Automatic domain decomposition of proteins by a Gaussian Network Model

Surveying the energy landscape of coarse-grained mappings

Simulations of soft materials often adopt low-resolution coarse-grained (CG) models. However, the CG representation is not unique and its impact upon simulated properties is poorly understood. In this work, we investigate the space of CG representations for ubiquitin, which is a typical globular protein with 72 amino acids. We employ Monte Carlo methods to ergodically sample this space and to characterize its landscape. By adopting the Gaussian network model as an analytically tractable atomistic model for equilibrium fluctuations, we exactly assess the intrinsic quality of each CG representation without introducing any approximations in sampling configurations or in modeling interactions. We focus on two metrics, the spectral quality and the information content, that quantify the extent to which the CG representation preserves low-frequency, large-amplitude motions and configurational information, respectively. The spectral quality and information content are weakly correlated among high-resolution representations but become strongly anticorrelated among low-resolution representations. Representations with maximal spectral quality appear consistent with physical intuition, while low-resolution representations with maximal information content do not. Interestingly, quenching studies indicate that the energy landscape of mapping space is very smooth and highly connected. Moreover, our study suggests a critical resolution below which a "phase transition" qualitatively distinguishes good and bad representations.

Assignment of structural domains in proteins using diffusion kernels on graphs

Though proposing algorithmic approaches for protein domain decomposition has been of high interest, the inherent ambiguity to the problem makes it still an active area of research. Besides, accurate automated methods are in high demand as the number of solved structures for complex proteins is on the rise. While majority of the previous efforts for decomposition of 3D structures are centered on the developing clustering algorithms, employing enhanced measures of proximity between the amino acids has remained rather uncharted. If there exists a kernel function that in its reproducing kernel Hilbert space, structural domains of proteins become well separated, then protein structures can be parsed into domains without the need to use a complex clustering algorithm. Inspired by this idea, we developed a protein domain decomposition method based on diffusion kernels on protein graphs. We examined all combinations of four graph node kernels and two clustering algorithms to investigate their capability to decompose protein structures. The proposed method is tested on five of the most commonly used benchmark datasets for protein domain assignment plus a comprehensive non-redundant dataset. The results show a competitive performance of the method utilizing one of the diffusion kernels compared to four of the best automatic methods. Our method is also able to offer alternative partitionings for the same structure which is in line with the subjective definition of protein domain. With a competitive accuracy and balanced performance for the simple and complex structures despite relying on a relatively naive criterion to choose optimal decomposition, the proposed method revealed that diffusion kernels on graphs in particular, and kernel functions in general are promising measures to facilitate parsing proteins into domains and performing different structural analysis on proteins. The size and interconnectedness of the protein graphs make them promising targets for diffusion kernels as measures of affinity between amino acids. The versatility of our method allows the implementation of future kernels with higher performance. The source code of the proposed method is accessible at https://github.com/taherimo/kludo . Also, the proposed method is available as a web application from https://cbph.ir/tools/kludo .

HOPMA: Boosting Protein Functional Dynamics with Colored Contact Maps

In light of the recent very rapid progress in protein structure prediction, accessing the multitude of functional protein states is becoming more central than ever before. Indeed, proteins are flexible macromolecules, and they often perform their function by switching between different conformations. However, high-resolution experimental techniques such as X-ray crystallography and cryogenic electron microscopy can catch relatively few protein functional states. Many others are only accessible under physiological conditions in solution. Therefore, there is a pressing need to fill this gap with computational approaches. We present HOPMA, a novel method to predict protein functional states and transitions by using a modified elastic network model. The method exploits patterns in a protein contact map, taking its 3D structure as input, and excludes some disconnected patches from the elastic network. Combined with nonlinear normal mode analysis, this strategy boosts the protein conformational space exploration, especially when the input structure is highly constrained, as we demonstrate on a set of more than 400 transitions. Our results let us envision the discovery of new functional conformations, which were unreachable previously, starting from the experimentally known protein structures. The method is computationally efficient and available at https://github.com/elolaine/HOPMA and https://team.inria.fr/nano-d/software/nolb-normal-modes.

Macrophages show higher levels of engulfment after disruption of cis interactions between CD47 and the checkpoint receptor SIRPα

The macrophage checkpoint receptor SIRPα signals against phagocytosis by binding CD47 expressed on all cells - including macrophages. Here, we found that inhibiting cis interactions between SIRPα and CD47 on the same macrophage increased engulfment ('eating') by approximately the same level as inhibiting trans interactions. Antibody blockade of CD47, as pursued in clinical trials against cancer, was applied separately to human-derived macrophages and to red blood cell (RBC) targets for phagocytosis, and both scenarios produced surprisingly similar increases in RBC engulfment. Blockade of both macrophages and targets resulted in hyper-phagocytosis, and knockdown of macrophage-CD47 likewise increased engulfment of 'foreign' cells and particles, decreased the baseline inhibitory signaling of SIRPα, and linearly increased binding of soluble CD47 in trans, consistent with cis-trans competition. Many cell types express both SIRPα and CD47, including mouse melanoma B16 cells, and CRISPR-mediated deletions modulate B16 phagocytosis, consistent with cis-trans competition. Additionally, soluble SIRPα binding to human CD47 displayed on Chinese hamster ovary (CHO) cells was suppressed by SIRPα co-display, and atomistic computations confirm SIRPα bends and binds CD47 in cis Safety and efficacy profiles for CD47-SIRPα blockade might therefore reflect a disruption of both cis and trans interactions.

Protein dynamic communities from elastic network models align closely to the communities defined by molecular dynamics

Dynamic communities in proteins comprise the cohesive structural units that individually exhibit rigid body motions. These can correspond to structural domains, but are usually smaller parts that move with respect to one another in a protein's internal motions, key to its functional dynamics. Previous studies emphasized their importance to understand the nature of ligand-induced allosteric regulation. These studies reported that mutations to key community residues can hinder transmission of allosteric signals among the communities. Usually molecular dynamic (MD) simulations (~ 100 ns or longer) have been used to identify the communities-a demanding task for larger proteins. In the present study, we propose that dynamic communities obtained from MD simulations can also be obtained alternatively with simpler models-the elastic network models (ENMs). To verify this premise, we compare the specific communities obtained from MD and ENMs for 44 proteins. We evaluate the correspondence in communities from the two methods and compute the extent of agreement in the dynamic cross-correlation data used for community detection. Our study reveals a strong correspondence between the communities from MD and ENM and also good agreement for the residue cross-correlations. Importantly, we observe that the dynamic communities from MD can be closely reproduced with ENMs. With ENMs, we also compare the community structures of stable and unstable mutant forms of T4 Lysozyme with its wild-type. We find that communities for unstable mutants show substantially poorer agreement with the wild-type communities than do stable mutants, suggesting such ENM-based community structures can serve as a means to rapidly identify deleterious mutants.

Effects of Charge State, Charge Distribution, and Structure on the Ion Mobility of Protein Ions in Helium Gas: Results from Trajectory Method Calculations

Collision cross section (Ω) values of gas-phase ions of proteins and protein complexes are used to probe the structures of the corresponding species in solution. Ions of many proteins exhibit increasing Ω-values with increasing charge state but most Ω-values calculated for protein ions have used simple collision models that do not explicitly account for charge. Here we use a combination of ion mobility mass spectrometry experiments with helium gas and trajectory method calculations to characterize the extents to which increases in experimental Ω-values with increasing charge state may be attributed to increased momentum transfer concomitant with enhanced long-range interactions between the protein ion and helium atoms. Ubiquitin and C-to-N terminally linked diubiquitin ions generated from different solution conditions exhibit more than a 2-fold increase in Ω with increasing charge state. For native and energy-relaxed models of the proteins and most methods for distributing charge, Ω-values calculated using the trajectory method increase by less than 1% over the range of charge states observed from typical solution conditions used for native mass spectrometry. However, the calculated Ω-values increase by 10% to 15% over the full range of charge states observed from all solution conditions. Therefore, contributions from enhanced ion-induced dipole interactions with increasing charge state are significant but without additional structural changes can account for only a fraction of the increase in Ω observed experimentally. On the basis of these results, we suggest guidelines for calculating Ω-values in the context of applications in biophysics and structural biology.

An ambiguity principle for assigning protein structural domains

Ambiguity is the quality of being open to several interpretations. For an image, it arises when the contained elements can be delimited in two or more distinct ways, which may cause confusion. We postulate that it also applies to the analysis of protein three-dimensional structure, which consists in dividing the molecule into subunits called domains. Because different definitions of what constitutes a domain can be used to partition a given structure, the same protein may have different but equally valid domain annotations. However, knowledge and experience generally displace our ability to accept more than one way to decompose the structure of an object-in this case, a protein. This human bias in structure analysis is particularly harmful because it leads to ignoring potential avenues of research. We present an automated method capable of producing multiple alternative decompositions of protein structure (web server and source code available at www.dsimb.inserm.fr/sword/). Our innovative algorithm assigns structural domains through the hierarchical merging of protein units, which are evolutionarily preserved substructures that describe protein architecture at an intermediate level, between domain and secondary structure. To validate the use of these protein units for decomposing protein structures into domains, we set up an extensive benchmark made of expert annotations of structural domains and including state-of-the-art domain parsing algorithms. The relevance of our "multipartitioning" approach is shown through numerous examples of applications covering protein function, evolution, folding, and structure prediction. Finally, we introduce a measure for the structural ambiguity of protein molecules.

Multiscale Gaussian network model (mGNM) and multiscale anisotropic network model (mANM)

Gaussian network model (GNM) and anisotropic network model (ANM) are some of the most popular methods for the study of protein flexibility and related functions. In this work, we propose generalized GNM (gGNM) and ANM methods and show that the GNM Kirchhoff matrix can be built from the ideal low-pass filter, which is a special case of a wide class of correlation functions underpinning the linear scaling flexibility-rigidity index (FRI) method. Based on the mathematical structure of correlation functions, we propose a unified framework to construct generalized Kirchhoff matrices whose matrix inverse leads to gGNMs, whereas, the direct inverse of its diagonal elements gives rise to FRI method. With this connection, we further introduce two multiscale elastic network models, namely, multiscale GNM (mGNM) and multiscale ANM (mANM), which are able to incorporate different scales into the generalized Kirchhoff matrices or generalized Hessian matrices. We validate our new multiscale methods with extensive numerical experiments. We illustrate that gGNMs outperform the original GNM method in the B-factor prediction of a set of 364 proteins. We demonstrate that for a given correlation function, FRI and gGNM methods provide essentially identical B-factor predictions when the scale value in the correlation function is sufficiently large. More importantly, we reveal intrinsic multiscale behavior in protein structures. The proposed mGNM and mANM are able to capture this multiscale behavior and thus give rise to a significant improvement of more than 11% in B-factor predictions over the original GNM and ANM methods. We further demonstrate the benefits of our mGNM through the B-factor predictions of many proteins that fail the original GNM method. We show that the proposed mGNM can also be used to analyze protein domain separations. Finally, we showcase the ability of our mANM for the analysis of protein collective motions.

Large scale rigidity-based flexibility analysis of biomolecules

KINematics And RIgidity (KINARI) is an on-going project for in silico flexibility analysis of proteins. The new version of the software, Kinari-2, extends the functionality of our free web server KinariWeb, incorporates advanced web technologies, emphasizes the reproducibility of its experiments, and makes substantially improved tools available to the user. It is designed specifically for large scale experiments, in particular, for (a) very large molecules, including bioassemblies with high degree of symmetry such as viruses and crystals, (b) large collections of related biomolecules, such as those obtained through simulated dilutions, mutations, or conformational changes from various types of dynamics simulations, and (c) is intended to work as seemlessly as possible on the large, idiosyncratic, publicly available repository of biomolecules, the Protein Data Bank. We describe the system design, along with the main data processing, computational, mathematical, and validation challenges underlying this phase of the KINARI project.

The Intrinsic Dynamics and Unfolding Process of an Antibody Fab Fragment Revealed by Elastic Network Model

Antibodies have been increasingly used as pharmaceuticals in clinical treatment. Thermal stability and unfolding process are important properties that must be considered in antibody design. In this paper, the structure-encoded dynamical properties and the unfolding process of the Fab fragment of the phosphocholine-binding antibody McPC603 are investigated by use of the normal mode analysis of Gaussian network model (GNM). Firstly, the temperature factors for the residues of the protein were calculated with GNM and then compared with the experimental measurements. A good result was obtained, which provides the validity for the use of GNM to study the dynamical properties of the protein. Then, with this approach, the mean-square fluctuation (MSF) of the residues, as well as the MSF in the internal distance (MSFID) between all pairwise residues, was calculated to investigate the mobility and flexibility of the protein, respectively. It is found that the mobility and flexibility of the constant regions are higher than those of the variable regions, and the six complementarity-determining regions (CDRs) in the variable regions also exhibit relative large mobility and flexibility. The large amplitude motions of the CDRs are considered to be associated with the immune function of the antibody. In addition, the unfolding process of the protein was simulated by iterative use of the GNM. In our method, only the topology of protein native structure is taken into account, and the protein unfolding process is simulated through breaking the native contacts one by one according to the MSFID values between the residues. It is found that the flexible regions tend to unfold earlier. The sequence of the unfolding events obtained by our method is consistent with the hydrogen-deuterium exchange experimental results. Our studies imply that the unfolding behavior of the Fab fragment of antibody McPc603 is largely determined by the intrinsic dynamics of the protein.

SPECTRUS: A Dimensionality Reduction Approach for Identifying Dynamical Domains in Protein Complexes from Limited Structural Datasets

Identifying dynamical, quasi-rigid domains in proteins provides a powerful means for characterizing functionally oriented structural changes via a parsimonious set of degrees of freedom. In fact, the relative displacements of few dynamical domains usually suffice to rationalize the mechanics underpinning biological functionality in proteins and can even be exploited for structure determination or refinement purposes. Here we present SPECTRUS, a general scheme that, by solely using amino acid distance fluctuations, can pinpoint the innate quasi-rigid domains of single proteins or large complexes in a robust way. Consistent domains are usually obtained by using either a pair of representative structures or thousands of conformers. The functional insights offered by the approach are illustrated for biomolecular systems of very different size and complexity such as kinases, ion channels, and viral capsids. The decomposition tool is available as a software package and web server at spectrus.sissa.it.

Network-based identification of biomarkers coexpressed with multiple pathways

Unraveling complex molecular interactions and networks and incorporating clinical information in modeling will present a paradigm shift in molecular medicine. Embedding biological relevance via modeling molecular networks and pathways has become increasingly important for biomarker identification in cancer susceptibility and metastasis studies. Here, we give a comprehensive overview of computational methods used for biomarker identification, and provide a performance comparison of several network models used in studies of cancer susceptibility, disease progression, and prognostication. Specifically, we evaluated implication networks, Boolean networks, Bayesian networks, and Pearson’s correlation networks in constructing gene coexpression networks for identifying lung cancer diagnostic and prognostic biomarkers. The results show that implication networks, implemented in Genet package, identified sets of biomarkers that generated an accurate prediction of lung cancer risk and metastases; meanwhile, implication networks revealed more biologically relevant molecular interactions than Boolean networks, Bayesian networks, and Pearson’s correlation networks when evaluated with MSigDB database.

Perspective: Coarse-grained models for biomolecular systems

By focusing on essential features, while averaging over less important details, coarse-grained (CG) models provide significant computational and conceptual advantages with respect to more detailed models. Consequently, despite dramatic advances in computational methodologies and resources, CG models enjoy surging popularity and are becoming increasingly equal partners to atomically detailed models. This perspective surveys the rapidly developing landscape of CG models for biomolecular systems. In particular, this review seeks to provide a balanced, coherent, and unified presentation of several distinct approaches for developing CG models, including top-down, network-based, native-centric, knowledge-based, and bottom-up modeling strategies. The review summarizes their basic philosophies, theoretical foundations, typical applications, and recent developments. Additionally, the review identifies fundamental inter-relationships among the diverse approaches and discusses outstanding challenges in the field. When carefully applied and assessed, current CG models provide highly efficient means for investigating the biological consequences of basic physicochemical principles. Moreover, rigorous bottom-up approaches hold great promise for further improving the accuracy and scope of CG models for biomolecular systems.

Efficient prediction of protein conformational pathways based on the hybrid elastic network model

Various computational models have gained immense attention by analyzing the dynamic characteristics of proteins. Several models have achieved recognition by fulfilling either theoretical or experimental predictions. Nonetheless, each method possesses limitations, mostly in computational outlay and physical reality. These limitations remind us that a new model or paradigm should advance theoretical principles to elucidate more precisely the biological functions of a protein and should increase computational efficiency. With these critical caveats, we have developed a new computational tool that satisfies both physical reality and computational efficiency. In the proposed hybrid elastic network model (HENM), a protein structure is represented as a mixture of rigid clusters and point masses that are connected with linear springs. Harmonic analyses based on the HENM have been performed to generate normal modes and conformational pathways. The results of the hybrid normal mode analyses give new physical insight to the 70S ribosome. The feasibility of the conformational pathways of hybrid elastic network interpolation (HENI) was quantitatively evaluated by comparing three different overlap values proposed in this paper. A remarkable observation is that the obtained mode shapes and conformational pathways are consistent with each other. Our timing results show that HENM has some advantage in computational efficiency over a coarse-grained model, especially for large proteins, even though it takes longer to construct the HENM. Consequently, the proposed HENM will be one of the best alternatives to the conventional coarse-grained ENMs and all-atom based methods (such as molecular dynamics) without loss of physical reality.

SCEDS: protein fragments for molecular replacement in Phaser

A method is described for generating protein fragments suitable for use as molecular-replacement (MR) template models. The template model for a protein suspected to undergo a conformational change is perturbed along combinations of low-frequency normal modes of the elastic network model. The unperturbed structure is then compared with each perturbed structure in turn and the structurally invariant regions are identified by analysing the difference distance matrix. These fragments are scored with SCEDS, which is a combined measure of the sphericity of the fragments, the continuity of the fragments with respect to the polypeptide chain, the equality in number of atoms in the fragments and the density of C(α) atoms in the triaxial ellipsoid of the fragment extents. The fragment divisions with the highest SCEDS are then used as separate template models for MR. Test cases show that where the protein contains fragments that undergo a change in juxtaposition between template model and target, SCEDS can identify fragments that lead to a lower R factor after ten cycles of all-atom refinement with REFMAC5 than the original template structure. The method has been implemented in the software Phaser.

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.

Mechanism of bacterial signal transduction revealed by molecular dynamics of Tsr dimers and trimers of dimers in lipid vesicles

Bacterial chemoreceptors provide an important model for understanding signalling processes. In the serine receptor Tsr from E. coli, a binding event in the periplasmic domain of the receptor dimer causes a shift in a single transmembrane helix of roughly 0.15 nm towards the cytoplasm. This small change is propagated through the ∼22 nm length of the receptor, causing downstream inhibition of the kinase CheA. This requires interactions within a trimer of receptor dimers. Additionally, the signal is amplified across a 53,000 nm² array of chemoreceptor proteins, including ∼5,200 receptor trimers-of-dimers, at the cell pole. Despite a wealth of experimental data on the system, including high resolution structures of individual domains and extensive mutagenesis data, it remains uncertain how information is communicated across the receptor from the binding event to the downstream effectors. We present a molecular model of the entire Tsr dimer, and examine its behaviour using coarse-grained molecular dynamics and elastic network modelling. We observe a large bending in dimer models between the linker domain HAMP and coiled-coil domains, which is supported by experimental data. Models of the trimer of dimers, built from the dimer models, are more constrained and likely represent the signalling state. Simulations of the models in a 70 nm diameter vesicle with a biologically realistic lipid mixture reveal specific lipid interactions and oligomerisation of the trimer of dimers. The results indicate a mechanism whereby small motions of a single helix can be amplified through HAMP domain packing, to initiate large changes in the whole receptor structure.

To understand cell signalling events requires a physical model of the structure and behaviour of the signalling proteins involved. The methyl-accepting chemoreceptor proteins direct bacterial movement towards food sources and away from toxins. Based on experimental data we have built structural models of the serine chemoreceptor (Tsr) as a dimer, which is incapable of activating the downstream kinase CheA, and as a trimer of dimers, which can activate CheA. We have performed molecular dynamics simulation to reveal the behaviour of these two forms in a planar lipid bilayer and in a 70 nm diameter lipid vesicle with a mixture of lipids mimicking the E. coli inner membrane. We show that in isolation the dimers undergo a bending movement around the central HAMP domain, whereas the trimer-of-dimers model does not. Comparison with published experimental data suggests that these bending motions are real, and that they occur in the trimer of dimers only in response to ligand binding. Drawing together these observations with studies showing that the signalling event involves small piston motions in the transmembrane helices suggests that the bending motion is frustrated in the unliganded trimer of dimers, and that ligand binding induces bending by repacking the HAMP interface.

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.

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.

On the applicability of elastic network normal modes in small-molecule docking

Incorporating backbone flexibility into protein-ligand docking is still a challenging problem. In protein-protein docking, normal mode analysis (NMA) has become increasingly popular as it can be used to describe the collective motions of a biological system, but the question of whether NMA can also be useful in predicting the conformational changes observed upon small-molecule binding has only been addressed in a few case studies. Here, we describe a large-scale study on the applicability of NMA for protein-ligand docking using 433 apo/holo pairs of the Astex data sets. On the basis of sets of the first normal modes from the apo structure, we first generated for each paired holo structure a set of conformations that optimally reproduce its C(α) trace with respect to the underlying normal mode subspace. Using AutoDock, GOLD, and FlexX we then docked the original ligands into these conformations to assess how the docking performance depends on the number of modes used to reproduce the holo structure. The results of our study indicate that, even for such a best-case scenario, the use of normal mode analysis in small-molecule docking is restricted and that a general rule on how many modes to use does not seem to exist or at least is not easy to find.

Vinculin motion modes analysis with elastic network model

Vinculin is an important protein for the linkage between adhesion molecules and the actin cytoskeleton. The activation mechanism of vinculin is still controversial. In order to provide useful information for a better understanding of its activation, we analyze the motion mode of vinculin with elastic network model in this work. The results show that, to some extent, the five domains will present structural rigidity in the motion process. The differences between the structure fluctuations of these domains are significant. When vinculin interacted with other partners, the central long alpha-helix of the first domain becomes bent. This bending deformation can weaken the interaction between the first domain and the tail domain. This motion mode of the first domain is in good agreement with the information extracted from some realistic complex structures. With the aid of the anisotropy elastic network mode, we analyze the motion directions of these domains. The fourth domain has a rotational motion. This rotation is favorable for the releasing of the tail domain from the pincer-like clamp, which is formed by the first and the third domain. All these motion modes are an inherent feature of the structure, and these modes mainly depend on the topology character of the structure.

Automating the search of molecular motor templates by evolutionary methods

Biological molecular motors are nanoscale devices capable of transforming chemical energy into mechanical work, which are being researched in many scientific disciplines. From a computational point of view, the characteristics and dynamics of these motors are studied at multiple time scales, ranging from very detailed and complex molecular dynamics simulations spanning a few microseconds, to extremely simple and coarse-grained theoretical models of their working cycles. However, this research is performed only in the (relatively few) instances known from molecular biology. In this work, results from elastic network analysis and behaviour-finding methods are applied to explore a subset of the configuration space of template molecular structures that are able to transform chemical energy into directed movement, for a fixed instance of working cycle. While using methods based on elastic networks limits the scope of our results, it enables the implementation of computationally lightweight methods, in a way that evolutionary search techniques can be applied to discover novel molecular motor templates. The results show that molecular motion can be attained from a variety of structural configurations, when a functional working cycle is provided. Additionally, these methods enable a new computational way to test hypotheses about molecular motors.

Minimalist models for proteins: a comparative analysis

The last decade has witnessed a renewed interest in the coarse-grained (CG) models for biopolymers, also stimulated by the needs of modern molecular biology, dealing with nano- to micro-sized bio-molecular systems and larger than microsecond timescale. This combination of size and timescale is, in fact, hard to access by atomic-based simulations. Coarse graining the system is a route to be followed to overcome these limits, but the ways of practically implementing it are many and different, making the landscape of CG models very vast and complex. In this paper, the CG models are reviewed and their features, applications and performances compared. This analysis, restricted to proteins, focuses on the minimalist models, namely those reducing at minimum the number of degrees of freedom without losing the possibility of explicitly describing the secondary structures. This class includes models using a single or a few interacting centers (beads) for each amino acid. From this analysis several issues emerge. The difficulty in building these models resides in the need for combining transferability/predictive power with the capability of accurately reproducing the structures. It is shown that these aspects could be optimized by accurately choosing the force field (FF) terms and functional forms, and combining different parameterization procedures. In addition, in spite of the variety of the minimalist models, regularities can be found in the parameters values and in FF terms. These are outlined and schematically presented with the aid of a generic phase diagram of the polypeptide in the parameter space and, hopefully, could serve as guidelines for the development of minimalist models incorporating the maximum possible level of predictive power and structural accuracy.

Integrating ion mobility mass spectrometry with molecular modelling to determine the architecture of multiprotein complexes

Current challenges in the field of structural genomics point to the need for new tools and technologies for obtaining structures of macromolecular protein complexes. Here, we present an integrative computational method that uses molecular modelling, ion mobility-mass spectrometry (IM-MS) and incomplete atomic structures, usually from X-ray crystallography, to generate models of the subunit architecture of protein complexes. We begin by analyzing protein complexes using IM-MS, and by taking measurements of both intact complexes and sub-complexes that are generated in solution. We then examine available high resolution structural data and use a suite of computational methods to account for missing residues at the subunit and/or domain level. High-order complexes and sub-complexes are then constructed that conform to distance and connectivity constraints imposed by IM-MS data. We illustrate our method by applying it to multimeric protein complexes within the Escherichia coli replisome: the sliding clamp, (β₂), the γ complex (γ₃δδ′), the DnaB helicase (DnaB₆) and the Single-Stranded Binding Protein (SSB₄).

Generalized spring tensor models for protein fluctuation dynamics and conformation changes

BACKGROUND

In the last decade, various coarse-grained elastic network models have been developed to study the large-scale motions of proteins and protein complexes where computer simulations using detailed all-atom models are not feasible. Among these models, the Gaussian Network Model (GNM) and Anisotropic Network Model (ANM) have been widely used. Both models have strengths and limitations. GNM can predict the relative magnitudes of protein fluctuations well, but due to its isotropy assumption, it can not be applied to predict the directions of the fluctuations. In contrast, ANM adds the ability to do the latter, but loses a significant amount of precision in the prediction of the magnitudes.

RESULTS

In this article, we develop a single model, called generalized spring tensor model (STeM), that is able to predict well both the magnitudes and the directions of the fluctuations. Specifically, STeM performs equally well in B-factor predictions as GNM and has the ability to predict the directions of fluctuations as ANM. This is achieved by employing a physically more realistic potential, the Go-like potential. The potential, which is more sophisticated than that of either GNM or ANM, though adds complexity to the derivation process of the Hessian matrix (which fortunately has been done once for all and the MATLAB code is freely available electronically at http://www.cs.iastate.edu/~gsong/STeM), causes virtually no performance slowdown.

CONCLUSIONS

Derived from a physically more realistic potential, STeM proves to be a natural solution in which advantages that used to exist in two separate models, namely GNM and ANM, are achieved in one single model. It thus lightens the burden to work with two separate models and to relate the modes of GNM with those of ANM at times. By examining the contributions of different interaction terms in the Gō potential to the fluctuation dynamics, STeM reveals, (i) a physical explanation for why the distance-dependent, inverse distance square (i.e., 1/(r)2) spring constants perform better than the uniform ones, and (ii), the importance of three-body and four-body interactions to properly modeling protein dynamics.

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.

BlockMaster: partitioning protein kinase structures using normal-mode analysis

Protein kinases are key signaling enzymes which are dysregulated in many health disorders and therefore represent major targets of extensive drug discovery efforts. Their regulation in the cell is exerted via various mechanisms, including control of the 3D conformation of their catalytic domains. We developed a procedure, BlockMaster, for partitioning protein structures into semirigid blocks and flexible regions based on residue-residue correlations calculated from normal modes. BlockMaster provided correct partitioning into domains and subdomains of several test set proteins for which documented expert annotation of subdomains exists. When applied to representative structures of protein kinases, BlockMaster identified semirigid blocks within the traditional N-terminal and C-terminal lobes of the kinase domain. In general, the block regions had elevated helical content and reduced, but significant, coil content compared to the nonblock (flexible) regions. The specificity-determining regions, previously used to derive inhibitory peptides, were found to be more flexible in the tyrosine kinases than in serine/threonine kinases. Two blocks were identified which spanned both lobes. The first, which we termed the "pivot" block, included the alphaC-beta4 loop in the N-terminal lobe and part of the activation loop in the C-terminal lobe and appeared in both the active and inactive conformations of the kinases. The second, which we termed the "loop" block, differed between the active and inactive conformations. In the structures of active kinases, this block included part of the activation loop in the C-terminal lobe and the alphaC helix in the N-terminal lobe, representing a known interaction that stabilizes the active conformation. In the inactive structures, this block included G loop residues instead of the alphaC residues. This novel inactive "loop" block may stabilize the inactive conformation and thus downregulate kinase activity.

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.

StoneHinge: hinge prediction by network analysis of individual protein structures

Hinge motions are important for molecular recognition, and knowledge of their location can guide the sampling of protein conformations for docking. Predicting domains and intervening hinges is also important for identifying structurally self-determinate units and anticipating the influence of mutations on protein flexibility and stability. Here we present StoneHinge, a novel approach for predicting hinges between domains using input from two complementary analyses of noncovalent bond networks: StoneHingeP, which identifies domain-hinge-domain signatures in ProFlex constraint counting results, and StoneHingeD, which does the same for DomDecomp Gaussian network analyses. Predictions for the two methods are compared to hinges defined in the literature and by visual inspection of interpolated motions between conformations in a series of proteins. For StoneHingeP, all the predicted hinges agree with hinge sites reported in the literature or observed visually, although some predictions include extra residues. Furthermore, no hinges are predicted in six hinge-free proteins. On the other hand, StoneHingeD tends to overpredict the number of hinges, while accurately pinpointing hinge locations. By determining the consensus of their results, StoneHinge improves the specificity, predicting 11 of 13 hinges found both visually and in the literature for nine different open protein structures, and making no false-positive predictions. By comparison, a popular hinge detection method that requires knowledge of both the open and closed conformations finds 10 of the 13 known hinges, while predicting four additional, false hinges.

HingeMaster: normal mode hinge prediction approach and integration of complementary predictors

Protein motion is often the link between structure and function and a substantial fraction of proteins move through a domain hinge bending mechanism. Predicting the location of the hinge from a single structure is thus a logical first step towards predicting motion. Here, we describe ways to predict the hinge location by grouping residues with correlated normal-mode motions. We benchmarked our normal-mode based predictor against a gold standard set of carefully annotated hinge locations taken from the Database of Macromolecular Motions. We then compared it with three existing structure-based hinge predictors (TLSMD, StoneHinge, and FlexOracle), plus HingeSeq, a sequence-based hinge predictor. Each of these methods predicts hinges using very different sources of information-normal modes, experimental thermal factors, bond constraint networks, energetics, and sequence, respectively. Thus it is logical that using these algorithms together would improve predictions. We integrated all the methods into a combined predictor using a weighted voting scheme. Finally, we encapsulated all our results in a web tool which can be used to run all the predictors on submitted proteins and visualize the results.

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.

Characterization of protein conformational states by normal-mode frequencies

Conformational change in polymers including proteins is central to many molecular processes. Defining conformational states, however, remains a difficult and increasingly common problem, with many existing methods based on arbitrary or potentially unrepresentative measures. Furthermore, the expanding length of molecular dynamics simulations and direct observation of transitions between different energy basins suggest that this issue will only become evermore important. Methods commonly used to characterize conformational states include principal component analysis, root-mean-square deviation-based clustering, and geometric measurements such as hinge angles and distances. Here we present a method where the eigenvector frequencies derived from a Gaussian network model (Bahar, I.; Atilgan, A. R.; Erman, B. Folding Des. 1997, 2, 173-181) of a trajectory of structures from a molecular dynamics simulation are used to describe the state of the protein at each time point. We apply the method to three proteins that share the same fold as the type II periplasmic binding proteins: The lysine-arginine-ornithine-binding protein, the glutamine-binding protein, and the ligand-binding domain from the NR1 N-methyl-D-aspartate receptor. We find that the method can distinguish different states in good agreement with a variety of previous analyses and additionally provides information on the dynamic properties of that system at a given time point.

DDOMAIN: Dividing structures into domains using a normalized domain-domain interaction profile

Dividing protein structures into domains is proven useful for more accurate structural and functional characterization of proteins. Here, we develop a method, called DDOMAIN, that divides structure into DOMAINs using a normalized contact-based domain-domain interaction profile. Results of DDOMAIN are compared to AUTHORS annotations (domain definitions are given by the authors who solved protein structures), as well as to popular SCOP and CATH annotations by human experts and automatic programs. DDOMAIN's automatic annotations are most consistent with the AUTHORS annotations (90% agreement in number of domains and 88% agreement in both number of domains and at least 85% overlap in domain assignment of residues) if its three adjustable parameters are trained by the AUTHORS annotations. By comparison, the agreement is 83% (81% with at least 85% overlap criterion) between SCOP-trained DDOMAIN and SCOP annotations and 77% (73%) between CATH-trained DDOMAIN and CATH annotations. The agreement between DDOMAIN and AUTHORS annotations goes beyond single-domain proteins (97%, 82%, and 56% for single-, two-, and three-domain proteins, respectively). For an "easy" data set of proteins whose CATH and SCOP annotations agree with each other in number of domains, the agreement is 90% (89%) between "easy-set"-trained DDOMAIN and CATH/SCOP annotations. The consistency between SCOP-trained DDOMAIN and SCOP annotations is superior to two other recently developed, SCOP-trained, automatic methods PDP (protein domain parser), and DomainParser 2. We also tested a simple consensus method made of PDP, DomainParser 2, and DDOMAIN and a different version of DDOMAIN based on a more sophisticated statistical energy function. The DDOMAIN server and its executable are available in the services section on http://sparks.informatics.iupui.edu.

FlexOracle: predicting flexible hinges by identification of stable domains

Background

Protein motions play an essential role in catalysis and protein-ligand interactions, but are difficult to observe directly. A substantial fraction of protein motions involve hinge bending. For these proteins, the accurate identification of flexible hinges connecting rigid domains would provide significant insight into motion. Programs such as GNM and FIRST have made global flexibility predictions available at low computational cost, but are not designed specifically for finding hinge points.

Results

Here we present the novel FlexOracle hinge prediction approach based on the ideas that energetic interactions are stronger within structural domains than between them, and that fragments generated by cleaving the protein at the hinge site are independently stable. We implement this as a tool within the Database of Macromolecular Motions, MolMovDB.org. For a given structure, we generate pairs of fragments based on scanning all possible cleavage points on the protein chain, compute the energy of the fragments compared with the undivided protein, and predict hinges where this quantity is minimal. We present three specific implementations of this approach. In the first, we consider only pairs of fragments generated by cutting at a single location on the protein chain and then use a standard molecular mechanics force field to calculate the enthalpies of the two fragments. In the second, we generate fragments in the same way but instead compute their free energies using a knowledge based force field. In the third, we generate fragment pairs by cutting at two points on the protein chain and then calculate their free energies.

Conclusion

Quantitative results demonstrate our method's ability to predict known hinges from the Database of Macromolecular Motions.

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.

Optimization and evaluation of a coarse-grained model of protein motion using x-ray crystal data

Simple coarse-grained models, such as the Gaussian network model, have been shown to capture some of the features of equilibrium protein dynamics. We extend this model by using atomic contacts to define residue interactions and introducing more than one interaction parameter between residues. We use B-factors from 98 ultra-high resolution (<or=1.0 A) x-ray crystal structures to optimize the interaction parameters. The average correlation between Gaussian network-model fluctuation predictions and the B-factors is 0.64 for the data set, consistent with a previous large-scale study. By separating residue interactions into covalent and noncovalent, we achieve an average correlation of 0.74, and addition of ligands and cofactors further improves the correlation to 0.75. However, further separating the noncovalent interactions into nonpolar, polar, and mixed yields no significant improvement. The addition of simple chemical information results in better prediction quality without increasing the size of the coarse-grained model.

The change of protein intradomain mobility on ligand binding: is it a commonly observed phenomenon?

Analysis of changes in the dynamics of protein domains on ligand binding is important in several aspects: for the understanding of the hierarchical nature of protein folding and dynamics at equilibrium; for analysis of signal transduction mechanisms triggered by ligand binding, including allostery; for drug design; and for construction of biosensors reporting on the presence of target ligand in studied media. In this work we use the recently developed HCCP computational technique for the analysis of stabilities of dynamic domains in proteins, their intrinsic motions and of their changes on ligand binding. The work is based on comparative studies of 157 ligand binding proteins, for which several crystal structures (in ligand-free and ligand-bound forms) are available. We demonstrate that the domains of the proteins presented in the Protein DataBank are far more robust than it was thought before: in the majority of the studied proteins (152 out of 157), the ligand binding does not lead to significant change of domain stability. The exceptions from this rule are only four bacterial periplasmic transport proteins and calmodulin. Thus, as a rule, the pattern of correlated motions in dynamic domains, which determines their stability, is insensitive to ligand binding. This rule may be the general feature for a vast majority of proteins.

Dynamic protein domains: identification, interdependence, and stability

Existing methods of domain identification in proteins usually provide no information about the degree of domain independence and stability. However, this information is vital for many areas of protein research. The recently developed hierarchical clustering of correlation patterns (HCCP) technique provides machine-based domain identification in a computationally simple and physically consistent way. Here we present the modification of this technique, which not only allows determination of the most plausible number of dynamic domains but also makes it possible to estimate the degree of their independence (the extent of correlated motion) and stability (the range of environmental conditions, where domains remain intact). With this technique we provided domain assignments and calculated intra- and interdomain correlations and interdomain energies for >2500 test proteins. It is shown that mean intradomain correlation of motions can serve as a quantitative criterion of domain independence, and the HCCP stability gap is a measure of their stability. Our data show that the motions of domains with high stability are usually independent. In contrast, the domains with moderate stability usually exhibit a substantial degree of correlated motions. It is shown that in multidomain proteins the domains are most stable if they are of similar size, and this correlates with the observed abundance of such proteins.

Coarse-grained normal mode analysis in structural biology

The realization that experimentally observed functional motions of proteins can be predicted by coarse-grained normal mode analysis has renewed interest in applications to structural biology. Notable applications include the prediction of biologically relevant motions of proteins and supramolecular structures driven by their structure-encoded collective dynamics; the refinement of low-resolution structures, including those determined by cryo-electron microscopy; and the identification of conserved dynamic patterns and mechanically key regions within protein families. Additionally, hybrid methods that couple atomic simulations with deformations derived from coarse-grained normal mode analysis are able to sample collective motions beyond the range of conventional molecular dynamics simulations. Such applications have provided great insight into the underlying principles linking protein structures to their dynamics and their dynamics to their functions.