Coarse-grained normal mode analysis in structural biology

Predicted dynamical couplings of protein residues characterize catalysis, transport and allostery

MOTIVATION

Protein function is intrinsically linked to native dynamics, but the systematic characterization of functionally relevant dynamics remains elusive besides specific examples. Here we exhaustively characterize three types of dynamical couplings between protein residues: co-directionality (moving along collinear directions), coordination (small fluctuations of the interatomic distance) and deformation (the extent by which perturbations applied at one residue modify the local structure of the other one), which we analytically compute through the torsional network model.

RESULTS

We find that ligand binding sites are characterized by large within-site coordination and co-directionality, much larger than expected for generic sets of residues with equivalent sequence distances. In addition, catalytic sites are characterized by high coordination couplings with other residues in the protein, supporting the view that the overall protein structure facilitates the catalytic dynamics. The binding sites of allosteric effectors are characterized by comparably smaller coordination and higher within-site deformation than other ligands, which supports their dynamic nature. Allosteric inhibitors are coupled to the active site more frequently through deformation than through coordination, while the contrary holds for activators. We characterize the dynamical couplings of the sodium-dependent Leucine transporter protein (LeuT). The couplings between and within sites progress consistently along the transport cycle, providing a mechanistic description of the coupling between the uptake and release of ions and substrate, and they highlight qualitative differences between the wild-type and a mutant for which chloride is necessary for transport.

AVAILABILITY AND IMPLEMENTATION

The program tnm is freely available at https://github.com/ugobas/tnm.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Coarse-Grained Models of RNA Nanotubes for Large Time Scale Studies in Biomedical Applications

In order to describe the physical properties of large time scale biological systems, coarse-grained models play an increasingly important role. In this paper we develop Coarse-Grained (CG) models for RNA nanotubes and then, by using Molecular Dynamics (MD) simulation, we study their physical properties. Our exemplifications include RNA nanotubes of 40 nm long, equivalent to 10 RNA nanorings connected in series. The developed methodology is based on a coarse-grained representation of RNA nanotubes, where each coarse bead represents a group of atoms. By decreasing computation cost, this allows us to make computations feasible for realistic structures of interest. In particular, for the developed coarse-grained models with three bead approximations, we calculate the histograms for the bond angles and the dihedral angles. From the dihedral angle histograms, we analyze the characteristics of the links used to build the nanotubes. Furthermore, we also calculate the bead distances along the chains of RNA strands in the nanoclusters. The variations in these features with the size of the nanotube are discussed in detail. Finally, we present the results on the calculation of the root mean square deviations for a developed RNA nanotube to demonstrate the equilibration of the systems for drug delivery and other biomedical applications such as medical imaging and tissue engineering.

Identification of Alternative Allosteric Sites in Glycolytic Enzymes for Potential Use as Species-Specific Drug Targets

Three allosteric glycolytic enzymes, phosphofructokinase, glyceraldehyde-3 phosphate dehydrogenase and pyruvate kinase, associated with bacterial, parasitic and human species, were explored to identify potential allosteric sites that would be used as prime targets for species-specific drug design purposes using a newly developed approach which incorporates solvent mapping, elastic network modeling, sequence and structural alignments. The majority of binding sites detected by solvent mapping overlapped with the interface regions connecting the subunits, thus appeared as promising target sites for allosteric regulation. Each binding site was then evaluated by its ability to alter the global dynamics of the receptor defined by the percentage change in the frequencies of the lowest-frequency modes most significantly and as anticipated, the most effective ones were detected in the vicinity of the well-reported catalytic and allosteric sites. Furthermore, some of our proposed regions intersected with experimentally resolved sites which are known to be critical for activity regulation, which further validated our approach. Despite the high degree of structural conservation encountered between bacterial/parasitic and human glycolytic enzymes, the majority of the newly presented allosteric sites exhibited a low degree of sequence conservation which further increased their likelihood to be used as species-specific target regions for drug design studies.

Perturb-Scan-Pull: A Novel Method Facilitating Conformational Transitions in Proteins

Conformational transitions in proteins facilitate precise physiological functions. Therefore, it is crucial to understand the mechanisms underlying these processes to modulate protein function. Yet, studying structural and dynamical properties of proteins is notoriously challenging due to the complexity of the underlying potential energy surfaces (PES). We have previously developed the perturbation-response scanning (PRS) method to identify key residues that participate in the communication network responsible for specific conformational transitions. PRS is based on a residue-by-residue scan of the protein to determine the subset of residues/forces which provide the closest conformational change leading to a target conformational state, inasmuch as linear response theory applies to these motions. Here, we develop a novel method to further evaluate if conformational transitions may be triggered on the PES. We aim to study functionally relevant conformational transitions in proteins by using results obtained from PRS and feeding them as inputs to steered molecular dynamics simulations. The success and the transferability of the method are evaluated on three protein systems having different complexities of motion on the PES: calmodulin, adenylate kinase, and bacterial ferric binding protein. We find that the method captures the target conformation, while providing key residues and the optimum paths with relatively low free energy profiles.

Carbohydrate-Binding Capability and Functional Conformational Changes of AbnE, an Arabino-oligosaccharide Binding Protein

ABC importers are membrane proteins responsible for the transport of nutrients into the cells of prokaryotes. Although the structures of ABC importers vary, all contain four conserved domains: two nucleotide-binding domains (NBDs), which bind and hydrolyze ATP, and two transmembrane domains (TMDs), which help translocate the substrate. ABC importers are also dependent on an additional protein component, a high-affinity substrate-binding protein (SBP) that specifically binds the target ligand for delivery to the appropriate ABC transporter. AbnE is a SBP belonging to the ABC importer for arabino-oligosaccharides in the Gram-positive thermophilic bacterium Geobacillus stearothermophilus. Using isothermal titration calorimetry (ITC), purified AbnE was shown to bind medium-sized arabino-oligosaccharides, in the range of arabino-triose (A3) to arabino-octaose (A8), all with K_d values in the nanomolar range. We describe herein the 3D structure of AbnE in its closed conformation in complex with a wide range of arabino-oligosaccharide substrates (A2-A8). These structures provide the basis for the detailed structural analysis of the AbnE-sugar complexes, and together with complementary quantum chemical calculations, site-specific mutagenesis, and isothermal titration calorimetry (ITC) experiments, provide detailed insights into the AbnE-substrate interactions involved. Small-angle X-ray scattering (SAXS) experiments and normal mode analysis (NMA) are used to study the conformational changes of AbnE, and these data, taken together, suggest clues regarding its binding mode to the full ABC importer.

Exploring Successful Parameter Region for Coarse-Grained Simulation of Biomolecules by Bayesian Optimization and Active Learning

Accompanied with an increase of revealed biomolecular structures owing to advancements in structural biology, the molecular dynamics (MD) approach, especially coarse-grained (CG) MD suitable for macromolecules, is becoming increasingly important for elucidating their dynamics and behavior. In fact, CG-MD simulation has succeeded in qualitatively reproducing numerous biological processes for various biomolecules such as conformational changes and protein folding with reasonable calculation costs. However, CG-MD simulations strongly depend on various parameters, and selecting an appropriate parameter set is necessary to reproduce a particular biological process. Because exhaustive examination of all candidate parameters is inefficient, it is important to identify successful parameters. Furthermore, the successful region, in which the desired process is reproducible, is essential for describing the detailed mechanics of functional processes and environmental sensitivity and robustness. We propose an efficient search method for identifying the successful region by using two machine learning techniques, Bayesian optimization and active learning. We evaluated its performance using F1-ATPase, a biological rotary motor, with CG-MD simulations. We successfully identified the successful region with lower computational costs (12.3% in the best case) without sacrificing accuracy compared to exhaustive search. This method can accelerate not only parameter search but also biological discussion of the detailed mechanics of functional processes and environmental sensitivity based on MD simulation studies.

Modulation of Toroidal Proteins Dynamics in Favor of Functional Mechanisms upon Ligand Binding

Toroidal proteins serve as molecular machines and play crucial roles in biological processes such as DNA replication and RNA transcription. Despite progress in the structural characterization of several toroidal proteins, we still lack a mechanistic understanding of the significance of their architecture, oligomerization states, and intermolecular interactions in defining their biological function. In this work, we analyze the collective dynamics of toroidal proteins with different oligomerization states, namely, dimeric and trimeric DNA sliding clamps, nucleocapsid proteins (4-, 5-, and 6-mers) and Trp RNA-binding attenuation proteins (11- and 12-mers). We observe common global modes, among which cooperative rolling stands out as a mechanism enabling DNA processivity, and clamshell motions as those underlying the opening/closure of the sliding clamps. Alterations in global dynamics due to complexation with DNA or the clamp loader are shown to assist in enhancing motions to enable robust function. The analysis provides new insights into the differentiation and enhancement of functional motions upon intersubunit and intermolecular interactions.

In silico Methods for Design of Kinase Inhibitors as Anticancer Drugs

Rational drug design implies usage of molecular modeling techniques such as pharmacophore modeling, molecular dynamics, virtual screening, and molecular docking to explain the activity of biomolecules, define molecular determinants for interaction with the drug target, and design more efficient drug candidates. Kinases play an essential role in cell function and therefore are extensively studied targets in drug design and discovery. Kinase inhibitors are clinically very important and widely used antineoplastic drugs. In this review, computational methods used in rational drug design of kinase inhibitors are discussed and compared, considering some representative case studies.

A comparative study of the low-frequency vibrations of l-histidine molecule in different solid states

Low-frequency vibrations of l-histidine in a neat solid state and its monohydrochloride monohydrate are both investigated using THz spectroscopy and DFT calculations. The molecular motions in those modes are further quantitatively decomposed into a number of submotions and discussed in terms of their contributions to a mode. The results show significant differences in the averaged contribution percentage of intermolecular motions and the dihedral angle distortions of the imidazole ring between these two crystals. Those phenomena are interpreted from the viewpoint of their hydrogen-bond configurations.

Evolutionary Analyses of Sequence and Structure Space Unravel the Structural Facets of SOD1

Superoxide dismutase (SOD) is the primary enzyme of the cellular antioxidant defense cascade. Misfolding, concomitant oligomerization, and higher order aggregation of human cytosolic SOD are linked to amyotrophic lateral sclerosis (ALS). Although, with two metal ion cofactors SOD1 is extremely robust, the de-metallated apo form is intrinsically disordered. Since the rise of oxygen-based metabolism and antioxidant defense systems are evolutionary coupled, SOD is an interesting protein with a deep evolutionary history. We deployed statistical analysis of sequence space to decode evolutionarily co-varying residues in this protein. These were validated by applying graph theoretical modelling to understand the impact of the presence of metal ion co-factors in dictating the disordered (apo) to hidden disordered (wild-type SOD1) transition. Contact maps were generated for different variants, and the selected significant residues were mapped on separate structure networks. Sequence space analysis coupled with structure networks helped us to map the evolutionarily coupled co-varying patches in the SOD1 and its metal-depleted variants. In addition, using structure network analysis, the residues with a major impact on the internal dynamics of the protein structure were investigated. Our results reveal that the bulk of these evolutionarily co-varying residues are localized in the loop regions and positioned differentially depending upon the metal residence and concomitant steric restrictions of the loops.

LARMD: integration of bioinformatic resources to profile ligand-driven protein dynamics with a case on the activation of estrogen receptor

Protein dynamics is central to all biological processes, including signal transduction, cellular regulation and biological catalysis. Among them, in-depth exploration of ligand-driven protein dynamics contributes to an optimal understanding of protein function, which is particularly relevant to drug discovery. Hence, a wide range of computational tools have been designed to investigate the important dynamic information in proteins. However, performing and analyzing protein dynamics is still challenging due to the complicated operation steps, giving rise to great difficulty, especially for nonexperts. Moreover, there is a lack of web protocol to provide online facility to investigate and visualize ligand-driven protein dynamics. To this end, in this study, we integrated several bioinformatic tools to develop a protocol, named Ligand and Receptor Molecular Dynamics (LARMD, http://chemyang.ccnu.edu.cn/ccb/server/LARMD/ and http://agroda.gzu.edu.cn:9999/ccb/server/LARMD/), for profiling ligand-driven protein dynamics. To be specific, estrogen receptor (ER) was used as a case to reveal ERβ-selective mechanism, which plays a vital role in the treatment of inflammatory diseases and many types of cancers in clinical practice. Two different residues (Ile373/Met421 and Met336/Leu384) in the pocket of ERβ/ERα were the significant determinants for selectivity, especially Met336 of ERβ. The helix H8, helix H11 and H7-H8 loop influenced the migration of selective agonist (WAY-244). These computational results were consistent with the experimental results. Therefore, LARMD provides a user-friendly online protocol to study the dynamic property of protein and to design new ligand or site-directed mutagenesis.

Methodological improvements for the analysis of domain movements in large biomolecular complexes

Domain movements play a prominent role in the function of many biomolecules such as the ribosome and F₀F₁-ATP synthase. As more structures of large biomolecules in different functional states become available as experimental techniques for structure determination advance, there is a need to develop methods to understand the conformational changes that occur. DynDom and DynDom3D were developed to analyse two structures of a biomolecule for domain movements. They both used an original method for domain recognition based on clustering of "rotation vectors". Here we introduce significant improvements in both the methodology and implementation of a tool for the analysis of domain movements in large multimeric biomolecules. The main improvement is in the recognition of domains by using all six degrees of freedom required to describe the movement of a rigid body. This is achieved by way of Chasles' theorem in which a rigid-body movement can be described as a screw movement about a unique axis. Thus clustering now includes, in addition to rotation vector data, screw-axis location data and axial climb data. This improves both the sensitivity of domain recognition and performance. A further improvement is the recognition and annotation of interdomain bending regions, something not done for multimeric biomolecules in DynDom3D. This is significant as it is these regions that collectively control the domain movement. The new stand-alone, platform-independent implementation, DynDom6D, can analyse biomolecules comprising protein, DNA and RNA, and employs an alignment method to automatically achieve the required equivalence of atoms in the two structures.

Can Conformational Changes of Proteins Be Represented in Torsion Angle Space? A Study with Rescaled Ridge Regression

Torsion angles are the natural degrees of freedom of protein structures. The ability to determine torsional variations corresponding to observed changes in Cartesian coordinates is highly valuable, notably to investigate the mechanisms of functional conformational changes or to develop computational models of protein dynamics. This issue is far from trivial in practice since the impact of modifying one torsion angle strongly depends on all other angles, and the compounding effects of small variations in bond lengths and valence angles can completely disrupt a protein fold. We demonstrate that naive strategies, such as directly comparing torsion angles between structures without correcting for variations in bond lengths and valence angles or fitting torsional variations without a proper regularization scheme, fail at producing an adequate representation of conformational changes in internal coordinates. In contrast, rescaled ridge regression, a method recently introduced to regularize multidimensional regressions with correlated explanatory variables, is shown to consistently identify a minimal set of torsion angles variations that closely reproduce changes in Cartesian coordinates. This torsional representation of conformational changes is shown to be robust to the choice of experimental structures. It also provides a better agreement with theoretical models of protein dynamics than the Cartesian representation, regarding notably the predominance of low-frequency normal modes in functional motions and the presence, in predicted equilibrium dynamics, of hints of natural selection for specific functional motions. The software is available at https://github.com/ugobas/tnm .

Structural properties and influence of solvent on the stability of telomeric four-stranded i-motif DNA

Repetitive cytosine rich i-motif forming sequences are abundant in the telomere, centromere and promoters of several oncogenes and in some instances are known to regulate transcription and gene expression. The in vivo existence of i-motif structures demands further insight into the factors affecting their formation and stability and development of better understanding of their gene regulatory functions. Most prior studies characterizing the conformational dynamics of i-motifs are based on i-motif forming synthetic constructs. Here, we present a systematic study on the stability and structural properties of biologically relevant i-motifs of telomeric and centromeric repeat fragments. Our results based on molecular dynamics simulations and quantum chemical calculations indicate that along with base pairing interactions within the i-motif core the overall folded conformation is associated with the stable C-HO sugar "zippers" in the narrow grooves and structured water molecules along the wide grooves. The stacked geometry of the hemi-protonated cytosine pairs within the i-motif core is mainly governed by the repulsive base stacking interaction. The loop sequence can affect the structural dynamics of the i-motif by altering the loop motion and backbone conformation. Overall this study provides microscopic insight into the i-motif structure that will be helpful to understand the structural aspect of mechanisms of gene regulation by i-motif DNA.

In silico analysis of nonsynonymous single-nucleotide polymorphisms (nsSNPs) of the SMPX gene

Mutations in the SMPX gene can disrupt the regular activity of the SMPX protein, which is involved in the hearing process. Recent reports showing a link between nonsynonymous single-nucleotide polymorphisms (nsSNPs) in SMPX and hearing loss, thus classifying deleterious SNPs in SMPX will be an uphill task before designing a more extensive population study. In this study, damaging nsSNPs of SMPX from the dbSNP database were identified by using 13 bioinformatics tools. Initially, the impact of nsSNPs in the SMPX gene were evaluated through different in silico predictors; and the deleterious convergent changes were analyzed by energy-minimization-guided residual network analysis. In addition, the pathogenic effects of mutations in SMPX-mediated protein-protein interactions were also characterized by structural modeling and binding energy calculations. A total of four mutations (N19D, A29T, K54N, and S71L) were found to be highly deleterious by all the tools, which are located at highly conserved regions. Furthermore, all four mutants showed structural alterations, and the communities of amino acids for mutant proteins were readily changed, compared to the wild-type. Among them, A29T (rs772775896) was revealed as the most damaging nsSNP, which caused significant structural deviation of the SMPX protein, as a result reducing the binding affinity to other functional partners. These findings reflect the computational insights into the deleterious role of nsSNPs in SMPX, which might be helpful for subjecting wet-lab confirmatory analysis.

Global Dynamics of Yeast Hsp90 Middle and C-Terminal Dimer Studied by Advanced Sampling Simulations

The Hsp90 protein complex is one of the most abundant molecular chaperone proteins that assists in folding of a variety of client proteins. During its functional cycle it undergoes large domain rearrangements coupled to the hydrolysis of ATP and association or dissociation of domain interfaces. In order to better understand the domain dynamics comparative Molecular Dynamics (MD) simulations of a sub-structure of Hsp90, the dimer formed by the middle (M) and C-terminal domain (C), were performed. Since this MC dimer lacks the ATP-binding N-domain it allows studying global motions decoupled from ATP binding and hydrolysis. Conventional (c)MD simulations starting from several different closed and open conformations resulted in only limited sampling of global motions. However, the application of a Hamiltonian Replica exchange (H-REMD) method based on the addition of a biasing potential extracted from a coarse-grained elastic network description of the system allowed much broader sampling of domain motions than the cMD simulations. With this multiscale approach it was possible to extract the main directions of global motions and to obtain insight into the molecular mechanism of the global structural transitions of the MC dimer.

Normal Mode Analysis as a Routine Part of a Structural Investigation

Normal mode analysis (NMA) is a technique that can be used to describe the flexible states accessible to a protein about an equilibrium position. These states have been shown repeatedly to have functional significance. NMA is probably the least computationally expensive method for studying the dynamics of macromolecules, and advances in computer technology and algorithms for calculating normal modes over the last 20 years have made it nearly trivial for all but the largest systems. Despite this, it is still uncommon for NMA to be used as a component of the analysis of a structural study. In this review, we will describe NMA, outline its advantages and limitations, explain what can and cannot be learned from it, and address some criticisms and concerns that have been voiced about it. We will then review the most commonly used techniques for reducing the computational cost of this method and identify the web services making use of these methods. We will illustrate several of their possible uses with recent examples from the literature. We conclude by recommending that NMA become one of the standard tools employed in any structural study.

Mechanical properties of tubulin intra- and inter-dimer interfaces and their implications for microtubule dynamic instability

Thirteen tubulin protofilaments, made of αβ-tubulin heterodimers, interact laterally to produce cytoskeletal microtubules. Microtubules exhibit the striking property of dynamic instability, manifested in their intermittent growth and shrinkage at both ends. This behavior is key to many cellular processes, such as cell division, migration, maintenance of cell shape, etc. Although assembly and disassembly of microtubules is known to be linked to hydrolysis of a guanosine triphosphate molecule in the pocket of β-tubulin, detailed mechanistic understanding of corresponding conformational changes is still lacking. Here we take advantage of the recent generation of in-microtubule structures of tubulin to examine the properties of protofilaments, which serve as important microtubule assembly and disassembly intermediates. We find that initially straight tubulin protofilaments, relax to similar non-radially curved and slightly twisted conformations. Our analysis further suggests that guanosine triphosphate hydrolysis primarily affects the flexibility and conformation of the inter-dimer interface, without a strong impact on the shape or flexibility of αβ-heterodimer. Inter-dimer interfaces are significantly more flexible compared to intra-dimer interfaces. We argue that such a difference in flexibility could be key for distinct stability of the plus and minus microtubule ends. The higher flexibility of the inter-dimer interface may have implications for development of pulling force by curving tubulin protofilaments during microtubule disassembly, a process of major importance for chromosome motions in mitosis.

Stochastic modeling of macromolecules in solution. I. Relaxation processes

A framework for the stochastic description of relaxation processes in flexible macromolecules, including dissipative effects, is introduced from an atomistic point of view. Projection-operator techniques are employed to obtain multidimensional Fokker-Planck operators governing the relaxation of internal coordinates and global degrees of freedom and depending upon parameters fully recoverable from classic force fields (energetics) and continuum models (friction tensors). A hierarchy of approaches of different complexity is proposed in this unified context, aimed primarily at the interpretation of magnetic resonance relaxation experiments. In particular, a model based on a harmonic internal Hamiltonian is discussed as a test case.

Ligand binding effects on the activation of the EGFR extracellular domain

The epidermal growth factor receptor (EGFR) is one of the most common target proteins in anti-cancer therapy. The binding of the EGF ligand to the EGFR extracellular domain (EGFR-ECD) promotes its inactive-to-active conformational transition (activation) but the relevant detailed mechanism remains elusive still. Here, the structural characterization and energetics of the EGFR-ECD conformational transition with and without the binding of the EGF are quantitatively explored using an innovative enhanced sampling MD simulation method. Intriguingly, the EGF offers hydrophobic interactions (e.g., EGF residues of Tyr44 and Leu47) and electrostatic interactions (e.g., the EGF residues of Glu5, Asp11, Asp17, and Arg41) to play a dominant role in dragging domain III to close the ligand binding domain gap. Subsequently, the correlation between domains III and II is enhanced through salt-bridges among Glu376, Arg403, and Arg405 from domain III and Glu293, Glu295, and Arg300 from domain II. Finally, the structural bending of domain II is regulated to facilitate the disengagement of domain II from domain IV. In this regard, the functional conformational transition of EGFR-ECD is a consequence of the cooperative motion of protein domains driven by the EGF ligand binding. The present study shows a detailed scenario of the EGF induced activation of EGFR-ECD and provides valuable information for drug discovery targeting the EGFR.

Generalization of the elastic network model for the study of large conformational changes in biomolecules

The elastic network (EN) is a prime model that describes the long-time dynamics of biomolecules. However, the use of harmonic potentials renders this model insufficient for studying large conformational changes of proteins (e.g. stretching of proteins, folding and thermal unfolding). Here, we extend the capabilities of the EN model by using a harmonic approximation described by Lennard-Jones (LJ) interactions for far contacts and native contacts obtained from the standard overlap criterion as in the case of Gō-like models. While our model is validated against the EN model by reproducing the equilibrium properties for a number of proteins, we also show that the model is suitable for the study of large conformation changes by providing various examples. In particular, this is illustrated on the basis of pulling simulations that predict with high accuracy the experimental data on the rupture force of the studied proteins. Furthermore, in the case of DDFLN4 protein, our pulling simulations highlight the advantages of our model with respect to Gō-like approaches, where the latter fail to reproduce previous results obtained by all-atom simulations that predict an additional characteristic peak for this protein. In addition, folding simulations of small peptides yield different folding times for α-helix and β-hairpin, in agreement with experiment, in this way providing further opportunities for the application of our model in studying large conformational changes of proteins. In contrast to the EN model, our model is suitable for both normal mode analysis and molecular dynamics simulation. We anticipate that the proposed model will find applications in a broad range of problems in biology, including, among others, protein folding and thermal unfolding.

Signalling networks and dynamics of allosteric transitions in bacterial chaperonin GroEL: implications for iterative annealing of misfolded proteins

Signal transmission at the molecular level in many biological complexes occurs through allosteric transitions. Allostery describes the responses of a complex to binding of ligands at sites that are spatially well separated from the binding region. We describe the structural perturbation method, based on phonon propagation in solids, which can be used to determine the signal-transmitting allostery wiring diagram (AWD) in large but finite-sized biological complexes. Application to the bacterial chaperonin GroEL-GroES complex shows that the AWD determined from structures also drives the allosteric transitions dynamically. From both a structural and dynamical perspective these transitions are largely determined by formation and rupture of salt-bridges. The molecular description of allostery in GroEL provides insights into its function, which is quantitatively described by the iterative annealing mechanism. Remarkably, in this complex molecular machine, a deep connection is established between the structures, reaction cycle during which GroEL undergoes a sequence of allosteric transitions, and function, in a self-consistent manner.This article is part of a discussion meeting issue 'Allostery and molecular machines'.

Interpreting the Dynamics of Binding Interactions of snRNA and U1A Using a Coarse-Grained Model

The binding interactions of small nuclear RNAs (snRNA) and the associated protein factors are critical to the function of spliceosomes in alternatively splicing primary RNA transcripts. Although molecular dynamics simulations are a powerful tool to interpret the mechanism of biological processes, the atomic-level simulations are, however, too expensive and with limited accuracy for the large-size systems, such as snRNA-protein complexes. We extend the coarse-grained Gaussian network model, which models the RNA-protein complexes as a harmonic chain of Cα, P, and O4' atoms, to investigating the impact of the snRNA-binding interaction on the dynamic stability of the human U1A protein, which is a major component of the spliceosomal U1 small nuclear ribonucleoprotein particle. The results reveal that the first and third loops and the C-terminal helix regions of the U1A domain undergo a significant loss of flexibility upon the RNA binding due to the forming of mostly electrostatic and hydrogen bond interactions with RNA 5' stem and loop. By examining the residues whose mutations significantly change the binding free energy between U1A and snRNA, the Gaussian network model-based calculations show that not only the residues at the binding sites that are traditionally considered to play a major role in U1A-RNA association but also those residues that are far away from the RNA-binding interface can participate in the long-range allosteric signal transmission; these calculations are quantitatively consistent with the data observed in the recent snRNA binding experiments. The study demonstrates a useful avenue to utilize the simplified elastic network model to investigate the dynamics characteristics of the biologically important macromolecular interactions.

The Influence of Protein Stability on Sequence Evolution: Applications to Phylogenetic Inference

Phylogenetic inference from protein data is traditionally based on empirical substitution models of evolution that assume that protein sites evolve independently of each other and under the same substitution process. However, it is well known that the structural properties of a protein site in the native state affect its evolution, in particular the sequence entropy and the substitution rate. Starting from the seminal proposal by Halpern and Bruno, where structural properties are incorporated in the evolutionary model through site-specific amino acid frequencies, several models have been developed to tackle the influence of protein structure on sequence evolution. Here we describe stability-constrained substitution (SCS) models that explicitly consider the stability of the native state against both unfolded and misfolded states. One of them, the mean-field model, provides an independent sites approximation that can be readily incorporated in maximum likelihood methods of phylogenetic inference, including ancestral sequence reconstruction. Next, we describe its validation with simulated and real proteins and its limitations and advantages with respect to empirical models that lack site specificity. We finally provide guidelines and recommendations to analyze protein data accounting for stability constraints, including computer simulations and inferences of protein evolution based on maximum likelihood. Some practical examples are included to illustrate these procedures.

Advances in the Computational Identification of Allosteric Sites and Pathways in Proteins

With the increasing difficulty to develop new drugs and the emergence of resistance to traditional orthosteric-site inhibitors, the search for alternatives is finally approaching the focus on allosteric sites. Allosteric sites offer opportunities to regulate many pharmacologically targeted pathways by inhibition or activation. In addition, allosteric sites tend to be less conserved than the functional site, which may facilitate the design of specific effectors in the protein families for which specific orthosteric inhibitors have proved difficult to design. Furthermore, recent evidence suggests that all proteins might be susceptible of allosteric regulation, increasing the space of druggable targets. Computational identification of allosteric sites has therefore become an active field of research. The problem can be approached from two sides: (1) the identification of allosteric-communication pathways between the functional site and potential allosteric sites and (2) the functional-site-independent identification of allosteric sites. While the first approach tends to be more laborious and thus restricted to a single protein, the second tends to be more amenable to larger-scale analysis, thus providing tools for the two drug discovery scenarios: the analysis of known targets and the screening for new potential targets. Here, I show some basic concepts and methods useful to the identification of allosteric sites and pathways, in line with these two approaches. I describe them in some detail to build a clear framework, at the risk of losing the interest of experts. Examples of recent studies involving these methods are also illustrated, focusing on the techniques rather than on their findings on allosterism.

Structural dynamics of lytic polysaccharide monoxygenases reveals a highly flexible substrate binding region

Lytic polysaccharide monooxygenases (LPMOs), which are found in fungi, bacteria, and viruses, are redox enzymes utilizing copper to break glycosidic bonds in recalcitrant crystalline form of polysaccharides, such as chitin and cellulose. They are classified by the Carbohydrate-Active enZYmes (CAZy) database under various families. LPMOs's structure with a flat substrate binding region has been shown to contribute to its function, however, the role that LPMOs structural dynamics play during polysaccharide degradation and its mechanism of binding towards substrate are relatively unknown. Here, we report an exhaustive implementation of coarse-grained simulations using Elastic Network Models on multiple LPMO structures to shed light on how their structural dynamics contribute to their chemical function. Using Gaussian network models and Anisotropic network models, we show that the substrate binding region is highly flexible with significant and sustained micro-scale level conformational changes. Significantly, the loops on the binding side of the substrate are most mobile, in concert with the dynamic modes influencing the motions during binding. We also observed dynamic differences between four families of LPMO, namely AA9, AA10, AA11, and AA13 that consist of more than one structure. Specifically, the patterns of motion in the loop regions among the AA9 structures are distinct from those in the AA10 structures.

Optimal Coarse-Grained Site Selection in Elastic Network Models of Biomolecules

Elastic network models, simple structure-based representations of biomolecules where atoms interact via short-range harmonic potentials, provide great insight into a molecule's internal dynamics and mechanical properties at extremely low computational cost. Their efficiency and effectiveness have made them a pivotal instrument in the computer-aided study of proteins and, since a few years, also of nucleic acids. In general, the coarse-grained sites, i.e. those effective force centers onto which the all-atom structure is mapped, are constructed based on intuitive rules: a typical choice for proteins is to retain only the C _α atoms of each amino acid. However, a mapping strategy relying only on the atom type and not the local properties of its embedding can be suboptimal compared to a more careful selection. Here, we present a strategy in which the subset of atoms, each of which is mapped onto a unique coarse-grained site of the model, is selected in a stochastic search aimed at optimizing a cost function. The latter is taken to be a simple measure of the consistency between the harmonic approximation of an elastic network model and the harmonic model obtained through exact integration of the discarded degrees of freedom. The method is applied to two representatives of structurally very different types of biomolecules: the protein adenylate kinase and the RNA molecule adenine riboswitch. Our analysis quantifies the substantial impact that an algorithm-driven selection of coarse-grained sites can have on a model's properties.

Coarse-Grained Protein Dynamics Studies Using Elastic Network Models

Elastic networks have been used as simple models of proteins to study their slow structural dynamics. They consist of point-like particles connected by linear Hookean springs and hence are convenient for linear normal mode analysis around a given reference structure. Furthermore, dynamic simulations using these models can provide new insights. As the computational cost associated with these models is considerably lower compared to that of all-atom models, they are also convenient for comparative studies between multiple protein structures. In this review, we introduce examples of coarse-grained molecular dynamics studies using elastic network models and their derivatives, focusing on the nonlinear phenomena, and discuss their applicability to large-scale macromolecular assemblies.

Modeling of Protein Structural Flexibility and Large-Scale Dynamics: Coarse-Grained Simulations and Elastic Network Models

Fluctuations of protein three-dimensional structures and large-scale conformational transitions are crucial for the biological function of proteins and their complexes. Experimental studies of such phenomena remain very challenging and therefore molecular modeling can be a good alternative or a valuable supporting tool for the investigation of large molecular systems and long-time events. In this minireview, we present two alternative approaches to the coarse-grained (CG) modeling of dynamic properties of protein systems. We discuss two CG representations of polypeptide chains used for Monte Carlo dynamics simulations of protein local dynamics and conformational transitions, and highly simplified structure-based elastic network models of protein flexibility. In contrast to classical all-atom molecular dynamics, the modeling strategies discussed here allow the quite accurate modeling of much larger systems and longer-time dynamic phenomena. We briefly describe the main features of these models and outline some of their applications, including modeling of near-native structure fluctuations, sampling of large regions of the protein conformational space, or possible support for the structure prediction of large proteins and their complexes.

Structure-Guided Protein Transition Modeling with a Probabilistic Roadmap Algorithm

Proteins are macromolecules in perpetual motion, switching between structural states to modulate their function. A detailed characterization of the precise yet complex relationship between protein structure, dynamics, and function requires elucidating transitions between functionally-relevant states. Doing so challenges both wet and dry laboratories, as protein dynamics involves disparate temporal scales. In this paper, we present a novel, sampling-based algorithm to compute transition paths. The algorithm exploits two main ideas. First, it leverages known structures to initialize its search and define a reduced conformation space for rapid sampling. This is key to address the insufficient sampling issue suffered by sampling-based algorithms. Second, the algorithm embeds samples in a nearest-neighbor graph where transition paths can be efficiently computed via queries. The algorithm adapts the probabilistic roadmap framework that is popular in robot motion planning. In addition to efficiently computing lowest-cost paths between any given structures, the algorithm allows investigating hypotheses regarding the order of experimentally-known structures in a transition event. This novel contribution is likely to open up new venues of research. Detailed analysis is presented on multiple-basin proteins of relevance to human disease. Multiscaling and the AMBER ff14SB force field are used to obtain energetically-credible paths at atomistic detail.

Interface Residues That Drive Allosteric Transitions Also Control the Assembly of l-Lactate Dehydrogenase

The allosteric enzyme, l-lactate dehydrogenase (LDH), is activated by fructose 1,6-metaphosphate (FBP) to reduce pyruvate to lactate. The molecular details of the FBP-driven transition from the low affinity T state to the high affinity R state in LDH, a tetramer composed of identical subunits, are not known. The dynamics of the T → R allosteric transition, investigated using Brownian dynamics (BD) simulations of the self-organized polymer (SOP) model, revealed that coordinated rotations of the subunits drive the T → R transition. We used the structural perturbation method (SPM), which requires only the static structure, to identify the allostery wiring diagram (AWD), a network of residues that transmits signals across the tetramer, as LDH undergoes the T → R transition. Interestingly, the residues that play a major role in the dynamics, which are predominantly localized at the interfaces, coincide with the AWD identified using the SPM. Although the allosteric pathways are highly heterogeneous, on the basis of our simulations, we surmise that predominantly the conformational changes in the T → R transition start from the region near the active site, comprised of helix αC, helix α1/2G, helix α3G, and helix α2F, and proceed to other structural units, thus completing the global motion. Brownian dynamics simulations of the tetramer assembly, triggered by a temperature quench from the fully disrupted conformations, show that the bottleneck for assembly is the formation of the correct orientational registry between the subunits, requiring contacts between the interface residues. Surprisingly, these residues are part of the AWD, which was identified using the SPM. Taken together, our results show that LDH, and perhaps other multidomain proteins, may have evolved to stabilize distinct states of allosteric enzymes using precisely the same AWD that also controls the functionally relevant allosteric transitions.

Fabrication and Characterization of Finite-Size DNA 2D Ring and 3D Buckyball Structures

In order to incorporate functionalization into synthesized DNA nanostructures, enhance their production yield, and utilize them in various applications, it is necessary to study their physical stabilities and dynamic characteristics. Although simulation-based analysis used for DNA nanostructures provides important clues to explain their self-assembly mechanism, structural function, and intrinsic dynamic characteristics, few studies have focused on the simulation of DNA supramolecular structures due to the structural complexity and high computational cost. Here, we demonstrated the feasibility of using normal mode analysis for relatively complex DNA structures with larger molecular weights, i.e., finite-size DNA 2D rings and 3D buckyball structures. The normal mode analysis was carried out using the mass-weighted chemical elastic network model (MWCENM) and the symmetry-constrained elastic network model (SCENM), both of which are precise and efficient modeling methodologies. MWCENM considers both the weight of the nucleotides and the chemical bonds between atoms, and SCENM can obtain mode shapes of a whole structure by using only a repeated unit and its connectivity with neighboring units. Our results show the intrinsic vibrational features of DNA ring structures, which experience inner/outer circle and bridge motions, as well as DNA buckyball structures having overall breathing and local breathing motions. These could be used as the fundamental basis for designing and constructing more complicated DNA nanostructures.

High-Precision Megahertz-to-Terahertz Dielectric Spectroscopy of Protein Collective Motions and Hydration Dynamics

The low-frequency collective vibrational modes in proteins as well as the protein-water interface have been suggested as dominant factors controlling the efficiency of biochemical reactions and biological energy transport. It is thus crucial to uncover the mystery of the hydration structure and dynamics as well as their coupling to collective motions of proteins in aqueous solutions. Here, we report dielectric properties of aqueous bovine serum albumin protein solutions as a model system using an extremely sensitive dielectric spectrometer with frequencies spanning from megahertz to terahertz. The dielectric relaxation spectra reveal several polarization mechanisms at the molecular level with different time constants and dielectric strengths, reflecting the complexity of protein-water interactions. Combining the effective-medium approximation and molecular dynamics simulations, we have determined collective vibrational modes at terahertz frequencies and the number of water molecules in the tightly bound and loosely bound hydration layers. High-precision measurements of the number of hydration water molecules indicate that the dynamical influence of proteins extends beyond the first solvation layer, to around 7 Å distance from the protein surface, with the largest slowdown arising from water molecules directly hydrogen-bonded to the protein. Our results reveal critical information of protein dynamics and protein-water interfaces, which determine biochemical functions and reactivity of proteins.

Atomic clusters with addressable complexity

A general formulation for constructing addressable atomic clusters is introduced, based on one or more reference structures. By modifying the well depths in a given interatomic potential in favour of nearest-neighbour interactions that are defined in the reference(s), the potential energy landscape can be biased to make a particular permutational isomer the global minimum. The magnitude of the bias changes the resulting potential energy landscape systematically, providing a framework to produce clusters that should self-organise efficiently into the target structure. These features are illustrated for small systems, where all the relevant local minima and transition states can be identified, and for the low-energy regions of the landscape for larger clusters. For a 55-particle cluster, it is possible to design a target structure from a transition state of the original potential and to retain this structure in a doubly addressable landscape. Disconnectivity graphs based on local minima that have no direct connections to a lower minimum provide a helpful way to visualise the larger databases. These minima correspond to the termini of monotonic sequences, which always proceed downhill in terms of potential energy, and we identify them as a class of biminimum. Multiple copies of the target cluster are treated by adding a repulsive term between particles with the same address to maintain distinguishable targets upon aggregation. By tuning the magnitude of this term, it is possible to create assemblies of the target cluster corresponding to a variety of structures, including rings and chains.

Green function of correlated genes in a minimal mechanical model of protein evolution

The function of proteins arises from cooperative interactions and rearrangements of their amino acids, which exhibit large-scale dynamical modes. Long-range correlations have also been revealed in protein sequences, and this has motivated the search for physical links between the observed genetic and dynamic cooperativity. We outline here a simplified theory of protein, which relates sequence correlations to physical interactions and to the emergence of mechanical function. Our protein is modeled as a strongly coupled amino acid network with interactions and motions that are captured by the mechanical propagator, the Green function. The propagator describes how the gene determines the connectivity of the amino acids and thereby, the transmission of forces. Mutations introduce localized perturbations to the propagator that scatter the force field. The emergence of function is manifested by a topological transition when a band of such perturbations divides the protein into subdomains. We find that epistasis-the interaction among mutations in the gene-is related to the nonlinearity of the Green function, which can be interpreted as a sum over multiple scattering paths. We apply this mechanical framework to simulations of protein evolution and observe long-range epistasis, which facilitates collective functional modes.

The maximum penalty criterion for ridge regression: application to the calibration of the force constant in elastic network models

Tikhonov regularization, or ridge regression, is a popular technique to deal with collinearity in multivariate regression. We unveil a formal analogy between ridge regression and statistical mechanics, where the objective function is comparable to a free energy, and the ridge parameter plays the role of temperature. This analogy suggests two novel criteria for selecting a suitable ridge parameter: specific-heat (C_v) and maximum penalty (MP). We apply these fits to evaluate the relative contributions of rigid-body and internal fluctuations, which are typically highly collinear, to crystallographic B-factors. This issue is particularly important for computational models of protein dynamics, such as the elastic network model (ENM), since the amplitude of the predicted internal motion is commonly calibrated using B-factor data. After validation on simulated datasets, our results indicate that rigid-body motions account on average for more than 80% of the amplitude of B-factors. Furthermore, we evaluate the ability of different fits to reproduce the amplitudes of internal fluctuations in X-ray ensembles from the B-factors in the corresponding single X-ray structures. The new ridge criteria are shown to be markedly superior to the commonly used two-parameter fit that neglects rigid-body rotations and to the full fits regularized under generalized cross-validation. In conclusion, the proposed fits ensure a more robust calibration of the ENM force constant and should prove valuable in other applications.

CATS (Coordinates of Atoms by Taylor Series): protein design with backbone flexibility in all locally feasible directions

Motivation

When proteins mutate or bind to ligands, their backbones often move significantly, especially in loop regions. Computational protein design algorithms must model these motions in order to accurately optimize protein stability and binding affinity. However, methods for backbone conformational search in design have been much more limited than for sidechain conformational search. This is especially true for combinatorial protein design algorithms, which aim to search a large sequence space efficiently and thus cannot rely on temporal simulation of each candidate sequence.

Results

We alleviate this difficulty with a new parameterization of backbone conformational space, which represents all degrees of freedom of a specified segment of protein chain that maintain valid bonding geometry (by maintaining the original bond lengths and angles and ω dihedrals). In order to search this space, we present an efficient algorithm, CATS, for computing atomic coordinates as a function of our new continuous backbone internal coordinates. CATS generalizes the iMinDEE and EPIC protein design algorithms, which model continuous flexibility in sidechain dihedrals, to model continuous, appropriately localized flexibility in the backbone dihedrals ϕ and ψ as well. We show using 81 test cases based on 29 different protein structures that CATS finds sequences and conformations that are significantly lower in energy than methods with less or no backbone flexibility do. In particular, we show that CATS can model the viability of an antibody mutation known experimentally to increase affinity, but that appears sterically infeasible when modeled with less or no backbone flexibility.

Availability and implementation

Our code is available as free software at https://github.com/donaldlab/OSPREY_refactor.

Supplementary information

Supplementary data are available at Bioinformatics online.

Heterodimer Binding Scaffolds Recognition via the Analysis of Kinetically Hot Residues

Physical interactions between proteins are often difficult to decipher. The aim of this paper is to present an algorithm that is designed to recognize binding patches and supporting structural scaffolds of interacting heterodimer proteins using the Gaussian Network Model (GNM). The recognition is based on the (self) adjustable identification of kinetically hot residues and their connection to possible binding scaffolds. The kinetically hot residues are residues with the lowest entropy, i.e., the highest contribution to the weighted sum of the fastest modes per chain extracted via GNM. The algorithm adjusts the number of fast modes in the GNM's weighted sum calculation using the ratio of predicted and expected numbers of target residues (contact and the neighboring first-layer residues). This approach produces very good results when applied to dimers with high protein sequence length ratios. The protocol's ability to recognize near native decoys was compared to the ability of the residue-level statistical potential of Lu and Skolnick using the Sternberg and Vakser decoy dimers sets. The statistical potential produced better overall results, but in a number of cases its predicting ability was comparable, or even inferior, to the prediction ability of the adjustable GNM approach. The results presented in this paper suggest that in heterodimers at least one protein has interacting scaffold determined by the immovable, kinetically hot residues. In many cases, interacting proteins (especially if being of noticeably different sizes) either behave as a rigid lock and key or, presumably, exhibit the opposite dynamic behavior. While the binding surface of one protein is rigid and stable, its partner's interacting scaffold is more flexible and adaptable.

Theoretical framework for analyzing structural compliance properties of proteins

We propose methods for directly analyzing structural compliance (SC) properties of elastic network models of proteins, and we also propose methods for extracting information about motion properties from the SC properties. The analysis of SC properties involves describing the relationships between the applied forces and the deformations. When decomposing the motion according to the magnitude of SC (SC mode decomposition), we can obtain information about the motion properties under the assumption that the lower SC mode motions or the softer motions occur easily. For practical applications, the methods are formulated in a general form. The parts where forces are applied and those where deformations are evaluated are separated from each other for enabling the analyses of allosteric interactions between the specified parts. The parts are specified not only by the points but also by the groups of points (the groups are treated as flexible bodies). In addition, we propose methods for quantitatively evaluating the properties based on the screw theory and the considerations of the algebraic structures of the basic equations expressing the SC properties. These methods enable quantitative discussions about the relationships between the SC mode motions and the motions estimated from two different conformations; they also help identify the key parts that play important roles for the motions by comparing the SC properties with those of partially constrained models. As application examples, lactoferrin and ATCase are analyzed. The results show that we can understand their motion properties through their lower SC mode motions or the softer motions.

Multiple Pathways and Time Scales for Conformational Transitions in apo-Adenylate Kinase

The open/close transition in adenylate kinase (AK) is regarded as a representative example for large-scale conformational transition in proteins, yet its mechanism remains unclear despite numerous experimental and computational studies. Using extensive (∼50 μs) explicit solvent atomistic simulations and Markov state analysis, we shed new lights on the mechanism of this transition in the apo form of AK. The closed basin of apo AK features an open NMP domain while the LID domain closes and rotates toward it. Therefore, although the computed structural properties of the closed ensemble are consistent with previously reported FRET and PRE measurements, our simulations suggest that NMP closure is likely to follow AMP binding, in contrast to the previous interpretation of FRET and PRE data that the apo state was able to sample the fully closed conformation for "ligand selection". The closed state ensemble is found to be kinetically heterogeneous; multiple pathways and time scales are associated with the open/close transition, providing new clues to the disparate time scales observed in different experiments. Besides interdomain interactions, a novel mutual information analysis identifies specific intradomain interactions that correlate strongly to transition kinetics, supporting observations from previous chimera experiments. While our results underscore the role of internal domain properties in determining the kinetics of open/close transition in apo AK, no evidence is observed for any significant degree of local unfolding during the transition. These observations about AK have general implications to our view of conformational states, transition pathways, and time scales of conformational changes in proteins. The key features and time scales of observed transition pathways are robust and similar from simulations using two popular fixed charge force fields.