Protein flexibility predictions using graph theory

Techniques from graph theory are applied to analyze the bond networks in proteins and identify the flexible and rigid regions. The bond network consists of distance constraints defined by the covalent and hydrogen bonds and salt bridges in the protein, identified by geometric and energetic criteria. We use an algorithm that counts the degrees of freedom within this constraint network and that identifies all the rigid and flexible substructures in the protein, including overconstrained regions (with more crosslinking bonds than are needed to rigidify the region) and underconstrained or flexible regions, in which dihedral bond rotations can occur. The number of extra constraints or remaining degrees of bond-rotational freedom within a substructure quantifies its relative rigidity/flexibility and provides a flexibility index for each bond in the structure. This novel computational procedure, first used in the analysis of glassy materials, is approximately a million times faster than molecular dynamics simulations and captures the essential conformational flexibility of the protein main and side-chains from analysis of a single, static three-dimensional structure. This approach is demonstrated by comparison with experimental measures of flexibility for three proteins in which hinge and loop motion are essential for biological function: HIV protease, adenylate kinase, and dihydrofolate reductase.     

600 ps Molecular dynamics reveals stable substructures and flexible hinge points in cAMP dependent protein kinase

Molecular dynamics simulations of the catalytic subunit of cAMP dependent protein kinase (cAPK) have been performed in an aqueous environment. The relations among the protein hydrogen‐bonding network, secondary structural elements, and the internal motions of rigid domains were examined. The values of fluctuations of protein dihedral angles during dynamics show quite distinct maxima in the regions of loops and minima in the regions of α‐helices and β‐strands. Analyses of conformation snapshots throughout the run show stable subdomains and indicate that these rigid domains are constrained during the dynamics by a stable network of hydrogen bonds. The most stable subdomain during the dynamics was in the small lobe including part of the carboxy‐terminal tail. The most significant flexible region was the highly conserved glycine‐rich loop between β strands 1 and 2 in the small lobe. Many of the main chain dihedral angle changes measured in a comparison of the crystallographic structures of “open” and “closed” conformations of cAPK correspond to the highly flexible residues found during dynamics. © 1999 John Wiley & Sons, Inc. Biopoly 50: 513–524, 1999     

1D2DSimScore: A novel method for comparing contacts in biomacromolecules and their complexes

The biologically relevant structures of proteins and nucleic acids and their complexes are dynamic. They include a combination of regions ranging from rigid structural segments to structural switches to regions that are almost always disordered, which interact with each other in various ways. Comparing conformational changes and variation in contacts between different conformational states is essential to understand the biological functions of proteins, nucleic acids, and their complexes. Here, we describe a new computational tool, 1D2DSimScore, for comparing contacts and contact interfaces in all kinds of macromolecules and macromolecular complexes, including proteins, nucleic acids, and other molecules. 1D2DSimScore can be used to compare structural features of macromolecular models between alternative structures obtained in a particular experiment or to score various predictions against a defined “ideal” reference structure. Comparisons at the level of contacts are particularly useful for flexible molecules, for which comparisons in 3D that require rigid-body superpositions are difficult, and in biological systems where the formation of specific inter-residue contacts is more relevant for the biological function than the maintenance of a specific global 3D structure. Similarity/dissimilarity scores calculated by 1D2DSimScore can be used to complement scores describing 3D structural similarity measures calculated by the existing tools.     

Molecular dynamics simulations and rigid body (TLS) analysis of aspartate carbamoyltransferase: evidence for an uncoupled R state.

In the R form of ATCase complexed with the bisubstrate analogue, N-(phosphonacetyl)-L-aspartate, large temperature factors are reported for the allosteric domains of the regulatory chains. We studied the conformational flexibility of the holoenzyme with molecular dynamics simulations and rigid body (TLS) analysis. The results of the molecular dynamics simulations suggest that, although local atomic fluctuations account for the temperature factors of the catalytic and zinc domains, they do not account for the large temperature factors of the allosteric regions. However, the temperature factors of the allosteric domains can be satisfactorily analyzed using a rigid body model. The simulations and rigid body analysis support the idea that the allosteric regions are mechanically uncoupled from the rest of the enzyme in the PALA structure. Implications of this uncoupling for allosteric regulation are discussed.     

Hierarchical domain‐motion analysis of conformational changes in sarcoplasmic reticulum Ca2+‐ATPase

Sarco(endo)plasmic reticulum Ca²⁺‐ATPase transports two Ca²⁺ per ATP‐hydrolyzed across biological membranes against a large concentration gradient by undergoing large conformational changes. Structural studies with X‐ray crystallography revealed functional roles of coupled motions between the cytoplasmic domains and the transmembrane helices in individual reaction steps. Here, we employed “Motion Tree (MT),” a tree diagram that describes a conformational change between two structures, and applied it to representative Ca²⁺‐ATPase structures. MT provides information of coupled rigid‐body motions of the ATPase in individual reaction steps. Fourteen rigid structural units, “common rigid domains (CRDs)” are identified from seven MTs throughout the whole enzymatic reaction cycle. CRDs likely act as not only the structural units, but also the functional units. Some of the functional importance has been newly revealed by the analysis. Stability of each CRD is examined on the morphing trajectories that cover seven conformational transitions. We confirmed that the large conformational changes are realized by the motions only in the flexible regions that connect CRDs. The Ca²⁺‐ATPase efficiently utilizes its intrinsic flexibility and rigidity to response different switches like ligand binding/dissociation or ATP hydrolysis. The analysis detects functional motions without extensive biological knowledge of experts, suggesting its general applicability to domain movements in other membrane proteins to deepen the understanding of protein structure and function. Proteins 2015; 83:746–756. © 2015 Wiley Periodicals, Inc.     

Active state-like conformational elements in the beta2-AR and a photoactivated intermediate of rhodopsin identified by dynamic properties of GPCRs

G-Protein-coupled receptors (GPCRs) adopt various functionally relevant conformational states in cell signaling processes. Recently determined crystal structures of rhodopsin and the beta 2-adrenergic receptor (beta 2-AR) offer insight into previously uncharacterized active conformations, but the molecular states of these GPCRs are likely to contain both inactive and active-like conformational elements. We have identified conformational rearrangements in the dynamics of the TM7-HX8 segment that relate to the properties of the conserved NPxxY(x)5,6F motif and show that they can be used to identify active state-like conformational elements in the corresponding regions of the new structures of rhodopsin and the beta 2-AR.     

Common conformational effects of p53 mutations

The tumor suppressor gene p53 has been identified as the most frequent target of genetic alterations in human cancers. Most of these mutations occur in highly conserved regions in the DNA-binding core domain of the p53 protein, suggesting that the amino acid residues in these regions are critical for maintaining normal p53 structure and function. We previously used molecular dynamics calculations to demonstrate that several amino acid substitutions in these regions that are induced by environmental carcinogens and found in human tumors produce certain common conformational changes in the mutant proteins that differ substantially from the wild-type structure. In order to determine whether these conformational changes are consistent for other p53 mutants, we have now used molecular dynamics to determine the structure of the DNA-binding core domain of seven other environmentally induced, cancer-related p53 mutants, namely His 175, Asp 245, Asn 245, Trp 248, Met 249, Ser 278, and Lys 286. The results indicate that all of these mutants differ substantially from the wild-type structure in certain discrete regions and that some of these conformational changes are similar for these mutants as well as those determined previously. The changes are also consistent with experimental evidence for alterations in structure in p53 mutants determined by epitope detectability using monoclonal antibodies directed against these regions of predicted conformational change.     

Conformational Equilibrium of CDK/Cyclin Complexes by Molecular Dynamics with Excited Normal Modes

Cyclin-dependent kinases (CDKs) and their associated regulatory cyclins are central for timely regulation of cell-cycle progression. They constitute attractive pharmacological targets for development of anticancer therapeutics, since they are frequently deregulated in human cancers and contribute to sustained, uncontrolled tumor proliferation. Characterization of their structural/dynamic features is essential to gain in-depth insight into structure-activity relationships. In addition, the identification of druggable pockets or key intermediate conformations yields potential targets for the development of novel classes of inhibitors. Structural studies of CDK2/cyclin A have provided a wealth of information concerning monomeric/heterodimeric forms of this kinase. There is, however, much less structural information for other CDK/cyclin complexes, including CDK4/cyclin D1, which displays an alternative (open) position of the cyclin partner relative to CDK, contrasting with the closed CDK2/cyclin A conformation. In this study, we carried out normal-mode analysis and enhanced sampling simulations with our recently developed method, molecular dynamics with excited normal modes, to understand the conformational equilibrium on these complexes. Interestingly, the lowest-frequency normal mode computed for each complex described the transition between the open and closed conformations. Exploration of these motions with an explicit-solvent representation using molecular dynamics with excited normal modes confirmed that the closed conformation is the most stable for the CDK2/cyclin A complex, in agreement with their experimentally available structures. On the other hand, we clearly show that an open↔closed equilibrium may exist in CDK4/cyclin D1, with closed conformations resembling that captured for CDK2/cyclin A. Such conformational preferences may result from the distinct distributions of frustrated contacts in each complex. Using the same approach, the putative roles of the Thr¹⁶⁰ phosphoryl group and the T-loop conformation were investigated. These results provide a dynamic view of CDKs revealing intermediate conformations not yet characterized for CDK members other than CDK2, which will be useful for the design of inhibitors targeting critical conformational transitions.     

Molecular insights of benzodipyrazole as CDK2 inhibitors: combined molecular docking,molecular dynamics,and 3D QSAR studies

Abstract

Benzodipyrazoles have been previously evaluated for their in vitro CDK2 inhibitory activity. In the current investigation, we identified a six-feature common pharmacophore model (AADDRR.33) which is predicted to be responsible for CDK2 inhibition. An efficient 3D QSAR (r^2?=?0.98 and q^2?=?0.82) model was also constructed by employing PLS regression analysis. From the molecular docking studies, we examined the binding patterns of compound 7aa with the target protein and also calculated the binding energy using MM-GBSA calculations. Three hydrogen bonds with Lys 33, Glu 81, and Leu 83 are conserved even after 1000?ps run in a molecular dynamics simulation. We identified the slight displacement in bond lengths and the conformational changes occurred during the dynamics. The results also elucidated the protein residue–ligand interaction fractions which clearly explained the involvement of non-H-bond interactions.     

FLIPDock: docking flexible ligands into flexible receptors

Conformational changes of biological macromolecules when binding with ligands have long been observed and remain a challenge for automated docking methods. Here we present a novel protein-ligand docking software called FLIPDock (Flexible LIgand-Protein Docking) allowing the automated docking of flexible ligand molecules into active sites of flexible receptor molecules. In FLIPDock, conformational spaces of molecules are encoded using a data structure that we have developed recently called the Flexibility Tree (FT). While the FT can represent fully flexible ligands, it was initially designed as a hierarchical and multiresolution data structure for the selective encoding of conformational subspaces of large biological macromolecules. These conformational subspaces can be built to span a range of conformations important for the biological activity of a protein. A variety of motions can be combined, ranging from domains moving as rigid bodies or backbone atoms undergoing normal mode-based deformations, to side chains assuming rotameric conformations. In addition, these conformational subspaces are parameterized by a small number of variables which can be searched during the docking process, thus effectively modeling the conformational changes in a flexible receptor. FLIPDock searches the variables using genetic algorithm-based search techniques and evaluates putative docking complexes with a scoring function based on the AutoDock3.05 force-field. In this paper, we describe the concepts behind FLIPDock and the overall architecture of the program. We demonstrate FLIPDock's ability to solve docking problems in which the assumption of a rigid receptor previously prevented the successful docking of known ligands. In particular, we repeat an earlier cross docking experiment and demonstrate an increased success rate of 93.5%, compared to original 72% success rate achieved by AutoDock over the 400 cross-docking calculations. We also demonstrate FLIPDock's ability to handle conformational changes involving backbone motion by docking balanol to an adenosine-binding pocket of protein kinase A.     

Cooperative Protein Allosteric Transition Mediated by a Fluctuating Transmission Network

Allosteric communication between distant protein sites represents a key mechanism of biomolecular regulation and signal transduction. Compared to other processes such as protein folding, however, the dynamical evolution of allosteric transitions is still not well understood. As an example of allosteric coupling between distant protein regions, we consider the global open-closed motion of the two domains of T4 lysozyme, which is triggered by local motion in the hinge region. Combining extensive molecular dynamics simulations with a correlation analysis of interresidue contacts, we identify a network of interresidue distances that move in a concerted manner. The cooperative process originates from a cogwheel-like motion of the hydrophobic core in the hinge region, which constitutes an evolutionary conserved and flexible transmission network. Through rigid contacts and the protein backbone, the small local changes of the hydrophobic core are passed on to the distant terminal domains and lead to the emergence of a rare global conformational transition. As in an Ising-type model, the cooperativity of the allosteric transition can be explained via the interaction of local fluctuations.     

From static structure to living protein: computational analysis of cytochrome c oxidase main-chain flexibility

Crystallographic structure and deuterium accessibility comparisons of CcO in different redox states have suggested conformational changes of mechanistic significance. To predict the intrinsic flexibility and low energy motions in CcO, this work has analyzed available high-resolution crystallographic structures with ProFlex and elNémo computational methods. The results identify flexible regions and potential conformational changes in CcO that correlate well with published structural and biochemical data and provide mechanistic insights. CcO is predicted to undergo rotational motions on the interior and exterior of the membrane, driven by transmembrane helical tilting and bending, coupled with rocking of the β-sheet domain. Consequently, the proton K-pathway becomes sufficiently flexible for internal water molecules to alternately occupy upper and lower parts of the pathway, associated with conserved Thr-359 and Lys-362 residues. The D-pathway helices are found to be relatively rigid, with a highly flexible entrance region involving the subunit I C-terminus, potentially regulating the uptake of protons. Constriction and dilation of hydrophobic channels in RsCcO suggest regulation of the oxygen supply to the binuclear center. This analysis points to coupled conformational changes in CcO and their potential to influence both proton and oxygen access.     

Statics of the Ribosomal Exit Tunnel: Implications for Cotranslational Peptide Folding, Elongation Regulation, and Antibiotics Binding

A sophisticated interplay between the static properties of the ribosomal exit tunnel and its functional role in cotranslational processes is revealed by constraint counting on topological network representations of large ribosomal subunits from four different organisms. As for the global flexibility characteristics of the subunit, the results demonstrate a conserved stable structural environment of the tunnel. The findings render unlikely that deformations of the tunnel move peptides down the tunnel in an active manner. Furthermore, the stable environment rules out that the tunnel can adapt widely so as to allow tertiary folding of nascent chains. Nevertheless, there are local zones of flexible nucleotides within the tunnel, between the peptidyl transferase center and the tunnel constriction, and at the tunnel exit. These flexible zones strikingly agree with previously identified folding zones. As for cotranslational elongation regulation, flexible residues in the β-hairpin of the ribosomal L22 protein were verified, as suggested previously based on structural results. These results support the hypothesis that L22 can undergo conformational changes that regulate the tunnel voyage of nascent polypeptides. Furthermore, rRNA elements, for which conformational changes have been observed upon interaction of the tunnel wall with a nascent SecM peptide, are less strongly coupled to the subunit core. Sequences of coupled rigid clusters are identified between the tunnel and some of these elements, suggesting signal transmission by a domino-like mechanical coupling. Finally, differences in the flexibility of the glycosidic bonds of bases that form antibiotics-binding crevices within the peptidyl transferase center and the tunnel region are revealed for ribosomal structures from different kingdoms. In order to explain antibiotics selectivity, action, and resistance, according to these results, differences in the degrees of freedom of the binding regions may need to be considered.     

The Role of Conformational Dynamics and Allostery in the Disease Development of Human Ferritin

Determining the three-dimensional structure of myoglobin, the first solved structure of a protein, fundamentally changed the way protein function was understood. Even more revolutionary was the information that came afterward: protein dynamics play a critical role in biological functions. Therefore, understanding conformational dynamics is crucial to obtaining a more complete picture of protein evolution. We recently analyzed the evolution of different protein families including green fluorescent proteins (GFPs), β-lactamase inhibitors, and nuclear receptors, and we observed that the alteration of conformational dynamics through allosteric regulation leads to functional changes. Moreover, proteome-wide conformational dynamics analysis of more than 100 human proteins showed that mutations occurring at rigid residue positions are more susceptible to disease than flexible residue positions. These studies suggest that disease-associated mutations may impair dynamic allosteric regulations, leading to loss of function. Thus, in this study, we analyzed the conformational dynamics of the wild-type light chain subunit of human ferritin protein along with the neutral and disease forms. We first performed replica exchange molecular dynamics simulations of wild-type and mutants to obtain equilibrated dynamics and then used perturbation response scanning (PRS), where we introduced a random Brownian kick to a position and computed the fluctuation response of the chain using linear response theory. Using this approach, we computed the dynamic flexibility index (DFI) for each position in the chain for the wild-type and the mutants. DFI quantifies the resilience of a position to a perturbation and provides a flexibility/rigidity measurement for a given position in the chain. The DFI analysis reveals that neutral variants and the wild-type exhibit similar flexibility profiles in which experimentally determined functionally critical sites act as hinges in controlling the overall motion. However, disease mutations alter the conformational dynamic profile, making hinges more loose (i.e., softening the hinges), thus impairing the allosterically regulated dynamics.     

The Role of Conformational Dynamics and Allostery in the Disease Development of Human Ferritin

Determining the three-dimensional structure of myoglobin, the first solved structure of a protein, fundamentally changed the way protein function was understood. Even more revolutionary was the information that came afterward: protein dynamics play a critical role in biological functions. Therefore, understanding conformational dynamics is crucial to obtaining a more complete picture of protein evolution. We recently analyzed the evolution of different protein families including green fluorescent proteins (GFPs), β-lactamase inhibitors, and nuclear receptors, and we observed that the alteration of conformational dynamics through allosteric regulation leads to functional changes. Moreover, proteome-wide conformational dynamics analysis of more than 100 human proteins showed that mutations occurring at rigid residue positions are more susceptible to disease than flexible residue positions. These studies suggest that disease-associated mutations may impair dynamic allosteric regulations, leading to loss of function. Thus, in this study, we analyzed the conformational dynamics of the wild-type light chain subunit of human ferritin protein along with the neutral and disease forms. We first performed replica exchange molecular dynamics simulations of wild-type and mutants to obtain equilibrated dynamics and then used perturbation response scanning (PRS), where we introduced a random Brownian kick to a position and computed the fluctuation response of the chain using linear response theory. Using this approach, we computed the dynamic flexibility index (DFI) for each position in the chain for the wild-type and the mutants. DFI quantifies the resilience of a position to a perturbation and provides a flexibility/rigidity measurement for a given position in the chain. The DFI analysis reveals that neutral variants and the wild-type exhibit similar flexibility profiles in which experimentally determined functionally critical sites act as hinges in controlling the overall motion. However, disease mutations alter the conformational dynamic profile, making hinges more loose (i.e., softening the hinges), thus impairing the allosterically regulated dynamics.     

Mechanism of Cohesin Loading onto Chromosomes: A Conformational Dynamics Study

The structure-function relationship of cohesin, an essential chromosome maintenance protein, is investigated by analyzing its collective dynamics and conformational flexibility, enhancing our understanding of the sister chromatid cohesion process. A three-dimensional model of cohesin has been constructed by homology modeling using both crystallographic and electron microscopy image data. The harmonic dynamics of the cohesin structure are calculated with a coarse-grained elastic network model. The model shows that the bending motion of the cohesin ring is able to adopt a head-to-tail conformation, in agreement with experimental data. Low-frequency conformational changes are observed to deform the highly conserved glycine residues at the interface of the cohesin heterodimer. Normal mode analysis further reveals that, near large globular structures such as nucleosome and accessory proteins docked to cohesin, the mobility of the coiled-coil regions is notably affected. Moreover, fully solvated molecular dynamics calculations, performed specifically on the hinge region, indicate that hinge opening starts from one side of the dimerization interface, and is coordinated by highly conserved glycine residues.