A method for the analysis of domain movements in large biomolecular complexes

A new method for the analysis of domain movements in large, multichain, biomolecular complexes is presented. The method is applicable to any molecule for which two atomic structures are available that represent a conformational change indicating a possible domain movement. The method is blind to atomic bonding and atom type and can, therefore, be applied to biomolecular complexes containing different constituent molecules such as protein, RNA, or DNA. At the heart of the method is the use of blocks located at grid points spanning the whole molecule. The rotation vector for the rotation of atoms from each block between the two conformations is calculated. Treating components of these vectors as coordinates means that each block is associated with a point in a “rotation space” and that blocks with atoms that rotate together, perhaps as part of the same rigid domain, will have colocated points. Thus a domain can be identified from the clustering of points from blocks that span it. Domain pairs are accepted for analysis of their relative movements in terms of screw axes based upon a set of reasonable criteria. Here, we report on the application of the method to biomolecules covering a considerable size range: hemoglobin, liver alcohol dehydrogenase, S‐Adenosylhomocysteine hydrolase, aspartate transcarbamylase, and the 70S ribosome. The results provide a depiction of the conformational change within each molecule that is easily understood, giving a perspective that is expected to lead to new insights. Of particular interest is the allosteric mechanism in some of these molecules. Results indicate that common boundaries between subunits and domains are good regions to focus on as movement in one subunit can be transmitted to another subunit through such interfaces. Proteins 2009. © 2008 Wiley‐Liss, Inc.     

Exploring the structural dynamics of the E.coli chaperonin GroEL using translation-libration-screw crystallographic refinement of intermediate states

Large rigid-body domain movements are critical to GroEL-mediated protein folding, especially apical domain elevation and twist associated with the formation of a folding chamber upon binding ATP and co-chaperonin GroES. Here, we have modeled the anisotropic displacements of GroEL domains from various crystallized states, unliganded GroEL, ATPgammaS-bound, ADP-AlFx/GroES-bound, and ADP/GroES bound, using translation-libration-screw (TLS) analysis. Remarkably, the TLS results show that the inherent motions of unliganded GroEL, a polypeptide-accepting state, are biased along the transition pathway that leads to the folding-active state. In the ADP-AlFx/GroES-bound folding-active state the dynamic modes of the apical domains become reoriented and coupled to the motions of bound GroES. The ADP/GroES complex exhibits these same motions, but they are increased in magnitude, potentially reflecting the decreased stability of the complex after nucleotide hydrolysis. Our results have allowed the visualization of the anisotropic molecular motions that link the static conformations previously observed by X-ray crystallography. Application of the same analyses to other macromolecules where rigid body motions occur may give insight into the large scale dynamics critical for function and thus has the potential to extend our fundamental understanding of molecular machines.     

Crystallographic snapshots of a replicative DNA polymerase encountering an abasic site

Abasic sites are common DNA lesions, which are strong blocks to replicative polymerases and are potentially mutagenic when bypassed. We report here the 2.8 A structure of the bacteriophage RB69 replicative DNA polymerase attempting to process an abasic site analog. Four different complexes were captured in the crystal asymmetric unit: two have DNA in the polymerase active site whereas the other two molecules are in the exonuclease mode. When compared to complexes with undamaged DNA, the DNA surrounding the abasic site reveals distinct changes suggesting why the lesion is so poorly bypassed: the DNA in the polymerase active site has not translocated and is therefore stalled, precluding extension. All four molecules exhibit conformations that differ from the previously published structures. The polymerase incorporates dAMP across the lesion under crystallization conditions, indicating that the different conformations observed in the crystal may be part of the active site switching reaction pathway.     

The morph server: a standardized system for analyzing and visualizing macromolecular motions in a database framework

The number of solved structures of macromolecules that have the same fold and thus exhibit some degree of conformational variability is rapidly increasing. It is consequently advantageous to develop a standardized terminology for describing this variability and automated systems for processing protein structures in different conformations. We have developed such a system as a 'front-end' server to our database of macromolecular motions. Our system attempts to describe a protein motion as a rigid-body rotation of a small 'core' relative to a larger one, using a set of hinges. The motion is placed in a standardized coordinate system so that all statistics between any two motions are directly comparable. We find that while this model can accommodate most protein motions, it cannot accommodate all; the degree to which a motion can be accommodated provides an aid in classifying it. Furthermore, we perform an adiabatic mapping (a restrained interpolation) between every two conformations. This gives some indication of the extent of the energetic barriers that need to be surmounted in the motion, and as a by-product results in a 'morph movie'. We make these movies available over the Web to aid in visualization. Many instances of conformational variability occur between proteins with somewhat different sequences. We can accommodate these differences in a rough fashion, generating an 'evolutionary morph'. Users have already submitted hundreds of examples of protein motions to our server, producing a comprehensive set of statistics. So far the statistics show that the median submitted motion has a rotation of approximately 10 degrees and a maximum Calpha displacement of 17 A. Almost all involve at least one large torsion angle change of >140 degrees. The server is accessible at http://bioinfo.mbb.yale. edu/MolMovDB     

Rigid-cluster models of conformational transitions in macromolecular machines and assemblies

We present a rigid-body-based technique (called rigid-cluster elastic network interpolation) to generate feasible transition pathways between two distinct conformations of a macromolecular assembly. Many biological molecules and assemblies consist of domains which act more or less as rigid bodies during large conformational changes. These collective motions are thought to be strongly related with the functions of a system. This fact encourages us to simply model a macromolecule or assembly as a set of rigid bodies which are interconnected with distance constraints. In previous articles, we developed coarse-grained elastic network interpolation (ENI) in which, for example, only Calpha atoms are selected as representatives in each residue of a protein. We interpolate distance differences of two conformations in ENI by using a simple quadratic cost function, and the feasible conformations are generated without steric conflicts. Rigid-cluster interpolation is an extension of the ENI method with rigid-clusters replacing point masses. Now the intermediate conformations in an anharmonic pathway can be determined by the translational and rotational displacements of large clusters in such a way that distance constraints are observed. We present the derivation of the rigid-cluster model and apply it to a variety of macromolecular assemblies. Rigid-cluster ENI is then modified for a hybrid model represented by a mixture of rigid clusters and point masses. Simulation results show that both rigid-cluster and hybrid ENI methods generate sterically feasible pathways of large systems in a very short time. For example, the HK97 virus capsid is an icosahedral symmetric assembly composed of 60 identical asymmetric units. Its original Hessian matrix size for a Calpha coarse-grained model is >(300,000)(2). However, it reduces to (84)(2) when we apply the rigid-cluster model with icosahedral symmetry constraints. The computational cost of the interpolation no longer scales heavily with the size of structures; instead, it depends strongly on the minimal number of rigid clusters into which the system can be decomposed.     

Comprehensive analysis of motions in molecular dynamics trajectories of the actin capping protein and its inhibitor complexes

The actin capping protein (CP) binds to actin filaments to block further elongation. The capping activity is inhibited by proteins V‐1 and CARMIL interacting with CP via steric and allosteric mechanisms, respectively. The crystal structures of free CP, CP/V‐1, and CP/CARMIL complexes suggest that the binding of CARMIL alters the flexibility of CP rather than the overall structure of CP, and this is an allosteric inhibition mechanism. Here, we performed molecular dynamics (MD) simulations of CP in the free form, and in complex with CARMIL or V‐1. The resulting trajectories were analyzed exhaustively using Motion Tree, which identifies various rigid‐body motions ranging from small local motions to large domain motions. After enumerating all the motions, CP flexibilities with different ligands were characterized by a list of frequencies for 20 dominant rigid‐body motions, some of which were not identified in previous studies. The comparative analysis highlights the influence of the binding of the CARMIL peptide to CP flexibility. In free CP and the CP/V‐1 complex, domain motions around a large crevice between the N‐stalk and the CP‐S domain occur frequently. The CARMIL peptide binds the crevice and suppresses the motions effectively. In addition, the binding of the CARMIL peptide enhances and alters local motions around the pocket that participates in V‐1 binding. These newly identified motions are likely to suppress the binding of V‐1 to CP. The observed changes in CP motion provide insights that describe the mechanism of allosteric regulation by CARMIL through modulating CP flexibility. Proteins 2016; 84:948–956. © 2016 Wiley Periodicals, Inc.     

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.     

OLDERADO: on-line database of ensemble representatives and domains. On Line Database of Ensemble Representatives And DOmains.

In cases where the structure of a single protein is represented by an ensemble of conformations, there is often a need to determine the common features and to choose a "representative" conformation. This occurs, for example, with structures determined by NMR spectroscopy, analysis of the trajectory from a molecular dynamics simulation, or an ensemble of structures produced by comparative modeling. We reported previously automatic methods for (1) defining the atoms with low spatial variance across an ensemble (i.e., the "core" atoms) and the domains in which these atoms lie, and (2) clustering an ensemble into conformationally related subfamilies. To extend the utility of these methods, we have developed a freely available server on the World Wide Web at http:/(/)neon.chem.le.ac.uk/olderado/. This (1) contains an automatically generated database of representative structures, core atoms, and domains determined for 449 ensembles of NMR-derived protein structures in the Protein Data Bank (PDB) in May 1997, and (2) allows the user to upload a PDB-formatted file containing the coordinates of an ensemble of structures. The server returns in real time: (1) information on the residues constituting domains: (2) the structures that constitute each conformational subfamily; and (3) an interactive java-based three-dimensional viewer to visualise the domains and clusters. Such information is useful, for example, when selecting conformations to be used in comparative modeling and when choosing parts of structures to be used in molecular replacement. Here we describe the OLDERADO server.     

Protein-protein docking with multiple residue conformations and residue substitutions

The protein docking problem has two major aspects: sampling conformations and orientations, and scoring them for fit. To investigate the extent to which the protein docking problem may be attributed to the sampling of ligand side‐chain conformations, multiple conformations of multiple residues were calculated for the uncomplexed (unbound) structures of protein ligands. These ligand conformations were docked into both the complexed (bound) and unbound conformations of the cognate receptors, and their energies were evaluated using an atomistic potential function. The following questions were considered: (1) does the ensemble of precalculated ligand conformations contain a structure similar to the bound form of the ligand? (2) Can the large number of conformations that are calculated be efficiently docked into the receptors? (3) Can near‐native complexes be distinguished from non‐native complexes? Results from seven test systems suggest that the precalculated ensembles do include side‐chain conformations similar to those adopted in the experimental complexes. By assuming additivity among the side chains, the ensemble can be docked in less than 12 h on a desktop computer. These multiconformer dockings produce near‐native complexes and also non‐native complexes. When docked against the bound conformations of the receptors, the near‐native complexes of the unbound ligand were always distinguishable from the non‐native complexes. When docked against the unbound conformations of the receptors, the near‐native dockings could usually, but not always, be distinguished from the non‐native complexes. In every case, docking the unbound ligands with flexible side chains led to better energies and a better distinction between near‐native and non‐native fits. An extension of this algorithm allowed for docking multiple residue substitutions (mutants) in addition to multiple conformations. The rankings of the docked mutant proteins correlated with experimental binding affinities. These results suggest that sampling multiple residue conformations and residue substitutions of the unbound ligand contributes to, but does not fully provide, a solution to the protein docking problem. Conformational sampling allows a classical atomistic scoring function to be used; such a function may contribute to better selectivity between near‐native and non‐native complexes. Allowing for receptor flexibility may further extend these results.     

Determining and visualizing flexibility in protein structures

How to compare the structures of an ensemble of protein conformations is a fundamental problem in structural biology. As has been previously observed, the widely used RMSD measure due to Kabsch, in which a rigid‐body superposition minimizing the least‐squares positional deviations is performed, has its drawbacks when comparing and visualizing a set of flexible protein structures. Here, we develop a method, fleximatch, of protein structure comparison that takes flexibility into account. Based on a distance matrix measure of flexibility, a weighted superposition of distance matrices rather than of atomic coordinates is performed. Subsequently, this allows a consistent determination of (a) a superposition of structures for visualization, (b) a partitioning of the protein structure into rigid molecular components (core atoms), and (c) an atomic mobility measure. The method is suitable for highlighting both particularly flexible and rigid parts of a protein from structures derived from NMR, X‐ray diffraction or molecular simulation. Proteins 2015; 83:820–826. © 2015 Wiley Periodicals, Inc.     

Normal modes for predicting protein motions: a comprehensive database assessment and associated Web tool

We carry out an extensive statistical study of the applicability of normal modes to the prediction of mobile regions in proteins. In particular, we assess the degree to which the observed motions found in a comprehensive data set of 377 nonredundant motions can be modeled by a single normal-mode vibration. We describe each motion in our data set by vectors connecting corresponding atoms in two crystallographically known conformations. We then measure the geometric overlap of these motion vectors with the displacement vectors of the lowest-frequency mode, for one of the conformations. Our study suggests that the lowest mode contains useful information about the parts of a protein that move most (i.e., have the largest amplitudes) and about the direction of this movement. Based on our findings, we developed a Web tool for motion prediction (available from http://molmovdb.org/nma) and apply it here to four representative motions--from bacteriorhodopsin, calmodulin, insulin, and T7 RNA polymerase.     

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.     

Protein docking and complementarity

Predicting the structures of protein-protein complexes is a difficult problem owing to the topographical and thermodynamic complexity of these structures. Past efforts in this area have focussed on fitting the interacting proteins together using rigid body searches, usually with the conformations of the proteins as they occur in crystal structure complexes. Here we present work which uses a rigid body docking method to generate the structures of three known protein complexes, using both the bound and unbound conformations of the interacting molecules. In all cases we can regenerate the geometry of the crystal complexes to high accuracy. We also are able to find geometries that do not resemble the crystal structure but nevertheless are surprisingly reasonable both mechanistically and by some simple physical criteria. In contrast to previous work in this area, we find that simple methods for evaluating the complementarity at the protein-protein interface cannot distinguish between the configurations that resemble the crystal structure complex and those that do not. Methods that could not distinguish between such similar and dissimilar configurations include surface area burial, solvation free energy, packing and mechanism-based filtering. Evaluations of the total interaction energy and the electrostatic interaction energy of the complexes were somewhat better. Of the techniques that we tried, energy minimization distinguished most clearly between the "true" and "false" positives, though even here the energy differences were surprisingly small. We found the lowest total interaction energy from amongst all of the putative complexes generated by docking was always within 5 A root-mean-square of the crystallographic structure. There were, however, several putative complexes that were very dissimilar to the crystallographic structure but had energies that were close to that of the low energy structure. The magnitude of the error in energy calculations has not been established in macromolecular systems, and thus the reliability of the small differences in energy remains to be determined. The ability of this docking method to regenerate the crystallographic configurations of the interacting proteins using their unbound conformations suggests that it will be a useful tool in predicting the structures of unsolved complexes.     

Method for identification of rigid domains and hinge residues in proteins based on exhaustive enumeration

Many proteins undergo large‐scale motions where relatively rigid domains move against each other. The identification of rigid domains, as well as the hinge residues important for their relative movements, is important for various applications including flexible docking simulations. In this work, we develop a method for protein rigid domain identification based on an exhaustive enumeration of maximal rigid domains, the rigid domains not fully contained within other domains. The computation is performed by mapping the problem to that of finding maximal cliques in a graph. A minimal set of rigid domains are then selected, which cover most of the protein with minimal overlap. In contrast to the results of existing methods that partition a protein into non‐overlapping domains using approximate algorithms, the rigid domains obtained from exact enumeration naturally contain overlapping regions, which correspond to the hinges of the inter‐domain bending motion. The performance of the algorithm is demonstrated on several proteins. Proteins 2015; 83:1054–1067. © 2015 Wiley Periodicals, Inc.