Analysis of domain motions in large proteins

Evaluation of Protein Elastic Network Models Based on an Analysis of Collective Motions

Elastic network models (ENMs) are valuable tools for investigating collective motions of proteins, and a rich variety of simple models have been proposed over the past decade. A good representation of the collective motions requires a good approximation of the covariances between the fluctuations of the individual atoms. Nevertheless, most studies have validated such models only by the magnitudes of the single-atom fluctuations they predict. In the present study, we have quantified the agreement between the covariance structure predicted by molecular dynamics (MD) simulations and those predicted by a representative selection of proposed coarse-grained ENMs. We then contrast this approach with the comparison to MD-predicted atomic fluctuations and comparison to crystallographic B-factors. While all the ENMs yield approximations to the MD-predicted covariance structure, we report large and consistent differences between proposed models. We also find that the ability of the ENMs to predict atomic fluctuations is correlated with their ability to capture the covariance structure. In contrast, we find that the models that agree best with B-factors model collective motions less reliably and recommend against using B-factors as a benchmark.

Mechanical and assembly units of viral capsids identified via quasi-rigid domain decomposition

Key steps in a viral life-cycle, such as self-assembly of a protective protein container or in some cases also subsequent maturation events, are governed by the interplay of physico-chemical mechanisms involving various spatial and temporal scales. These salient aspects of a viral life cycle are hence well described and rationalised from a mesoscopic perspective. Accordingly, various experimental and computational efforts have been directed towards identifying the fundamental building blocks that are instrumental for the mechanical response, or constitute the assembly units, of a few specific viral shells. Motivated by these earlier studies we introduce and apply a general and efficient computational scheme for identifying the stable domains of a given viral capsid. The method is based on elastic network models and quasi-rigid domain decomposition. It is first applied to a heterogeneous set of well-characterized viruses (CCMV, MS2, STNV, STMV) for which the known mechanical or assembly domains are correctly identified. The validated method is next applied to other viral particles such as L-A, Pariacoto and polyoma viruses, whose fundamental functional domains are still unknown or debated and for which we formulate verifiable predictions. The numerical code implementing the domain decomposition strategy is made freely available.

The genetic material of viruses is packaged inside capsids constituted from a few tens to thousands of proteins. The latter can organize in multimers that serve as fundamental blocks for the viral shell assembly or that control the capsid conformational transitions and response to mechanical stress. In this work, we introduce and apply a computational scheme that identifies the fundamental protein blocks from the structural fluctuations of the capsids in thermal equilibrium. These can be derived from phenomenological elastic network models with minimal computational expenditure. Accordingly, the basic functional protein units of a capsid can be obtained from the sole input of the capsid crystal structure. The method is applied to a heterogeneous set of viruses of various size and geometries. These include well-characterised instances for validation purposes, as well as debated ones for which predictions are formulated.

Large-scale analysis of the dynamics of enzymes

Protein enzymes enable the cell to execute chemical reactions in short time by accelerating the rate of the reactions in a selective manner. The motions or dynamics of the enzymes are essential for their function. Comparison of the dynamics of a set of 1247 nonhomologous enzymes was performed. For each enzyme, the slowest modes of motion are calculated using the Gaussian network model (GNM) and they are globally aligned. Alignment is done using the dynamic programming algorithm of Needleman and Wunsch, commonly used for sequence alignment. Only 96 pairs of proteins were identified to have three similar GNM slow modes with 63 of them having a similar structure. The most frequent slowest mode of motion describes a two domains anticorrelated motion that characterizes at least 23% of the enzymes. Therefore, dynamics uniqueness cannot be accounted for by the slowest mode itself but rather by the combination of several slow modes. Different quaternary structure packing can restrain the motion of enzyme subunits differently and may serve as another mechanism that increases the dynamics uniqueness.

ΔΔPT: a comprehensive toolbox for the analysis of protein motion

Background

Normal Mode Analysis is one of the most successful techniques for studying motions in proteins and macromolecules. It can provide information on the mechanism of protein functions, used to aid crystallography and NMR data reconstruction, and calculate protein free energies.

Results

ΔΔPT is a toolbox allowing calculation of elastic network models and principle component analysis. It allows the analysis of pdb files or trajectories taken from; Gromacs, Amber, and DL_POLY. As well as calculation of the normal modes it also allows comparison of the modes with experimental protein motion, variation of modes with mutation or ligand binding, and calculation of molecular dynamic entropies.

Conclusions

This toolbox makes the respective tools available to a wide community of potential NMA users, and allows them unrivalled ability to analyse normal modes using a variety of techniques and current software.

On the binding affinity of macromolecular interactions: daring to ask why proteins interact

Interactions between proteins are orchestrated in a precise and time-dependent manner, underlying cellular function. The binding affinity, defined as the strength of these interactions, is translated into physico-chemical terms in the dissociation constant (K_d), the latter being an experimental measure that determines whether an interaction will be formed in solution or not. Predicting binding affinity from structural models has been a matter of active research for more than 40 years because of its fundamental role in drug development. However, all available approaches are incapable of predicting the binding affinity of protein–protein complexes from coordinates alone. Here, we examine both theoretical and experimental limitations that complicate the derivation of structure–affinity relationships. Most work so far has concentrated on binary interactions. Systems of increased complexity are far from being understood. The main physico-chemical measure that relates to binding affinity is the buried surface area, but it does not hold for flexible complexes. For the latter, there must be a significant entropic contribution that will have to be approximated in the future. We foresee that any theoretical modelling of these interactions will have to follow an integrative approach considering the biology, chemistry and physics that underlie protein–protein recognition.

Comparing proteins by their internal dynamics: exploring structure-function relationships beyond static structural alignments

The growing interest for comparing protein internal dynamics owes much to the realisation that protein function can be accompanied or assisted by structural fluctuations and conformational changes. Analogously to the case of functional structural elements, those aspects of protein flexibility and dynamics that are functionally oriented should be subject to evolutionary conservation. Accordingly, dynamics-based protein comparisons or alignments could be used to detect protein relationships that are more elusive to sequence and structural alignments. Here we provide an account of the progress that has been made in recent years towards developing and applying general methods for comparing proteins in terms of their internal dynamics and advance the understanding of the structure-function relationship.

Exploring the essential collective dynamics of interacting proteins: application to prion protein dimers

Essential collective dynamics is a promising and robust approach for analysing the slow motions of macromolecules from short molecular dynamics trajectories. In this study, an extension of the method to treat a collection of interacting protein molecules is presented. The extension is applied to investigate the effects of dimerization on the collective dynamics of ovine prion protein molecules in two different arrangements. Examination of the structural plasticity shows that aggregation has a restricting effect on the local mobility of the prion protein molecules in the interfacial regions. Domain motions of the two dimeric ovine prion protein conformations are distinctly different and can be related to interatomic correlations at the interface. Correlated motions are among the slow collective modes extensively analysed by considering both main-chain and side-chain atoms. Correlation maps reveal the existence of a vast network of dynamically correlated side groups, which extends beyond individual subunits via interfacial interconnections. The network is formed by a core of hydrophobic side chains surrounded by hydrophilic groups at the periphery. The relevance of these findings are discussed in the context of mutations associated with prion diseases. The binding free energy of the dimeric conformations is evaluated to probe their thermodynamic stability. The descriptions afforded by the analysis of the essential collective dynamics of the prion dimers are consistent with their binding free energies. The agreement validates the extension of the methodology and provides a means of interpreting the collective dynamics in terms of the thermodynamic stability of ovine prion proteins.

FlexE: Using elastic network models to compare models of protein structure

It is often valuable to compare protein structures to determine how similar they are. Structure comparison methods such as RMSD and GDT-TS are based solely on fixed geometry and do not take into account the intrinsic flexibility or energy landscape of the protein. We propose a method, which we call FlexE, that is based on a simple elastic network model and uses the deformation energy as measure of the similarity between two structures. FlexE can distinguish biologically relevant conformational changes from random changes, while existing geometry-based methods cannot. Additionally, FlexE incorporates the concept of thermal energy, which provides a rational way to determine when two models are "the same". FlexE provides a unique measure of the similarity between protein structures that is complementary to existing methods.

Density-cluster NMA: A new protein decomposition technique for coarse-grained normal mode analysis

Normal mode analysis has emerged as a useful technique for investigating protein motions on long time scales. This is largely due to the advent of coarse-graining techniques, particularly Hooke's Law-based potentials and the rotational-translational blocking (RTB) method for reducing the size of the force-constant matrix, the Hessian. Here we present a new method for domain decomposition for use in RTB that is based on hierarchical clustering of atomic density gradients, which we call Density-Cluster RTB (DCRTB). The method reduces the number of degrees of freedom by 85-90% compared with the standard blocking approaches. We compared the normal modes from DCRTB against standard RTB using 1-4 residues in sequence in a single block, with good agreement between the two methods. We also show that Density-Cluster RTB and standard RTB perform well in capturing the experimentally determined direction of conformational change. Significantly, we report superior correlation of DCRTB with B-factors compared with 1-4 residue per block RTB. Finally, we show significant reduction in computational cost for Density-Cluster RTB that is nearly 100-fold for many examples.

Identification of domains in protein structures from the analysis of intramolecular interactions

The subdivision of protein structures into smaller and independent structural domains has a fundamental importance in understanding protein evolution and function and in the development of protein classification methods as well as in the interpretation of experimental data. Due to the rapid growth in the number of solved protein structures, the need for devising new accurate algorithmic methods has become more and more urgent. In this paper, we propose a new computational approach that is based on the concept of domain as a compact and independent folding unit and on the analysis of the residue-residue energy interactions obtainable through classical all-atom force field calculations. In particular, starting from the analysis of the nonbonded interaction energy matrix associated with a protein, our method filters out and selects only those specific subsets of interactions that define possible independent folding nuclei within a complex protein structure. This allows grouping different protein fragments into energy clusters that are found to correspond to structural domains. The strategy has been tested using proper benchmark data sets, and the results have shown that the new approach is fast and reliable in determining the number of domains in a totally ab initio manner and without making use of any training set or knowledge of the systems in exam. Moreover, our method, identifying the most relevant residues for the stabilization of each domain, may complement the results given by other classification techniques and may provide useful information to design and guide new experiments.

The effects of rigid motions on elastic network model force constants

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

iMod: multipurpose normal mode analysis in internal coordinates

MOTIVATION

Dynamic simulations of systems with biologically relevant sizes and time scales are critical for understanding macromolecular functioning. Coarse-grained representations combined with normal mode analysis (NMA) have been established as an alternative to atomistic simulations. The versatility and efficiency of current approaches normally based on Cartesian coordinates can be greatly enhanced with internal coordinates (IC).

RESULTS

Here, we present a new versatile tool chest to explore conformational flexibility of both protein and nucleic acid structures using NMA in IC. Consideration of dihedral angles as variables reduces the computational cost and non-physical distortions of classical Cartesian NMA methods. Our proposed framework operates at different coarse-grained levels and offers an efficient framework to conduct NMA-based conformational studies, including standard vibrational analysis, Monte-Carlo simulations or pathway exploration. Examples of these approaches are shown to demonstrate its applicability, robustness and efficiency.

CONTACT

pablo@chaconlab.org

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Predicting the open conformations of protein kinases using molecular dynamics simulations

Protein kinases (PK) control phosphorylation in eukaryotic cells, and thereby regulate metabolic pathways, cell cycle progression, apoptosis, and transcription. Consequently, there is significant interest in manipulating PK activity and treat diseases by using small-molecule drugs. All PK catalytic domains undergo large conformational changes as a result of substrate binding and phosphorylation. The "closed" state of a PK catalytic domain is the only state able to phosphorylate the target substrate, which makes the two other observed states (the "open" and the "intermediate" states) interesting drug targets. We investigate whether molecular dynamics (MD) simulations starting from the closed state of the catalytic domain of protein kinase A (C-PKA) can be used to produce realistic structures representing the intermediate and/or open conformation of C-PKA, because this would allow for drug docking calculations and drug design using MD snapshots. We perform 36 ten-nanosecond MD simulations starting from the closed conformation [PDB ID: ATP] of C-PKA in various liganded and phosphorylated states. The results show that MD simulations are capable of reproducing the open conformation of C-PKA with good accuracy within 1 ns of simulation as measured by Cα root mean square deviations (RMSDs) and RMSDs of atoms defining the ATP-binding pocket. Importantly, we are able to show that even without knowledge of the structure of the open form of C-PKA, we can identify the MD snapshots resembling the open conformation most using the open structure of a different PK displaying only 23% sequence identity to C-PKA.

The elastic network model reveals a consistent picture on intrinsic functional dynamics of type II restriction endonucleases

The vibrational dynamics of various type II restriction endonucleases, in complex with cognate/non-cognate DNA and in the apo form, are investigated with the elastic network model in order to reveal common functional mechanisms in this enzyme family. Scissor-like and tong-like motions observed in the slowest modes of all enzymes and their complexes point to common DNA recognition and cleavage mechanisms. Normal mode analysis further points out that the scissor-like motion has an important role in differentiating between cognate and non-cognate sequences at the recognition site, thus implying its catalytic relevance. Flexible regions observed around the DNA-binding site of the enzyme usually concentrate on the highly conserved β-strands, especially after DNA binding. These β-strands may have a structurally stabilizing role in functional dynamics for target site recognition and cleavage. In addition, hot spot residues based on high-frequency modes reveal possible communication pathways between the two distant cleavage sites in the enzyme family. Some of these hot spots also exist on the shortest path between the catalytic sites and are highly conserved.

A normal mode-based geometric simulation approach for exploring biologically relevant conformational transitions in proteins

A three-step approach for multiscale modeling of protein conformational changes is presented that incorporates information about preferred directions of protein motions into a geometric simulation algorithm. The first two steps are based on a rigid cluster normal-mode analysis (RCNMA). Low-frequency normal modes are used in the third step (NMSim) to extend the recently introduced idea of constrained geometric simulations of diffusive motions in proteins by biasing backbone motions of the protein, whereas side-chain motions are biased toward favorable rotamer states. The generated structures are iteratively corrected regarding steric clashes and stereochemical constraint violations. The approach allows performing three simulation types: unbiased exploration of conformational space; pathway generation by a targeted simulation; and radius of gyration-guided simulation. When applied to a data set of proteins with experimentally observed conformational changes, conformational variabilities are reproduced very well for 4 out of 5 proteins that show domain motions, with correlation coefficients r > 0.70 and as high as r = 0.92 in the case of adenylate kinase. In 7 out of 8 cases, NMSim simulations starting from unbound structures are able to sample conformations that are similar (root-mean-square deviation = 1.0-3.1 Å) to ligand bound conformations. An NMSim generated pathway of conformational change of adenylate kinase correctly describes the sequence of domain closing. The NMSim approach is a computationally efficient alternative to molecular dynamics simulations for conformational sampling of proteins. The generated conformations and pathways of conformational transitions can serve as input to docking approaches or as starting points for more sophisticated sampling techniques.

Functional modes and residue flexibility control the anisotropic response of guanylate kinase to mechanical stress

The coupling between the mechanical properties of enzymes and their biological activity is a well-established feature that has been the object of numerous experimental and theoretical works. In particular, recent experiments show that enzymatic function can be modulated anisotropically by mechanical stress. We study such phenomena using a method for investigating local flexibility on the residue scale that combines a reduced protein representation with Brownian dynamics simulations. We performed calculations on the enzyme guanylate kinase to study its mechanical response when submitted to anisotropic deformations. The resulting modifications of the protein's rigidity profile can be related to the changes in substrate binding affinity observed experimentally. Further analysis of the principal components of motion of the trajectories shows how the application of a mechanical constraint on the protein can disrupt its dynamics, thus leading to a decrease of the enzyme's catalytic rate. Eventually, a systematic probe of the protein surface led to the prediction of potential hotspots where the application of an external constraint would produce a large functional response both from the mechanical and dynamical points of view. Such enzyme-engineering approaches open the possibility to tune catalytic function by varying selected external forces.

Large-scale comparison of protein essential dynamics from molecular dynamics simulations and coarse-grained normal mode analyses

A large-scale comparison of essential dynamics (ED) modes from molecular dynamic simulations and normal modes from coarse-grained normal mode methods (CGNM) was performed on a dataset of 335 proteins. As CGNM methods, the elastic network model (ENM) and the rigid cluster normal mode analysis (RCNMA) were used. Low-frequency normal modes from ENM correlate very well with ED modes in terms of directions of motions and relative amplitudes of motions. Notably, a similar performance was found if normal modes from RCNMA were used, despite a higher level of coarse graining. On average, the space spanned by the first quarter of ENM modes describes 84% of the space spanned by the five ED modes. Furthermore, no prominent differences for ED and CGNM modes among different protein structure classes (CATH classification) were found. This demonstrates the general potential of CGNM approaches for describing intrinsic motions of proteins with little computational cost. For selected cases, CGNM modes were found to be more robust among proteins that have the same topology or are of the same homologous superfamily than ED modes. In view of recent evidence regarding evolutionary conservation of vibrational dynamics, this suggests that ED modes, in some cases, might not be representative of the underlying dynamics that are characteristic of a whole family, probably due to insufficient sampling of some of the family members by MD.

Internal motion in protein crystal structures

The binding states of the substrates and the environment have significant influence on protein motion. We present the analysis of such motion derived from anisotropic atomic displacement parameters (ADPs) in a set of atomic resolution protein structures. Local structural motion caused by ligand binding as well as functional loops showing cooperative patterns of motion could be inferred. The results are in line with proposed protonation states, hydrogen bonding patterns and the location of distinctly flexible regions: we could locate the mobile active site loop in a virus integrase, distinguish the subdomains in RNAse A and hydroxynitrile lyase, and reconstruct the molecular architecture in a xylanase. We demonstrate that the ADP-based motion analysis provides information at high level of detail and that the structural changes needed for substrate attachment or release may be derived from single X-ray structures.

Using entropy maximization to understand the determinants of structural dynamics beyond native contact topology

Comparison of elastic network model predictions with experimental data has provided important insights on the dominant role of the network of inter-residue contacts in defining the global dynamics of proteins. Most of these studies have focused on interpreting the mean-square fluctuations of residues, or deriving the most collective, or softest, modes of motions that are known to be insensitive to structural and energetic details. However, with increasing structural data, we are in a position to perform a more critical assessment of the structure-dynamics relations in proteins, and gain a deeper understanding of the major determinants of not only the mean-square fluctuations and lowest frequency modes, but the covariance or the cross-correlations between residue fluctuations and the shapes of higher modes. A systematic study of a large set of NMR-determined proteins is analyzed using a novel method based on entropy maximization to demonstrate that the next level of refinement in the elastic network model description of proteins ought to take into consideration properties such as contact order (or sequential separation between contacting residues) and the secondary structure types of the interacting residues, whereas the types of amino acids do not play a critical role. Most importantly, an optimal description of observed cross-correlations requires the inclusion of destabilizing, as opposed to exclusively stabilizing, interactions, stipulating the functional significance of local frustration in imparting native-like dynamics. This study provides us with a deeper understanding of the structural basis of experimentally observed behavior, and opens the way to the development of more accurate models for exploring protein dynamics.

As more protein structures are solved, we are able to perform a more critical assessment of the relationship between protein structure and dynamics, and to gain a deeper understanding of the major determinants of structural dynamics. Here we perform a systematic study on a set of proteins structurally determined by NMR spectroscopy. The dynamics are analyzed using elastic network models and a novel method based on entropy maximization to demonstrate that properties such as contact order and secondary structure do play a role in defining the experimentally observed covariance data. Most importantly, an optimal description of observed cross-correlations requires the inclusion of destabilizing, as well as stabilizing, interactions, stipulating the functional significance of local frustration in imparting native-like dynamics.

Alzheimer's abeta(1-40) amyloid fibrils feature size-dependent mechanical properties

Amyloid fibrils are highly ordered protein aggregates that are associated with several pathological processes, including prion propagation and Alzheimer's disease. A key issue in amyloid science is the need to understand the mechanical properties of amyloid fibrils and fibers to quantify biomechanical interactions with surrounding tissues, and to identify mechanobiological mechanisms associated with changes of material properties as amyloid fibrils grow from nanoscale to microscale structures. Here we report a series of computational studies in which atomistic simulation, elastic network modeling, and finite element simulation are utilized to elucidate the mechanical properties of Alzheimer's Abeta(1-40) amyloid fibrils as a function of the length of the protein filament for both twofold and threefold symmetric amyloid fibrils. We calculate the elastic constants associated with torsional, bending, and tensile deformation as a function of the size of the amyloid fibril, covering fibril lengths ranging from nanometers to micrometers. The resulting Young's moduli are found to be consistent with available experimental measurements obtained from long amyloid fibrils, and predicted to be in the range of 20-31 GPa. Our results show that Abeta(1-40) amyloid fibrils feature a remarkable structural stability and mechanical rigidity for fibrils longer than approximately 100 nm. However, local instabilities that emerge at the ends of short fibrils (on the order of tens of nanometers) reduce their stability and contribute to their disassociation under extreme mechanical or chemical conditions, suggesting that longer amyloid fibrils are more stable. Moreover, we find that amyloids with lengths shorter than the periodicity of their helical pitch, typically between 90 and 130 nm, feature significant size effects of their bending stiffness due the anisotropy in the fibril's cross section. At even smaller lengths (50 nm), shear effects dominate lateral deformation of amyloid fibrils, suggesting that simple Euler-Bernoulli beam models fail to describe the mechanics of amyloid fibrils appropriately. Our studies reveal the importance of size effects in elucidating the mechanical properties of amyloid fibrils. This issue is of great importance for comparing experimental and simulation results, and gaining a general understanding of the biological mechanisms underlying the growth of ectopic amyloid materials.

Protein flexibility from discrete molecular dynamics simulations using quasi-physical potentials

We have applied all atoms discrete molecular dynamics (DMD) based on a quasi-physical potential to study the flexibility of an extended set of proteins for which atomistic MD simulations are available. The method uses pure physical potentials supplemented by information on secondary structure and despite its simplicity is able to reproduce with good accuracy the dynamics of proteins in solution. The method presents a clear improvement with respect to coarse-grained methods based on structure potentials and opens the possibility to explore dynamics of proteins out from the equilibrium and to trace conformational changes induced by interaction of proteins with both small and macromolecular ligands.

RigidFinder: a fast and sensitive method to detect rigid blocks in large macromolecular complexes

Advances in structure determination have made possible the analysis of large macromolecular complexes (some with nearly 10,000 residues, such as GroEL). The large-scale conformational changes associated with these complexes require new approaches. Historically, a crucial component of motion analysis has been the identification of moving rigid blocks from the comparison of different conformations. However, existing tools do not allow consistent block identification in very large structures. Here, we describe a novel method, RigidFinder, for such identification of rigid blocks from different conformations-across many scales, from large complexes to small loops. RigidFinder defines rigidity in terms of blocks, where inter-residue distances are conserved across conformations. Distance conservation, unlike the averaged values (e.g., RMSD) used by many other methods, allows for sensitive identification of motions. A further distinguishing feature of our method, is that, it is capable of finding blocks made from nonconsecutive fragments of multiple polypeptide chains. In our implementation, we utilize an efficient quasi-dynamic programming search algorithm that allows for real-time application to very large structures. RigidFinder can be used at a dedicated web server (http://rigidfinder.molmovdb.org). The server also provides links to examples at various scales such as loop closure, domain motions, partial refolding, and subunit shifts. Moreover, here we describe the detailed application of RigidFinder to four large structures: Pyruvate Phosphate Dikinase, T7 RNA polymerase, RNA polymerase II, and GroEL. The results of the method are in excellent agreement with the expert-described rigid blocks.

From electron microscopy maps to atomic structures using normal mode-based fitting

Electron microscopy (EM) has made possible to solve the structure of many proteins. However, the resolution of some of the EM maps is too low for interpretation at the atomic level, which is particularly important to describe function. We describe methods that combine low-resolution EM data with atomic structures for different conformations of the same protein in order to produce atomic models compatible with the EM map.We illustrate these methods with EM data from decavanadate-induced tubular crystals of a pseudo-phosphorylated intermediate of Ca-ATPase and the various atomic structures of other intermediates available in the Protein Data Bank (PDB). Determination of atomic structure permits not only to analyse protein-protein interactions in the crystals, but also to localize residues in the proximity of the crystallizing agent both within Ca-ATPase and between Ca-ATPase molecules.

Collective dynamics of periplasmic glutamine binding protein upon domain closure

The glutamine binding protein is a vital component of the associated ATP binding cassette transport systems responsible for the uptake of glutamine into the cell. We have investigated the global movements of this protein by molecular dynamics simulations and principal component analysis (PCA). We confirm that the most dominant mode corresponds to the biological function of the protein, i.e., a hinge-type motion upon ligand binding. The closure itself was directly observed from two independent trajectories whereby PCA was used to elucidate the nature of this closing reaction. Two intermediary states are identified and described in detail. The ligand binding induces the structural change of the hinge regions from a discontinuous beta-sheet to a continuous one, which also enhances softness of the hinge and modifies the direction of hinge motion to enable closing. We also investigated the convergence behavior of PCA modes, which were found to converge rather quickly when the associated magnitudes of the eigenvalues are well separated.

Structure-based predictive models for allosteric hot spots

In allostery, a binding event at one site in a protein modulates the behavior of a distant site. Identifying residues that relay the signal between sites remains a challenge. We have developed predictive models using support-vector machines, a widely used machine-learning method. The training data set consisted of residues classified as either hotspots or non-hotspots based on experimental characterization of point mutations from a diverse set of allosteric proteins. Each residue had an associated set of calculated features. Two sets of features were used, one consisting of dynamical, structural, network, and informatic measures, and another of structural measures defined by Daily and Gray [1]. The resulting models performed well on an independent data set consisting of hotspots and non-hotspots from five allosteric proteins. For the independent data set, our top 10 models using Feature Set 1 recalled 68–81% of known hotspots, and among total hotspot predictions, 58–67% were actual hotspots. Hence, these models have precision P = 58–67% and recall R = 68–81%. The corresponding models for Feature Set 2 had P = 55–59% and R = 81–92%. We combined the features from each set that produced models with optimal predictive performance. The top 10 models using this hybrid feature set had R = 73–81% and P = 64–71%, the best overall performance of any of the sets of models. Our methods identified hotspots in structural regions of known allosteric significance. Moreover, our predicted hotspots form a network of contiguous residues in the interior of the structures, in agreement with previous work. In conclusion, we have developed models that discriminate between known allosteric hotspots and non-hotspots with high accuracy and sensitivity. Moreover, the pattern of predicted hotspots corresponds to known functional motifs implicated in allostery, and is consistent with previous work describing sparse networks of allosterically important residues.

Allostery is the process whereby a molecule binds to one site in a protein and alters the function of a distant site. This phenomenon is ubiquitous, as proteins frequently must adapt their behavior to changes in the cellular milieu. The mechanism(s) underlying allostery remains incompletely understood. In particular, predictive models are needed that distinguish amino-acid residues that are critical to allostery, or “hotspots”, from non-hotspots. Here we have used data-mining approaches to infer rules that distinguish hotspots from non-hotspots. Starting with a data set of known hotspot and non-hotspot residues from a diverse set of allosteric proteins, the training data set, we applied machine learning to this data to “learn” models, or sets of rules, for distinguishing hotspots and non-hotspots by inferring associations between the classification (hotspot or non-hotspot) and an associated set of calculated attributes. Many models that showed the highest predictive power on the training data also exhibited high accuracy and sensitivity when applied to an independent data set. Moreover, the pattern of predicted hotspots in the proteins we studied was consistent with known structure/function relationships and previous work suggesting that a network of essential residues mediates the allosteric transition.

Coarse-grained description of protein internal dynamics: an optimal strategy for decomposing proteins in rigid subunits

The possibility of accurately describing the internal dynamics of proteins, in terms of movements of a few approximately-rigid subparts, is an appealing biophysical problem with important implications for the analysis and interpretation of data from experiments or numerical simulations. The problem is tackled here by means of a novel variational approach that exploits information about equilibrium fluctuations of interresidues distances, provided, e.g., by atomistic molecular dynamics simulations or coarse-grained models. No contiguity in primary sequence or in space is enforced a priori for amino acids grouped in the same rigid unit. The identification of the rigid protein moduli, or dynamical domains, provides valuable insight into functionally oriented aspects of protein internal dynamics. To illustrate this point, we first discuss the decomposition of adenylate kinase and HIV-1 protease and then extend the investigation to several representatives of the hydrolase enzymatic class. The known catalytic site of these enzymes is found to be preferentially located close to the boundary separating the two primary dynamical subdomains.

Relating protein conformational changes to packing efficiency and disorder

Changes in protein conformation play key roles in facilitating various biochemical processes, ranging from signaling and phosphorylation to transport and catalysis. While various factors that drive these motions such as environmental changes and binding of small molecules are well understood, specific causative effects on the structural features of the protein due to these conformational changes have not been studied on a large scale. Here, we study protein conformational changes in relation to two key structural metrics: packing efficiency and disorder. Packing has been shown to be crucial for protein stability and function by many protein design and engineering studies. We study changes in packing efficiency during conformational changes, thus extending the analysis from a static context to a dynamic perspective and report some interesting observations. First, we study various proteins that adopt alternate conformations and find that tendencies to show motion and change in packing efficiency are correlated: residues that change their packing efficiency show larger motions. Second, our results suggest that residues that show higher changes in packing during motion are located on the changing interfaces which are formed during these conformational changes. These changing interfaces are slightly different from shear or static interfaces that have been analyzed in previous studies. Third, analysis of packing efficiency changes in the context of secondary structure shows that, as expected, residues buried in helices show the least change in packing efficiency, whereas those embedded in bends are most likely to change packing. Finally, by relating protein disorder to motions, we show that marginally disordered residues which are ordered enough to be crystallized but have sequence patterns indicative of disorder show higher dislocation and a higher change in packing than ordered ones and are located mostly on the changing interfaces. Overall, our results demonstrate that between the two conformations, the cores of the proteins remain mostly intact, whereas the interfaces display the most elasticity, both in terms of disorder and change in packing efficiency. By doing a variety of tests, we also show that our observations are robust to the solvation state of the proteins.

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.

Fuzzy domains: new way of describing flexibility and interdependence of the protein domains

We proposed the innovative method of domain identification based on the concept of the fuzzy domains. In this method each residue of the protein can belong to several domains simultaneously with certain weights, which reflect to what extent this residue shares the motion pattern of the given domain. Our method allows describing the fuzzy boundaries between the domains and the gradual changes of the motion pattern from one domain to the other. It provides the reasonable compromise between the continuous change of the protein dynamics from one residue to the other and the discrete description of the structure in terms of small number of domains. We suggested quantitative criterion, which shows the overall degree of domain flexibility in the protein. The concept of the fuzzy domains provides an innovative way of visualization of domain flexibility, which makes the gradual transitions between the domains clearly visible and comparable to available experimental and structural data. In the future, the concept of the fuzzy domains can be used in the coarse-grained simulations of the domain dynamics in order to account for internal protein flexibility.

Allosteric communication occurs via networks of tertiary and quaternary motions in proteins

Allosteric proteins bind an effector molecule at one site resulting in a functional change at a second site. We hypothesize that allosteric communication in proteins relies upon networks of quaternary (collective, rigid-body) and tertiary (residue-residue contact) motions. We argue that cyclic topology of these networks is necessary for allosteric communication. An automated algorithm identifies rigid bodies from the displacement between the inactive and the active structures and constructs "quaternary networks" from these rigid bodies and the substrate and effector ligands. We then integrate quaternary networks with a coarse-grained representation of contact rearrangements to form "global communication networks" (GCNs). The GCN reveals allosteric communication among all substrate and effector sites in 15 of 18 multidomain and multimeric proteins, while tertiary and quaternary networks exhibit such communication in only 4 and 3 of these proteins, respectively. Furthermore, in 7 of the 15 proteins connected by the GCN, 50% or more of the substrate-effector paths via the GCN are "interdependent" paths that do not exist via either the tertiary or the quaternary network. Substrate-effector "pathways" typically are not linear but rather consist of polycyclic networks of rigid bodies and clusters of rearranging residue contacts. These results argue for broad applicability of allosteric communication based on structural changes and demonstrate the utility of the GCN. Global communication networks may inform a variety of experiments on allosteric proteins as well as the design of allostery into non-allosteric proteins.

Exploring the suitability of coarse-grained techniques for the representation of protein dynamics

A systematic study of two coarse-grained techniques for the description of protein dynamics is presented. The two techniques exploit either Brownian or discrete molecular dynamics algorithms applied in the context of simple C(alpha)-C(alpha) potentials, like those used in coarse-grained normal mode analysis. Coarse-grained simulations of the flexibility of protein metafolds are compared to those computed with fully atomistic molecular dynamics simulations using state-of-the-art physical potentials and explicit solvent. Both coarse-grained models efficiently capture critical features of the protein dynamics.

Close correspondence between the motions from principal component analysis of multiple HIV-1 protease structures and elastic network modes

The large number of available HIV-1 protease structures provides a remarkable sampling of conformations of the different conformational states, which can be viewed as direct structural information about the dynamics of the HIV-1 protease. After structure matching, we apply principal component analysis (PCA) to obtain the important apparent motions for both bound and unbound structures. There are significant similarities between the first few key motions and the first few low-frequency normal modes calculated from a static representative structure with an elastic network model (ENM), strongly suggesting that the variations among the observed structures and the corresponding conformational changes are facilitated by the low-frequency, global motions intrinsic to the structure. Similarities are also found when the approach is applied to an NMR ensemble, as well as to molecular dynamics (MD) trajectories. Thus, a sufficiently large number of experimental structures can directly provide important information about protein dynamics, but ENM can also provide similar sampling of conformations.

GANDivAWeb: a web server for detecting early folding units ("foldons") from protein 3D structures

Background

It has long been known that small regions of proteins tend to fold independently and are then stabilized by interactions between these distinct subunits or modules. Such units, also known as autonomous folding units (AFUs) or"foldons" play a key role in protein folding. A knowledge of such early folding units has diverse applications in protein engineering as well as in developing an understanding of the protein folding process. Such AFUs can also be used as model systems in order to study the structural organization of proteins.

Results

In an earlier work, we had utilized a global network partitioning algorithm to identify modules in proteins. We had shown that these modules correlate well with AFUs. In this work, we have developed a webserver, GANDivAWeb, to identify early folding units or "foldons" in networks using the algorithm described earlier. The website has three functionalities: (a) It is able to display information on the modularity of a database of 1420 proteins used in the original work, (b) It can take as input an uploaded PDB file, identify the modules using the GANDivA algorithm and email the results back to the user and (c) It can take as input an uploaded PDB file and a results file (obtained from functionality (b)) and display the results using the embedded viewer. The results include the module decomposition of the protein, plots of cartoon representations of the protein colored by module identity and connectivity as well as contour plots of the hydrophobicity and relative accessible surface area (RASA) distributions.

Conclusion

We believe that the GANDivAWeb server, will be a useful tool for scientists interested in the phenomena of protein folding as well as in protein engineering. Our tool not only provides a knowledge of the AFUs through a natural graph partitioning approach but is also able to identify residues that are critical during folding. It is our intention to use this tool to study the topological determinants of protein folding by analyzing the topological changes in proteins over the unfolding/folding pathways.

Coarse-grained models reveal functional dynamics--I. Elastic network models--theories, comparisons and perspectives

In this review, we summarize the progress on coarse-grained elastic network models (CG-ENMs) in the past decade. Theories were formulated to allow study of conformational dynamics in time/space frames of biological interest. Several highlighted models and their underlined hypotheses are introduced in physical depth. Important ENM offshoots, motivated to reproduce experimental data as well as to address the slow-mode-encoded configurational transitions, are also introduced. With the theoretical developments, computational cost is significantly reduced due to simplified potentials and coarse-grained schemes. Accumulating wealth of data suggest that ENMs agree equally well with experiment in describing equilibrium dynamics despite their distinct potentials and levels of coarse-graining. They however do differ in the slowest motional components that are essential to address large conformational changes of functional significance. The difference stems from the dissimilar curvatures of the harmonic energy wells described for each model. We also provide our views on the predictability of 'open to close' (open-->close) transitions of biomolecules on the basis of conformational selection theory. Lastly, we address the limitations of the ENM formalism which are partially alleviated by the complementary CG-MD approach, to be introduced in the second paper of this two-part series.

Dynamics of essential collective motions in proteins: theory

A general theoretical background is introduced for characterization of conformational motions in protein molecules, and for building reduced coarse-grained models of proteins, based on the statistical analysis of their phase trajectories. Using the projection operator technique, a system of coupled generalized Langevin equations is derived for essential collective coordinates, which are generated by principal component analysis of molecular dynamic trajectories. The number of essential degrees of freedom is not limited in the theory. An explicit analytic relation is established between the generalized Langevin equation for essential collective coordinates and that for the all-atom phase trajectory projected onto the subspace of essential collective degrees of freedom. The theory introduced is applied to identify correlated dynamic domains in a macromolecule and to construct coarse-grained models representing the conformational motions in a protein through a few interacting domains embedded in a dissipative medium. A rigorous theoretical background is provided for identification of dynamic correlated domains in a macromolecule. Examples of domain identification in protein G are given and employed to interpret NMR experiments. Challenges and potential outcomes of the theory are discussed.

Thorough validation of protein normal mode analysis: a comparative study with essential dynamics

The deformation patterns of a large set of representative proteins determined by essential dynamics extracted from atomistic simulations and coarse-grained normal mode analysis are compared. Our analysis shows that the deformational space obtained with both approaches is quite similar when taking into account a representative number of modes. The results provide not only a comprehensive validation of the use of a low-frequency modal spectrum to describe protein flexibility, but also a complete picture of normal mode limitations.

Normal-mode analysis of the glycine alpha1 receptor by three separate methods

Predicting collective dynamics and structural changes in biological macromolecules is pivotal toward a better understanding of many biological processes. Limitations due to large system sizes and inaccessible time scales have prompted the development of alternative techniques for the calculation of such motions. In this work, we present the results of a normal-mode analysis technique based on molecular mechanics that enables the calculation of accurate force-field based vibrations of extremely large molecules and compare it with two elastic network approximate models. When applied to the glycine alpha1 receptor, all three normal-mode analysis algorithms demonstrate an "iris-like" gating motion. Such gating motions have implications for understanding the effects of anesthetic and other ligand binding sites and for the means of transducing agonist binding into ion channel opening. Unlike the more approximate methods, molecular mechanics based analyses can also reveal approximate vibrational frequencies. Such analyses may someday allow the use of protein dynamics elucidated via normal-mode calculations as additional endpoints for future drug design.

How well can we understand large-scale protein motions using normal modes of elastic network models?

In this article, we apply a coarse-grained elastic network model (ENM) to study conformational transitions to address the following questions: How well can a conformational change be predicted by the mode motions? Is there a way to improve the model to gain better results? To answer these questions, we use a dataset of 170 pairs having "open" and "closed" structures from Gerstein's protein motion database. Our results show that the conformational transitions fall into three categories: 1), the transitions of these proteins that can be explained well by ENM; 2), the transitions that are not explained well by ENM, but the results are significantly improved after considering the rigidity of some residue clusters and modeling them accordingly; and 3), the intrinsic nature of these transitions, specifically the low degree of collectivity, prevents their conformational changes from being represented well with the low frequency modes of any elastic network models. Our results thus indicate that the applicability of ENM for explaining conformational changes is not limited by the size of the studied protein or even the scale of the conformational change. Instead, it depends strongly on how collective the transition is.