Comparison of full-atomic and coarse-grained models to examine the molecular fluctuations of c-AMP dependent protein kinase

Molecular fluctuations of the native conformation of c-AMP dependent protein kinase (cAPK) have been investigated with three different approaches. The first approach is the full atomic normal mode analysis (NMA) with empirical force fields. The second and third approaches are based on a coarse-grained model with a single single-parameter- harmonic potential between close residues in the crystal structure of the molecule without any residue specificity. The second method calculates only the magnitude of fluctuations whereas the third method is developed to find the directionality of the fluctuations which are essential to understand the functional importance of biological molecules. The aim, in this study, is to determine whether using such coarse-grained models are appropriate for elucidating the global dynamic characteristics of large proteins which reduces the size of the system at least by a factor of ten. The mean-square fluctuations of C(alpha) atoms and the residue cross-correlations are obtained by three approaches. These results are then compared to test the results of coarse grained models on the overall collective motions. All three of the approaches show that highly flexible regions correspond to the activation and solvent exposed loops, whereas the conserved residues (especially in substrate binding regions) exhibit almost no flexibility, adding stability to the structure. The anti-correlated motions of the two lobes of the catalytic core provide flexibility to the molecule. High similarities among the results of these methods indicate that the slowest modes governing the most global motions are preserved in the coarse grained models for proteins. This finding may suggest that the general shapes of the structures are representative of their dynamic characteristics and the dominant motions of protein structures are robust at coarse-grained levels.     

Free energies for coarse-grained proteins by integrating multibody statistical contact potentials with entropies from elastic network models

We propose a novel method of calculation of free energy for coarse grained models of proteins by combining our newly developed multibody potentials with entropies computed from elastic network models of proteins. Multi-body potentials have been of much interest recently because they take into account three dimensional interactions related to residue packing and capture the cooperativity of these interactions in protein structures. Combining four-body non-sequential, four-body sequential and pairwise short range potentials with optimized weights for each term, our coarse-grained potential improved recognition of native structure among misfolded decoys, outperforming all other contact potentials for CASP8 decoy sets and performance comparable to the fully atomic empirical DFIRE potentials. By combing statistical contact potentials with entropies from elastic network models of the same structures we can compute free energy changes and improve coarse-grained modeling of protein structure and dynamics. The consideration of protein flexibility and dynamics should improve protein structure prediction and refinement of computational models. This work is the first to combine coarse-grained multibody potentials with an entropic model that takes into account contributions of the entire structure, investigating native-like decoy selection.     

Altered dynamics upon oligomerization corresponds to key functional sites

It is known that over half of the proteins encoded by most organisms function as oligomeric complexes. Oligomerization confers structural stability and dynamics changes in proteins. We investigate the effects of oligomerization on protein dynamics and its functional significance for a set of 145 multimeric proteins. Using coarse‐grained elastic network models, we inspect the changes in residue fluctuations upon oligomerization and then compare with residue conservation scores to identify the functional significance of these changes. Our study reveals conservation of about ½ of the fluctuations, with ¼ of the residues increasing in their mobilities and ¼ having reduced fluctuations. The residues with dampened fluctuations are evolutionarily more conserved and can serve as orthosteric binding sites, indicating their importance. We also use triosephosphate isomerase as a test case to understand why certain enzymes function only in their oligomeric forms despite the monomer including all required catalytic residues. To this end, we compare the residue communities (groups of residues which are highly correlated in their fluctuations) in the monomeric and dimeric forms of the enzyme. We observe significant changes to the dynamical community architecture of the catalytic core of this enzyme. This relates to its functional mechanism and is seen only in the oligomeric form of the protein, answering why proteins are oligomeric structures. Proteins 2017; 85:1422–1434. © 2017 Wiley Periodicals, Inc.     

Dynamical structure of transfer RNA studied by normal mode analysis

The internal motion of yeast phenylalanine transfer RNA is studied by normal mode analysis in extended dihedral angle space, in which the flexibility of five-membered ribose rings is treated faithfully by introducing a variable for its pseudo-rotational motion. Analysis of global molecular motions reveals that the molecule is very soft. We show that this softness comes not from the property of the “material” comprising the molecule but from its slender shape. Analysis of thermal distance fluctuations reveals that this molecule can be regarded as consisting dynamically of three blocks. Thermal fluctuations of the mainchain dihedral angles show rigidity of the anticodon region. They also show flexibility of regions around nonstacking bases. Base-stacking interactions cause suppression of the correlated functions of mainchain dihedral angles beyond a ribose ring. We analyze the thermal fluctuation of parameters describing the positions of two adjacent bases. Fluctuations of relative translational parameters in the anticodon and acceptor stem regions are found to be larger than those in other stem regions. The relative translational motions cause the two stem regions to undergo global twisting and bending motions. We show that the role of pseudo-rotational motion of sugars is important in regions around bases which are involved in nonregular interactions. Received: 29 October 1998 / Revised version: 8 February 1999 / Accepted: 11 February 1999     

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.     

Deoxymyoglobin studied by the conformational normal mode analysis. I. Dynamics of globin and the heme-globin interaction

Dynamic properties of deoxymyoglobin are studied theoretically by the analysis of conformational fluctuations. Root-mean-square atomic fluctuations and distance fluctuations between different segments reveal the mechanical construction of the molecule. Eight alpha-helices behave as relatively rigid bodies and corner regions are more flexible, showing larger fluctuations. More particularly, corner regions EF and GH are specific in that flanking alpha-helices extend their rigidity up to a point in the corner region and the two rigid segments are connected flexibly at that point. The FG corner is exceptional. A segment from the F helix to the beginning of the G helix, in which the FG corner is included, becomes relatively rigid by means of strong interactions with the heme group. The whole myoglobin molecule is divided into two large units of motion, one extending from the B to the E helix, and the other from the F to the H helix. These two units are connected covalently by the EF corner. However, dynamic interactions between these two units take place mainly through contacts between helices B and G and not through the EF corner. From correlation coefficients between fluctuational motions of residues and the heme group, 55 residues are identified as having strong dynamic interactions with the heme moiety. Among them, 18 residues in the three segments, one consisting of residues from the C helix to the CD corner, a second consisting of the E helix, and a third from the F helix to the beginning of the G helix, are in close contact with the heme group. Twenty-two of the 55 residues are within four residues of the 18 residues in their sequential residue number and are more than 3 A away from the heme group. The other 15 residues are located further in the sequential residue number and are all found in helices A and H. They are more than 6 A away from the heme group. By the use of correlation coefficients of fluctuations between residues, it is found that dynamic interaction with the heme group is transmitted to the A helix and the beginning of the H helix in the direction Leu(E15)----[Val(All) and Trp(A12)]. The transmission to the C-terminal end of the H helix is mediated by a long segment, from the end of the EF corner to the beginning of the G helix, that lies on the heme group and has close contacts over a wide range.(ABSTRACT TRUNCATED AT 400 WORDS)     

Functional motions of influenza virus hemagglutinin: a structure-based analytical approach.

Influenza virus hemagglutinin (HA), a homotrimeric integral membrane glycoprotein essential for viral infection, is engaged in two biological functions: recognition of target cells' receptor proteins and fusion of viral and endosomal membranes, both requiring substantial conformational flexibility from the part of the glycoprotein. The different modes of collective motions underlying the functional mobility/adaptability of the protein are determined in the present study using an extension of the Gaussian network model (GNM) to treat concerted anisotropic motions. We determine the molecular mechanisms that may underlie HA function, along with the structural regions or residues whose mutations are expected to impede function. Good agreement between theoretically predicted fluctuations of individual residues and corresponding x-ray crystallographic temperature factors is found, which lends support to the GNM elucidation of the conformational dynamics of HA by focusing upon a subset of dominant modes. The lowest frequency mode indicates a global torsion of the HA trimer about its longitudinal axis, accompanied by a substantial mobility at the viral membrane connection. This mode is proposed to constitute the dominant molecular mechanism for the translocation and aggregation of HAs, and for the opening and dilation of the fusion pore. The second and third collective modes indicate a global bending, allowing for a large lateral surface exposure, which is likely to facilitate the close association of the viral and endosomal membranes before pore opening. The analysis of kinetically hot residues, in contrast, reveals a localization of energy centered around the HA2 residue Asp112, which apparently triggers the solvent exposure of the fusion peptide.     

Relating molecular flexibility to function: a case study of tubulin

Microtubules (MT), along with a variety of associated motor proteins, are involved in a range of cellular functions including vesicle movement, chromosome segregation, and cell motility. MTs are assemblies of heterodimeric proteins, alpha beta-tubulins, the structure of which has been determined by electron crystallography of zinc-induced, pacilitaxel-stabilized tubulin sheets. These data provide a basis for examining relationships between structural features and protein function. Here, we study the fluctuation dynamics of the tubulin dimer with the aim of elucidating its functional motions relevant to substrate binding, polymerization/depolymerization and MT assembly. A coarse-grained model, harmonically constrained according to the crystal structure, is used to explore the global dynamics of the dimer. Our results identify six regions of collective motion, comprised of structurally close but discontinuous sequence fragments, observed only in the dimeric form, dimerization being a prerequisite for domain identification. Boundaries between regions of collective motions appear to act as linkages, found primarily within secondary-structure elements that lack sequence conservation, but are located at minima in the fluctuation curve, at positions of hydrophobic residues. Residue fluctuations within these domains identify the most mobile regions as loops involved in recognition of the adjacent regions. The least mobile regions are associated with nucleotide binding sites where lethal mutations occur. The functional coupling of motions between and within regions identifies three global motions: torsional and wobbling movements, en bloc, between the alpha- and beta-tubulin monomers, and stretching longitudinally. Further analysis finds the antitumor drug pacilitaxel (TaxotereR) to reduce flexibility in the M loop of the beta-tubulin monomer; an effect that may contribute to tightening lateral interactions between protofilaments assembled into MTs. Our analysis provides insights into relationships between intramolecular tubulin movements of MT organization and function.     

Predicting order of conformational changes during protein conformational transitions using an interpolated elastic network model

The decryption of sequence of structural events during protein conformational transitions is essential to a detailed understanding of molecular functions ofvarious biological nanomachines. Coarse‐grained models have proven useful by allowing highly efficient simulations of protein conformational dynamics. By combining two coarse‐grained elastic network models constructed based on the beginning and end conformations of a transition, we have developed an interpolated elastic network model to generate a transition pathway between the two protein conformations. For validation, we have predicted the order of local and global conformational changes during key ATP‐driven transitions in three important biological nanomachines (myosin, F₁ ATPase and chaperonin GroEL). We have found that the local conformational change associated with the closing of active site precedes the global conformational change leading to mechanical motions. Our finding is in good agreement with the distribution of intermediate experimental structures, and it supports the importance of local motions at active site to drive or gate various conformational transitions underlying the workings of a diverse range of biological nanomachines. Proteins 2010. © 2010 Wiley‐Liss, Inc.     

Improving ranking of models for protein complexes with side chain modeling and atomic potentials

An atomically detailed potential for docking pairs of proteins is derived using mathematical programming. A refinement algorithm that builds atomically detailed models of the complex and combines coarse grained and atomic scoring is introduced. The refinement step consists of remodeling the interface side chains of the top scoring decoys from rigid docking followed by a short energy minimization. The refined models are then re‐ranked using a combination of coarse grained and atomic potentials. The docking algorithm including the refinement and re‐ranking, is compared favorably to other leading docking packages like ZDOCK, Cluspro, and PATCHDOCK, on the ZLAB 3.0 Benchmark and a test set of 30 novel complexes. A detailed analysis shows that coarse grained potentials perform better than atomic potentials for realistic unbound docking (where the exact structures of the individual bound proteins are unknown), probably because atomic potentials are more sensitive to local errors. Nevertheless, the atomic potential captures a different signal from the residue potential and as a result a combination of the two scores provides a significantly better prediction than each of the approaches alone. Proteins 2013. © 2012 Wiley Periodicals, Inc.     

Wiggle—Predicting Functionally Flexible Regions from Primary Sequence

The Wiggle series are support vector machine–based predictors that identify regions of functional flexibility using only protein sequence information. Functionally flexible regions are defined as regions that can adopt different conformational states and are assumed to be necessary for bioactivity. Many advances have been made in understanding the relationship between protein sequence and structure. This work contributes to those efforts by making strides to understand the relationship between protein sequence and flexibility. A coarse-grained protein dynamic modeling approach was used to generate the dataset required for support vector machine training. We define our regions of interest based on the participation of residues in correlated large-scale fluctuations. Even with this structure-based approach to computationally define regions of functional flexibility, predictors successfully extract sequence-flexibility relationships that have been experimentally confirmed to be functionally important. Thus, a sequence-based tool to identify flexible regions important for protein function has been created. The ability to identify functional flexibility using a sequence based approach complements structure-based definitions and will be especially useful for the large majority of proteins with unknown structures. The methodology offers promise to identify structural genomics targets amenable to crystallization and the possibility to engineer more flexible or rigid regions within proteins to modify their bioactivity.     

All‐atom and coarse‐grained simulations of the forced unfolding pathways of the SNARE complex

The SNARE complex, consisting of three proteins (VAMP2, syntaxin, and SNAP‐25), is thought to drive membrane fusion by assembling into a four‐helix bundle through a zippering process. In support of the above zippering model, a recent single‐molecule optical tweezers experiment by Gao et al. revealed a sequential unzipping of SNARE along VAMP2 in the order of the linker domain → the C‐terminal domain → the N‐terminal domain. To offer detailed structural insights to this unzipping process, we have performed all‐atom and coarse‐grained steered molecular dynamics (sMD) simulations of the forced unfolding pathways of SNARE using different models and force fields. Our findings are summarized as follows: First, the sMD simulations based on either an all‐atom force field (with an implicit solvent model) or a coarse‐grained Go model were unable to capture the forced unfolding pathway of SNARE as observed by Gao et al., which may be attributed to insufficient simulation time and inaccurate force fields. Second, the sMD simulations based on a reparameterized coarse‐grained model (i.e., modified elastic network model) were able to predict a sequential unzipping of SNARE in good agreement with the findings by Gao et al. The key to this success is to reparameterize the intrahelix and interhelix nonbonded force constants against the pair‐wise residue–residue distance fluctuations collected from all‐atom MD simulations of SNARE. Therefore, our finding supports the importance of accurately describing the inherent dynamics/flexibility of SNARE (in the absence of force), in order to correctly simulate its unfolding behaviors under force. This study has established a useful computational framework for future studies of the zippering function of SNARE and its perturbations by point mutations with amino‐acid level of details, and more generally the forced unfolding pathways of other helix bundle proteins. Proteins 2014; 82:1376–1386. © 2014 Wiley Periodicals, Inc.     

Coarse-Grained Simulation of Full-Length Integrin Activation

Integrin conformational dynamics are critical to their receptor and signaling functions in many cellular processes, including spreading, adhesion, and migration. However, assessing integrin conformations is both experimentally and computationally challenging because of limitations in resolution and dynamic sampling. Thus, structural changes that underlie transitions between conformations are largely unknown. Here, focusing on integrin αvβ₃, we developed a modified form of the coarse-grained heterogeneous elastic network model (hENM), which allows sampling conformations at the onset of activation by formally separating local fluctuations from global motions. Both local fluctuations and global motions are extracted from all-atom molecular dynamics simulations of the full-length αvβ₃ bent integrin conformer, but whereas the former are incorporated in the hENM as effective harmonic interactions between groups of residues, the latter emerge by systematically identifying and treating weak interactions between long-distance domains with flexible and anharmonic connections. The new hENM model allows integrins and single-point mutant integrins to explore various conformational states, including the initiation of separation between α- and β-subunit cytoplasmic regions, headpiece extension, and legs opening.     

Wiggle-predicting functionally flexible regions from primary sequence

The Wiggle series are support vector machine-based predictors that identify regions of functional flexibility using only protein sequence information. Functionally flexible regions are defined as regions that can adopt different conformational states and are assumed to be necessary for bioactivity. Many advances have been made in understanding the relationship between protein sequence and structure. This work contributes to those efforts by making strides to understand the relationship between protein sequence and flexibility. A coarse-grained protein dynamic modeling approach was used to generate the dataset required for support vector machine training. We define our regions of interest based on the participation of residues in correlated large-scale fluctuations. Even with this structure-based approach to computationally define regions of functional flexibility, predictors successfully extract sequence-flexibility relationships that have been experimentally confirmed to be functionally important. Thus, a sequence-based tool to identify flexible regions important for protein function has been created. The ability to identify functional flexibility using a sequence based approach complements structure-based definitions and will be especially useful for the large majority of proteins with unknown structures. The methodology offers promise to identify structural genomics targets amenable to crystallization and the possibility to engineer more flexible or rigid regions within proteins to modify their bioactivity.     

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.     

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   

Backbone dynamics of the first, second, and third immunoglobulin modules of the neural cell adhesion molecule (NCAM)

The neural cell adhesion molecule (NCAM) is a cell surface multimodular protein, which plays an important role in cell-cell adhesion by homophilic (NCAM-NCAM) and heterophilic (NCAM-non-NCAM molecules) binding. In the present study, the backbone dynamics of the first three immunoglobulin-like (Ig) modules of NCAM have been investigated by NMR spectroscopy. Ig1, Ig2, and Ig3 share low sequence identity but possess the same fold and have very similar three-dimensional structures. (15)N longitudinal and transverse relaxation rates and heteronuclear NOEs have been measured and subsequently analyzed by the axial symmetric Lipari-Szabo modelfree formalism to characterize fast (pico- to nanosecond) and slow (micro- to millisecond) motions in the three protein modules. We found that backbone motions of residues located in the beta-strand regions are generally restricted, while increased flexibility is observed in turns and loops. In all three modules, residues located in the segments connecting the C- and D-strand plus residues located in the segment connecting the E- and F-strand show significant chemical exchange on the micro- to millisecond time scale. In addition, a number of residues with small chemical exchange contribution seem to form contiguous regions in the beta sheets, suggesting that these motions might be correlated. Only few residues in the homophilic binding sites in the NCAM Ig1 and Ig2 modules show increased flexibility, indicating that the Ig1-Ig2-mediated NCAM homophilic binding does not depend on the local backbone mobility of the interacting modules.     

Probing the structural dynamics of the SNARE recycling machine based on coarse‐grained modeling

Membrane fusion in eukaryotes is driven by the formation of a four‐helix bundle by three SNARE proteins. To recycle the SNARE proteins, they must be disassembled by the ATPase NSF and four SNAP proteins which together form a 20S supercomplex. Recently, the first high‐resolution structures of the NSF (in both ATP and ADP state) and 20S (in four distinct states termed I, II, IIIa, and IIIb) were solved by cryo‐electron microscopy (cryo‐EM), which have paved the way for structure‐driven studies of the SNARE recycling mechanism. To probe the structural dynamics of SNARE disassembly at amino‐acid level of details, a systematic coarse‐grained modeling based on an elastic network model and related analyses were performed. Our normal mode analysis of NSF, SNARE, and 20S predicted key modes of collective motions that partially account for the observed structural changes, and illuminated how the SNARE complex can be effectively destabilized by untwisting and bending motions of the SNARE complex driven by the amino‐terminal domains of NSF in state II. Our flexibility analysis identified regions with high/low flexibility that coincide with key functional sites (such as the NSF‐SNAPs‐SNARE binding sites). A subset of hotspot residues that control the above collective motions, which will make promising targets for future mutagenesis studies were also identified. Finally, the conformational changes in 20S as induced by the transition of NSF from ATP to ADP state were modeled, and a concerted untwisting motion of SNARE/SNAPs and a sideway flip of two amino‐terminal domains were observed. In sum, the findings have offered new structural and dynamic details relevant to the SNARE disassembly mechanism, and will guide future functional studies of the SNARE recycling machinery. Proteins 2016; 84:1055–1066. © 2016 Wiley Periodicals, Inc.