them. Single-atom representations using the backbone atoms C(α), C, N, and C(β) are considered. Combinations of some of these atoms are also tested. The force constants between the representative atoms are extracted from the Hessian matrix of the energy function and served as the force constants between the corresponding residues. The residue mean-square-fluctuations and their correlations with the experimental B-factors are calculated for a large set of proteins. The results are compared with all-atom normal mode analysis and the residue-level Gaussian Network Model. The coarse-grained methods perform more efficiently than all-atom normal mode analysis, while their B-factor correlations are also higher. Their B-factor correlations are comparable with those estimated by the Gaussian Network Model and in many cases better. The extracted force constants are surveyed for different pairs of residues with different numbers of separation residues in sequence. The statistical averages are used to build a refined Gaussian Network Model, which is able to predict residue-level structural fluctuations significantly better than the conventional Gaussian Network Model in many test cases.

Insights Into The Working Mechanism and Unfolding Property of Arthrobacter chlorophenolicus Amylosucrase

Amylosucrase (AS) is a kind of glucosyltransferase (B.C. 2.4.1.4) belonging to the glycoside hydrolase (GH) family 13. In the presence of an activator polymer, in vitro, AS is able to catalyze the synthesis of an amylose-like polysaccharide composed of only alpha-1,4-linkages using sucrose as the only energy source. Unlike AS, other enzymes responsible for the synthesis of such amylose-like polymers require the addition of expensive nucleotide-activated sugars. These properties make AS an interesting enzyme for industrial applications. In spite of the great application potential, industrial applications of AS were largely hampered by its low stability. In this work, the structure of Arthrobacter chlorophenolicus amylosucrase (AcAS) was modeled according to crystal structures of Neisseria polysaccharea amylosucrase (NpAS) and Deinococcus geothermalis amylosucrase (DgAS). The structural difference of the three AS were investigated for the sake of exploring the working mechanism of AcAS. The dynamics and functional motions of AcAS were also investigated by the Gaussian network model (GNM). Based on GNM, it was found that AcAS can be divided into two regions with different moving directions. Finally, the unfolding property of AcAS was studied by the iterative GNM, and several kinetically weak regions were identified on the basis of the predicted unfolding pathway. These discoveries may be helpful to the industrial development of AS.

Detailed Conformational Changes Involved in TopoII DNA Binding, Bending and Cleavage

We have used Molecular Dynamics (MD) simulation methods and two analytical approaches(the Gaussian Net- work Model(GNM) and Anisotropic Network Model (ANM)) to investigate the structural and energetic details of the S.cerevisiae topoII during the first step of its catalytic cycle. At the initial state of the first step of its catalytic cycle, the protein and 34 bp straight-DNA structure have no interaction. At the final state of the cycle, we have the bended-DNA/TopoII complex where the protein binds to DNA. The results show that DNA-gate and C-gate opening/closing mechanism causes the DNA-bending before the DNA G- gate cleavage. There is strong agreement between the theoratical and the experimental DNA-bending results where its global bending is ≈ 150∧0.The results also show that there is a hysteresis between DNA-bending and gate openings/closings. The transition of 3 helices on Winked Helix Domain during DNA bending and cleavage states has been also investigated because this transition might be important for the T-segment DNA passage through the G-Segment DNA. Normal mode analysis is ad- ditionally used to characterize the functional flexibity of the protein,especially C-gate domain closing/opening during the DNA binding process and before its cleavage.The Plastic Network Model(PNM) is also used to generate a conformational change pathway for S.cerevisiae topoII based on two (C-gate closed and open) crystal structures. PNM connects the energy basins corresponding to known two crystal structures at their lowest common energies. Analysis of PNM provides an identification of hinge motion upon DNA binding/bending. We also showed that ’trapdoor’ mechanism causes faster closing of C-gate domain of the protein than the closing of the same domain without TYR residue upward motion. Because of its clinical importance, our study may provide new insight into the dynamics and structure of TopoII-DNA complex.

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.

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.

Structural features that predict real‐value fluctuations of globular proteins

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

Dynamics alignment: Comparison of protein dynamics in the scop database

A novel methodology for comparison of protein dynamics is presented. Protein dynamics is calculated using the Gaussian network model and the modes of motion are globally aligned using the dynamic programming algorithm of Needleman and Wunsch, commonly used for sequence alignment. The alignment is fast and can be used to analyze large sets of proteins. The methodology is applied to the four major classes of the SCOP database: "all alpha proteins," "all beta proteins," "alpha and beta proteins," and "alpha/beta proteins". We show that different domains may have similar global dynamics. In addition, we report that the dynamics of "all alpha proteins" domains are less specific to structural variations within a given fold or superfamily compared with the other classes. We report that domain pairs with the most similar and the least similar global dynamics tend to be of similar length. The significance of the methodology is that it suggests a new and efficient way of mapping between the global structural features of protein families/subfamilies and their encoded dynamics.

A Large-Scale Comparison of Computational Models on the Residue Flexibility for NMR-derived Proteins

As an alternative to X-ray crystallography, nuclear magnetic resonance (NMR) has also emerged as the method of choice for studying both protein structure and dynamics in solution. However, little work using computational models such as Gaussian network model (GNM) and machine learning approaches has focused on NMR-derived proteins to predict the residue flexibility, which is represented by the root mean square deviation (RMSD) with respect to the average structure. We provide a large-scale comparison of computational models, including GNM, parameter-free GNM and several linear regression models using local solvent exposures as inputs, based on a dataset of 1609 protein chains whose structures were resolved by NMR. The result again confirmed that the correlation of GNM outputs with raw RMSD values was better than that using B-factors of X-ray data. Nevertheless, it was also concluded that the parameter-free GNM and the solvent exposure based linear regression models performed worse than GNM when predicting RMSD, contrary to results using X-ray data. The discrepancy of residue flexibility prediction between NMR and X-ray data is likely attributable to a combination of their physical and methodological differences.

Dynamic structure factor of vibrating fractals: Proteins as a case study

We study the dynamic structure factor S(k,t) of proteins at large wave numbers k, kR(g)≫1, where R(g) is the gyration radius. At this regime measurements are sensitive to internal dynamics, and we focus on vibrational dynamics of folded proteins. Exploiting the analogy between proteins and fractals, we perform a general analytic calculation of the displacement two-point correlation functions, <[u(−>)(i)(t)-u(−>)(j)(0)](2)>. We confront the derived expressions with numerical evaluations that are based on protein data bank (PDB) structures and the Gaussian network model (GNM) for a few proteins and for the Sierpinski gasket as a controlled check. We use these calculations to evaluate S(k,t) with arrested rotational and translational degrees of freedom, and show that the decay of S(k,t) is dominated by the spatially averaged mean-square displacement of an amino acid. The latter has been previously shown to evolve subdiffusively in time, <[u(−>)(i)(t)-u(−>)(i)(0)](2)> ~t(ν), where ν is the anomalous diffusion exponent that depends on the spectral dimension d(s) and fractal dimension d(f). As a result, for wave numbers obeying k(2)<u(−>)(2)>≳1, S(k,t) effectively decays as a stretched exponential S(k,t)≃S(k)e(-(Γ(k)t)(β)) with β≃ν, where the relaxation rate is Γ(k)~(k(B)T/mω(o)(2))(1/β)k(2/β), T is the temperature, and mω(o)(2) the GNM effective spring constant describing the interaction between neighboring amino acids. The static structure factor is dominated by the fractal character of the native fold, S(k)~k(-d(f)), with negligible to marginal influence of vibrations. The analytical expressions are first confronted with numerically based calculations on the Sierpinski gasket, and very good agreement is found between simulations and theory. We then perform PDB-GNM-based numerical calculations for a few proteins, and an effective stretched exponential decay of the dynamic structure factor is found, albeit their relatively small size. However, when rotational and translational diffusion are added, we find that their contribution is never negligible due to finite size effects. While we can still attribute an effective stretching exponent β to the relaxation profile, this exponent is significantly larger than the anomalous diffusion exponent ν. We compare our theory with recent neutron spin-echo studies of myoglobin and hemoglobin and conclude that experiments in which the rotational and translational degrees of freedom are arrested, e.g., by anchoring the proteins to a surface, will improve the detection of internal vibrational dynamics.

Prion Protein Motion Modes Analysis with Gaussian Network Model

Prion diseases are fatal neurodegenerative disorders caused by an aberrant accumulation of the misfolded cellular prion protein (PrPC) conformer, denoted as infectious scrapie isoform (PrPSc). The slow and fast motion models of huPrP and huPrP (E200K) structures were analyzed with the GNM in this paper. It can be seen that the largest fluctuation values corresponding to the helix 1. Residue 147 and residue 150 play an important role in the stability of the helix 1. The major consequence of the E200K substitution appears to be the redistribution of surface charges, resulting in an altered electrostatic potential in the mutant protein. This change is likely to affect the stability of the helix 1. Thus, their behavior might reflect that of wild-type PrP or that of mutants associated with transmissible forms of the disease.

The redundancy of NMR restraints can be used to accelerate the unfolding behavior of an SH3 domain during molecular dynamics simulations

1 BackgroundThe simulation of protein unfolding usually requires recording long molecular dynamics trajectories. The present work aims to figure out whether NMR restraints data can be used to probe protein conformations in order to accelerate the unfolding simulation. The SH3 domain of nephrocystine (nph SH3) was shown by NMR to be destabilized by point mutations, and was thus chosen to illustrate the proposed method.ResultsThe NMR restraints observed on the WT nph SH3 domain were sorted from the least redundant to the most redundant ones. Protein NMR conformations were then calculated with: (i) the set full including all NMR restraints measured on nph SH3, (ii) the set reduced where the least redundant restraints with respect to the set full were removed, (iii) the sets random where randomly picked-up restraints were removed. From each set of conformations, we recorded series of 5-ns MD trajectories. The β barrel architecture of nph SH3 in the trajectories starting from sets (i) and (iii) appears to be stable. On the contrary, on trajectories based on the set (ii), a displacement of the hydrophobic core residues and a variation of the β barrel inner cavity profile were observed. The overall nph SH3 destabilization agrees with previous experimental and simulation observations made on other SH3 domains. The destabilizing effect of mutations was also found to be enhanced by the removal of the least redundant restraints.ConclusionsWe conclude that the NMR restraint redundancy is connected to the instability of the SH3 nph domain. This restraint redundancy generalizes the contact order parameter, which is calculated from the contact map of a folded protein and was shown in the literature to be correlated to the protein folding rate. The relationship between the NMR restraint redundancy and the protein folding is also reminiscent of the previous use of the Gaussian Network Model to predict protein folding parameters.

Cooperative dynamics of proteins unraveled by network models.

Recent years have seen a significant increase in the number of computational studies that adopted network models for investigating biomolecular systems dynamics and interactions. In particular, elastic network models have proven useful in elucidating the dynamics and allosteric signaling mechanisms of proteins and their complexes. Here we present an overview of two most widely used elastic network models, the Gaussian Network Model (GNM) and Anisotropic Network Model (ANM). We illustrate their use in (i) explaining the anisotropic response of proteins observed in external pulling experiments, (ii) identifying residues that possess high allosteric potentials, and demonstrating in this context the propensity of catalytic sites and metal-binding sites for enabling efficient signal transduction, and (iii) assisting in structure refinement, molecular replacement and comparative modeling of ligand-bound forms via efficient sampling of energetically favored conformers.

ATP Binding Enables Broad Antibiotic Selectivity of Aminoglycoside Phosphotransferase(3′)-IIIa: An Elastic Network Analysis

The bacterial enzyme aminoglycoside phosphotransferase(3′)-IIIa (APH) confers resistance against a wide range of aminoglycoside antibiotics. In this study, we use the Gaussian network model to investigate how the binding of nucleotides and antibiotics influences the dynamics and thereby the ligand binding properties of APH. Interestingly, in NMR experiments, the dynamics differ significantly in various APH complexes, although crystallographic studies indicate that no larger conformational changes occur upon ligand binding. Isothermal titration calorimetry also shows different thermodynamic contributions to ligand binding. Formation of aminoglycoside–APH complexes is enthalpically driven, while the enthalpic change upon aminoglycoside binding to the nucleotide–APH complex is much smaller. The differential effects of nucleotide binding and antibiotic binding to APH can be explained theoretically by single-residue fluctuations and correlated motions of the enzyme. The surprising destabilization of β-sheet residues upon nucleotide binding, as seen in hydrogen/deuterium exchange experiments, shows that the number of closest neighbors does not fully explain residue flexibility. Additionally, we must consider correlated motions of dynamic protein domains, which show that not only connectivity but also the overall protein architecture is important for protein dynamics.

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.

Vectorial Network Model (VNM) for Protein Dynamics: An Analytical Tool for Protein Fluctuations

Dynamics play important roles in how proteins function. Coarse grained network model such as Gaussian Network Model (GNM) and Anisotropic Network Model (ANM) are widely used for studying dynamic changes of proteins. It provides an analytical treatment of different eigen modes of protein fluctuations based on the Gaussian assumption. However, GNM and ANM have limitations. For example, detailed mode analysis needed in these models often requires additional ad hoc knowledge for model selection. ANM can only describe mode specific relative movement between residues.

Binding of Isoflurane to Glic Alters the Structure and Dynamics of the Protein

General anesthetics are thought to interact with proteins to produce anesthesia. Most of the experimental efforts to date have been focused on searching for discrete anesthetic binding sites. How exactly anesthetics work after the events of anesthetic binding is rarely explored. With the recent availability of two crystal structures for the bacterial Gloeobacter violaceus pentameric ligand-gated ion channel (GLIC), which is sensitive to a variety of general anesthetics, we performed multiple replica molecular dynamics simulations for more than 100 ns with and without the general anesthetic isoflurane. Multiple sites within the protein, primarily in the extracellular domain and at the interface of extracellular and transmembrane domains, provided favorable binding environments for isoflurane, showing little isoflurane translational displacement over the course of the simulations. Isoflurane caused changes to the structure and dynamics of GLIC when compared to the control simulation. Subunit-subunit interactions in the extracellular domain of the pentamer were disrupted, resulting in increased flexibility of the subunit pairs, as measured by Gaussian network model analysis. Salt-bridge linkages between and within the extracellular region of subunits containing isoflurane binding sites were altered by the presence of isoflurane, reflecting a change in the tertiary and quaternary structure of the channel. Changes were not isolated to the extracellular domain. The subunits containing more isoflurane binding sites also showed a greater change in tilt angle of the second transmembrane helices. Taken together, anesthetic binding at subunit interfaces can lead to changes in quaternary structure and global dynamics, causing allosteric changes in channel motional characteristics critical to gating. Supported by the NIH (R01GM56257, R01GM66358, R37GM049202, and T32GM075770), and the NSF through TeraGrid resources provided by PSC, NICS and TACC (TG-MCB050030N).

Hierarchical Elastic Network Modeling of cryo-EM Data

Cryo-EM images of molecules are increasing in resolution, extending their uses from rigid-body docking to generation of atomistic density maps independent of prior structural information. Single molecule cryo-EM provides images of a molecule from many viewpoints, which are averaged and compiled to form a 3D reconstruction. This reconstruction determines the smallest possible hull enclosing the molecule, but sacrifices information about dynamic properties of the molecule intrinsically contained in the varied image set.We suggest projecting the images into 3D space, without averaging out inconsistent densities, to form a probability map for the reconstruction. This map contains flexibility information neglected by earlier analyses of dynamics from density maps. To highlight different levels of molecular flexibility found in this map, we use a hierarchical elastic network model (hENM). The hENM uses the Markov transition probabilities between the voxels in the density map to segment the map into sets of multi-resolution nodes. Each voxel is initially taken as a node in the network, after-which the network is iteratively reduced to increasingly coarser sets of important nodes, forming a hierarchy. This method provides a unifying framework in allowing the derivation of dynamics concurrently with the study of information propagation through the network, with segmentation of the protein into structural sub-regions as an additional benefit. As these nodes highlight the core structural regions of the protein, they can also be used as anchor points for fitting high-resolution structures into EM maps. Preliminary results show excellent overlap between the dynamics computed using a Gaussian Network Model of the C-alpha atoms of proteins and those computed from our hENM nodes, validating the role of hENM in predicting intrinsic protein motions. With the greater goal of inferring function from dynamics, we work here to predict dynamics directly from cryo-EM images.

Identification of Ligand Binding Sites of Proteins Using the Gaussian Network Model

The nonlocal nature of the protein-ligand binding problem is investigated via the Gaussian Network Model with which the residues lying along interaction pathways in a protein and the residues at the binding site are predicted. The predictions of the binding site residues are verified by using several benchmark systems where the topology of the unbound protein and the bound protein-ligand complex are known. Predictions are made on the unbound protein. Agreement of results with the bound complexes indicates that the information for binding resides in the unbound protein. Cliques that consist of three or more residues that are far apart along the primary structure but are in contact in the folded structure are shown to be important determinants of the binding problem. Comparison with known structures shows that the predictive capability of the method is significant.