Analysis of domain motions in large proteins

Scalable computation of anisotropic vibrations for large macromolecular assemblies

The Normal Mode Analysis (NMA) is a standard approach to elucidate the anisotropic vibrations of macromolecules at their folded states, where low-frequency collective motions can reveal rearrangements of domains and changes in the exposed surface of macromolecules. Recent advances in structural biology have enabled the resolution of megascale macromolecules with millions of atoms. However, the calculation of their vibrational modes remains elusive due to the prohibitive cost associated with constructing and diagonalizing the underlying eigenproblem and the current approaches to NMA are not readily adaptable for efficient parallel computing on graphic processing unit (GPU). Here, we present eigenproblem construction and diagonalization approach that implements level-structure bandwidth-reducing algorithms to transform the sparse computation in NMA to a globally-sparse-yet-locally-dense computation, allowing batched tensor products to be most efficiently executed on GPU. We map, optimize, and compare several low-complexity Krylov-subspace eigensolvers, supplemented by techniques such as Chebyshev filtering, sum decomposition, external explicit deflation and shift-and-inverse, to allow fast GPU-resident calculations. The method allows accurate calculation of the first 1000 vibrational modes of some largest structures in PDB ( > 2.4 million atoms) at least 250 times faster than existing methods.

Normal mode analysis and comparative study of intrinsic dynamics of alcohol oxidase enzymes from GMC protein family

Glucose-Methanol-Choline (GMC) family enzymes are very important in catalyzing the oxidation of a wide range of structurally diverse substrates. Enzymes that constitute the GMC family, share a common tertiary fold but < 25% sequence identity. Cofactor FAD, FAD binding signature motif, and similar structural scaffold of the active site are common features of oxidoreductase enzymes of the GMC family. Protein functionality mainly depends on protein three-dimensional structures and dynamics. In this study, we used the normal mode analysis method to search the intrinsic dynamics of GMC family enzymes. We have explored the dynamical behavior of enzymes with unique substrate catabolism and active site characteristics from different classes of the GMC family. Analysis of individual enzymes and comparative ensemble analysis of enzymes from different classes has shown conserved dynamic motion at FAD binding sites. The present study revealed that GMC enzymes share a strong dynamic similarity (Bhattacharyya coefficient >90% and root mean squared inner product >52%) despite low sequence identity across the GMC family enzymes. The study predicts that local deformation energy between atoms of the enzyme may be responsible for the catalysis of different substrates. This study may help that intrinsic dynamics can be used to make meaningful classifications of proteins or enzymes from different organisms.Communicated by Ramaswamy H. Sarma.

A Retrospective on the Development of Methods for the Analysis of Protein Conformational Ensembles

Analysing protein conformational ensembles whether from molecular dynamics (MD) simulation or other sources for functionally relevant conformational changes can be very challenging. In the nineteen nineties dimensional reduction methods were developed primarily for analysing MD trajectories to determine dominant motions with the aim of understanding their relationship to function. Coarse-graining methods were also developed so the conformational change between two structures could be described in terms of the relative motion of a small number of quasi-rigid regions rather than in terms of a large number of atoms. When these methods are combined, they can characterize the large-scale motions inherent in a conformational ensemble providing insight into possible functional mechanism. The dimensional reduction methods first applied to protein conformational ensembles were referred to as Quasi-Harmonic Analysis, Principal Component Analysis and Essential Dynamics Analysis. A retrospective on the origin of these methods is presented, the relationships between them explained, and more recent developments reviewed.

Identification and characterization of molecular entities differentially expressed in bacteria genome upon treatment with glyphosate shock

Antimetabolites developed from enzymes in the shikimate pathway are appealing targets. There are, however, certain unidentified molecular entities that show bacterial sensitivity to glyphosate shock. This study aims to identify the expression pattern of such entities following treatment with glyphosate shock and to characterize them structurally and functionally. Understanding such entities' catalytic structure and modulatory role guides the design and development of novel antibiotics. This study's functional profiling of 16S rRNA sequencing data and transcriptome analysis of glyphosate-exposedE. coli revealed that two genes were upregulated and twenty-eight were downregulated after glyphosate shock. We discovered the differential expression of some processes based on functional gene analysis, such as global and overview maps (4.2195 on average), carbohydrate metabolism (0.6858 on average), amino acid metabolism (0.5032 on average), and co-factor and vitamin metabolism (0.5032 on average) (0.2876 on average). After examining the two data sets, we discovered that some unidentified proteins were strongly expressed after glyphosate treatment. After examining the two datasets, we discovered a protein with no unique features expressed when treated with glyphosate. The Ecs2020 model looks to be the most stable in structural modeling investigations, while the catalytic residues sought in drug development are anticipated. Furthermore, biological processes and cellular component enrichment analysis revealed that the differentially expressed genes were strongly related to the trehalose manufacturing process and represented the cell membrane's outer membrane component. To estimate the functional gene content of soil sample metagenomics based on 16S rRNA, predictive functional analysis was done with R using the Tax4Fun2 package. On the other hand, transcriptome analysis was carried out using the R tool GEO2R. The results could be a good starting point for making new antibiotic medicines.

Altered Dynamics of S. aureus Phosphofructokinase via Bond Restraints at Two Distinct Allosteric Binding Sites

The effect of perturbation at the allosteric site was investigated through several replicas of molecular dynamics (MD) simulations conducted on bacterial phosphofructokinase (SaPFK). In our previous work, an alternative binding site was estimated to be allosteric in addition to the experimentally reported one. To highlight the effect of both allosteric sites on receptor's dynamics, MD runs were carried out on apo forms with and without perturbation. Perturbation was achieved via incorporating multiple bond restraints for residue pairs located at the allosteric site. Restraints applied to the predicted site caused one dimer to stiffen, whereas an increase in mobility was detected in the same dimer when the experimentally resolved site was restrained. Fluctuations in C_α-C_α distances which is used to disclose residues with high potential of communication indicated a marked increase in signal transmission within each dimer as the receptor switched to a restrained state. Cross-correlation of positional fluctuations indicated an overall decrease in the magnitude of both positive and negative correlations when restraints were employed on the predicted allosteric site whereas an exact opposite effect was observed for the reported site. Finally, mutual correspondence between positional fluctuations noticeably increased with restraints on predicted allosteric site, whereas an opposite effect was observed for restraints applied on experimentally reported one. In view of these findings, it is clear that the perturbation of either one of two allosteric sites effected the dynamics of the receptor with a distinct and contrasting character.

D3PM: a comprehensive database for protein motions ranging from residue to domain

Background

Knowledge of protein motions is significant to understand its functions. While currently available databases for protein motions are mostly focused on overall domain motions, little attention is paid on local residue motions. Albeit with relatively small scale, the local residue motions, especially those residues in binding pockets, may play crucial roles in protein functioning and ligands binding.

Results

A comprehensive protein motion database, namely D3PM, was constructed in this study to facilitate the analysis of protein motions. The protein motions in the D3PM range from overall structural changes of macromolecule to local flip motions of binding pocket residues. Currently, the D3PM has collected 7679 proteins with overall motions and 3513 proteins with pocket residue motions. The motion patterns are classified into 4 types of overall structural changes and 5 types of pocket residue motions. Impressively, we found that less than 15% of protein pairs have obvious overall conformational adaptations induced by ligand binding, while more than 50% of protein pairs have significant structural changes in ligand binding sites, indicating that ligand-induced conformational changes are drastic and mainly confined around ligand binding sites. Based on the residue preference in binding pocket, we classified amino acids into “pocketphilic” and “pocketphobic” residues, which should be helpful for pocket prediction and drug design.

Conclusion

D3PM is a comprehensive database about protein motions ranging from residue to domain, which should be useful for exploring diverse protein motions and for understanding protein function and drug design. The D3PM is available on www.d3pharma.com/D3PM/index.php.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12859-022-04595-0.

GTP Cyclohydrolase I as a Potential Drug Target: New Insights into Its Allosteric Modulation via Normal Mode Analysis

Guanosine triphosphate (GTP) cyclohydrolase I (GCH1) catalyzes the conversion of GTP into dihydroneopterin triphosphate (DHNP). DHNP is the first intermediate of the folate de novo biosynthesis pathway in prokaryotic and lower eukaryotic microorganisms and the tetrahydrobiopterin (BH4) biosynthesis pathway in higher eukaryotes. The de novo folate biosynthesis provides essential cofactors for DNA replication, cell division, and synthesis of key amino acids in rapidly replicating pathogen cells, such as Plasmodium falciparum (P. falciparum), a causative agent of malaria. In eukaryotes, the product of the BH4 biosynthesis pathway is essential for the production of nitric oxide and several neurotransmitter precursors. An increased copy number of the malaria parasite P. falciparum GCH1 gene has been reported to influence antimalarial antifolate drug resistance evolution, whereas mutations in the human GCH1 are associated with neuropathic and inflammatory pain disorders. Thus, GCH1 stands as an important and attractive drug target for developing therapeutics. The GCH1 intrinsic dynamics that modulate its activity remains unclear, and key sites that exert allosteric effects across the structure are yet to be elucidated. This study employed the anisotropic network model to analyze the intrinsic motions of the GCH1 structure alone and in complex with its regulatory partner protein. We showed that the GCH1 tunnel-gating mechanism is regulated by a global shear motion and an outward expansion of the central five-helix bundle. We further identified hotspot residues within sites of structural significance for the GCH1 intrinsic allosteric modulation. The obtained results can provide a solid starting point to design novel antineuropathic treatments for humans and novel antimalarial drugs against the malaria parasite P. falciparum GCH1 enzyme.

Structural Analysis of a Genetically Encoded FRET Biosensor by SAXS and MD Simulations

Inspired by the modular architecture of natural signaling proteins, ligand binding proteins are equipped with two fluorescent proteins (FPs) in order to obtain Förster resonance energy transfer (FRET)-based biosensors. Here, we investigated a glucose sensor where the donor and acceptor FPs were attached to a glucose binding protein using a variety of different linker sequences. For three resulting sensor constructs the corresponding glucose induced conformational changes were measured by small angle X-ray scattering (SAXS) and compared to recently published single molecule FRET results (Höfig et al., ACS Sensors, 2018). For one construct which exhibits a high change in energy transfer and a large change of the radius of gyration upon ligand binding, we performed coarse-grained molecular dynamics simulations for the ligand-free and the ligand-bound state. Our analysis indicates that a carefully designed attachment of the donor FP is crucial for the proper transfer of the glucose induced conformational change of the glucose binding protein into a well pronounced FRET signal change as measured in this sensor construct. Since the other FP (acceptor) does not experience such a glucose induced alteration, it becomes apparent that only one of the FPs needs to have a well-adjusted attachment to the glucose binding protein.

Using normal mode analysis on protein structural models. How far can we go on our predictions?

Normal mode analysis (NMA) is a fast and inexpensive approach that is largely used to gain insight into functional protein motions, and more recently to create conformations for further computational studies. However, when the protein structure is unknown, the use of computational models is necessary. Here, we analyze the capacity of NMA in internal coordinate space to predict protein motion, its intrinsic flexibility, and atomic displacements, using protein models instead of native structures, and the possibility to use it for model refinement. Our results show that NMA is quite insensitive to modeling errors, but that calculations are strictly reliable only for very accurate models. Our study also suggests that internal NMA is a more suitable tool for the improvement of structural models, and for integrating them with experimental data or in other computational techniques, such as protein docking or more refined molecular dynamics simulations.

Computational Analysis of Dynamical Fluctuations of Oncoprotein E7 (HPV 16) for the Hot Spot Residue Identification Using Elastic Network Model

Aims:

To find out Potential Drug targets against HPV E7.

Background:

Oncoprotein E7 of Human Papilloma Virus (HPV-16), after invading human body alter host protein-protein interaction networks caused by the fluctuations of amino acid residues present in E7. E7 interacts with Rb protein of human host with variable residual fluctuations, leading towards the progression of cervical cancer.

Objective:

Our study was focused our computational analysis of the binding and competing interactions of the E7 protein of HPV with Rb protein.

Methods:

Our study is based on analysis of dynamic fluctuations of E7 in host cell and correlation analysis of specific residue found in motif of LxCxE, that is the key region in stabilizing interaction between E7 and Rb.

Results and Discussion:

Cysteine, Leucine and Glutamic acid have been identified as hot spot residues of E7 which can provide platform for drug designing and understanding of pathogenesis of cervical cancer, in future. Our study shows validation of the vitality of linear binding motifs LxCxE of E7 of HPV in interacting with Rb as an important event in propagation of HPV in human cells and transformation of infection into cervical cancer.

Conclusion:

Our study shows validation of the vitality of linear binding motifs LxCxE of E7 of HPV in interacting with Rb as an important event in propagation of HPV in human cells and transformation of infection into cervical cancer.

Other:

E7 interacts with Rb protein of human host with variable residual fluctuations, leading towards the progression of cervical cancer.

Exploring the intrinsic dynamics of SARS-CoV-2, SARS-CoV and MERS-CoV spike glycoprotein through normal mode analysis using anisotropic network model

COVID-19 caused by SARS-CoV-2 have become a global pandemic with serious rate of fatalities. SARS-CoV and MERS-CoV have also caused serious outbreak previously but the intensity was much lower than the ongoing SARS-CoV-2. The main infectivity factor of all the three viruses is the spike glycoprotein. In this study we have examined the intrinsic dynamics of the prefusion, lying state of trimeric S protein of these viruses through Normal Mode Analysis using Anisotropic Network Model. The dynamic modes of the S proteins of the aforementioned viruses were compared by root mean square inner product (RMSIP), spectral overlap and cosine correlation matrix. S proteins show homogenous correlated or anticorrelated motions among their domains but direction of C_α atom among the spike proteins show less similarity. SARS-CoV-2 spike shows high vertically upward motion of the receptor binding motif implying its propensity for binding with the receptor even in the lying state. MERS-CoV spike shows unique dynamical motion compared to the other two S protein indicated by low RMSIP, spectral overlap and cosine correlation value. This study will guide in developing common potential inhibitor molecules against closed state of spike protein of these viruses to prevent conformational switching from lying to standing state.

Implicit Modeling of the Impact of Adsorption on Solid Surfaces for Protein Mechanics and Activity with a Coarse-Grained Representation

Surface immobilized enzymes play a key role in numerous biotechnological applications such as biosensors, biofuel cells, or biocatalytic synthesis. As a consequence, the impact of adsorption on the enzyme structure, dynamics, and function needs to be understood on the molecular level as it is critical for the improvement of these technologies. With this perspective in mind, we used a theoretical approach for investigating local protein flexibility on the residue scale that couples a simplified protein representation with an elastic network and Brownian dynamics simulations. The impact of protein adsorption on a solid surface is implicitly modeled via additional external constraints between the residues in contact with the surface. We first performed calculations on a redox enzyme, bilirubin oxidase (BOD) from M. verrucaria, to study the impact of adsorption on its mechanical properties. The resulting rigidity profiles show that, in agreement with the available experimental data, the mechanical variations observed in the adsorbed BOD will depend on its orientation and its anchor residues (i.e., residues that are in contact with the functionalized surface). Additional calculations on ribonuclease A and nitroreductase shed light on how seemingly stable adsorbed enzymes can nonetheless display an important decrease in their catalytic activity resulting from a perturbation of their mechanics and internal dynamics.

Investigation of sequence features of hinge-bending regions in proteins with domain movements using kernel logistic regression

Background

Hinge-bending movements in proteins comprising two or more domains form a large class of functional movements. Hinge-bending regions demarcate protein domains and collectively control the domain movement. Consequently, the ability to recognise sequence features of hinge-bending regions and to be able to predict them from sequence alone would benefit various areas of protein research. For example, an understanding of how the sequence features of these regions relate to dynamic properties in multi-domain proteins would aid in the rational design of linkers in therapeutic fusion proteins.

Results

The DynDom database of protein domain movements comprises sequences annotated to indicate whether the amino acid residue is located within a hinge-bending region or within an intradomain region. Using statistical methods and Kernel Logistic Regression (KLR) models, this data was used to determine sequence features that favour or disfavour hinge-bending regions. This is a difficult classification problem as the number of negative cases (intradomain residues) is much larger than the number of positive cases (hinge residues). The statistical methods and the KLR models both show that cysteine has the lowest propensity for hinge-bending regions and proline has the highest, even though it is the most rigid amino acid. As hinge-bending regions have been previously shown to occur frequently at the terminal regions of the secondary structures, the propensity for proline at these regions is likely due to its tendency to break secondary structures. The KLR models also indicate that isoleucine may act as a domain-capping residue. We have found that a quadratic KLR model outperforms a linear KLR model and that improvement in performance occurs up to very long window lengths (eighty residues) indicating long-range correlations.

Conclusion

In contrast to the only other approach that focused solely on interdomain hinge-bending regions, the method provides a modest and statistically significant improvement over a random classifier. An explanation of the KLR results is that in the prediction of hinge-bending regions a long-range correlation is at play between a small number amino acids that either favour or disfavour hinge-bending regions. The resulting sequence-based prediction tool, HingeSeek, is available to run through a webserver at hingeseek.cmp.uea.ac.uk.

Delineating elastic properties of kinesin linker and their sensitivity to point mutations

We analyze free energy estimators from simulation trials mimicking single-molecule pulling experiments on a neck linker of a kinesin motor. For that purpose, we have performed a version of steered molecular dynamics (SMD) calculations. The sample trajectories have been analyzed to derive distribution of work done on the system. In order to induce stretching of the linker, we have applied a constant pulling force to the molecule and allowed for a subsequent relaxation of its structure. The use of fluctuation relations (FR) relevant to non-equilibrium systems subject to thermal fluctuations allows us to assess the difference in free energy between stretched and relaxed conformations. To further understand effects of potential mutations on elastic properties of the linker, we have performed similar in silico studies on a structure formed of a polyalanine sequence (Ala-only) and on three other structures, created by substituting selected types of amino acid residues in the linker’s sequence with alanine (Ala) ones. The results of SMD simulations indicate a crucial role played by the Asparagine (Asn) and Lysine (Lys) residues in controlling stretching and relaxation properties of the linker domain of the motor.

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.

Coarse-grain simulations on NMR conformational ensembles highlight functional residues in proteins

Dynamics are a key feature of protein function, and this is especially true of gating residues, which occupy cavity or tunnel lining positions in the protein structure, and will reversibly switch between open and closed conformations in order to control the diffusion of small molecules within a protein's internal matrix. Earlier work on globins and hydrogenases have shown that these gating residues can be detected using a multiscale scheme combining all-atom classic molecular dynamics simulations and coarse-grain calculations of the resulting conformational ensemble mechanical properties. Here, we show that the structural variations observed in the conformational ensembles produced by NMR spectroscopy experiments are sufficient to induce noticeable mechanical changes in a protein, which in turn can be used to identify residues important for function and forming a mechanical nucleus in the protein core. This new approach, which combines experimental data and rapid coarse-grain calculations and no longer needs to resort to time-consuming all-atom simulations, was successfully applied to five different protein families.

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.

Dynamics based clustering of globin family members

A methodology to cluster proteins based on their dynamics’ similarity is presented. For each pair of proteins from a dataset, the structures are superimposed, and the Anisotropic Network Model modes of motions are calculated. The twelve slowest modes from each protein are matched using a local mode alignment algorithm based on the local sequence alignment algorithm of Smith–Waterman. The dynamical similarity distance matrix is calculated based on the top scoring matches of each pair and the proteins are clustered using a hierarchical clustering algorithm. The utility of this method is exemplified on a dataset of protein chains from the globin family and a dataset of tetrameric hemoglobins. The results demonstrate the effect of the quaternary structure of globin members on their intrinsic dynamics and show good ability to distinguish between different states of hemoglobin, revealing the dynamical relations between them.

Dynamical comparison between myoglobin and hemoglobin

Myoglobin and hemoglobin are globular hemeproteins, when the former is a monomer and the latter a heterotetramer. Despite the structural similarity of myoglobin to α and β subunits of hemoglobin, there is a functional difference between the two proteins, owing to the quaternary structure of hemoglobin. The effect of the quaternary structure of hemoglobin on the intrinsic dynamics of its subunits is explored by dynamical comparison of the two proteins. Anisotropic Network Model modes of motion were calculated for hemoglobin and myoglobin. Dynamical comparison between the proteins was performed using global and local Anisotropic Network Model mode alignment algorithms based on the algorithms of Smith-Waterman and Needleman-Wunsch for sequence comparison. The results indicate that the quaternary structure of hemoglobin substantially alters the intrinsic dynamics of its subunits, an effect that may contribute to the functional difference between the two proteins. Local dynamics similarity between the proteins is still observed at the major exit route of the ligand.

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.

Elastic moduli of biological fibers in a coarse-grained model: crystalline cellulose and β-amyloids

We study the mechanical response of cellulose and β-amyloid microfibrils to three types of deformation: tensile, indentational, and shear. The cellulose microfibrils correspond to the allomorphs Iα or Iβ whereas the β-amyloid microfibrils correspond to the polymorphs of either two- or three-fold symmetry. This response can be characterized by three elastic moduli, namely, Y_L, Y_T, and S. We use a structure-based coarse-grained model to analyze the deformations in a unified manner. We find that each of the moduli is almost the same for the two allomorphs of cellulose but Y_L is about 20 times larger than Y_T (140 GPa vs. 7 GPa), indicating the existence of significant anisotropy. For cellulose we note that the anisotropy results from the involvement of covalent bonds in stretching. For β-amyloid, the sense of anisotropy is opposite to that of cellulose. In the three-fold symmetry case, Y_L is about half of Y_T (3 vs. 7) whereas for two-fold symmetry the anisotropy is much larger (1.6 vs. 21 GPa). The S modulus is derived to be 1.2 GPa for three-fold symmetry and one half of it for the other symmetry and 3.0 GPa for cellulose. The values of the moduli reflect deformations in the hydrogen-bond network. Unlike in our theoretical approach, no experiment can measure all three elastic moduli with the same apparatus. However, our theoretical results are consistent with various measured values: typical Y_L for cellulose Iβ ranges from 133 to 155 GPa, Y_T from 2 to 25 GPa, and S from 1.8 to 3.8 GPa. For β-amyloid, the experimental values of S and Y_T are about 0.3 GPa and 3.3 GPa respectively, while the value of Y_L has not been reported.

Structural changes of homodimers in the PDB

Protein complexes are involved in various biological phenomena. These complexes are intrinsically flexible, and structural changes are essential to their functions. To perform a large-scale automated analysis of the structural changes of complexes, we combined two original methods. An application, SCPC, compares two structures of protein complexes and decides the match of binding mode. Another application, Motion Tree, identifies rigid-body motions in various sizes and magnitude from the two structural complexes with the same binding mode. This approach was applied to all available homodimers in the Protein Data Bank (PDB). We defined two complex-specific motions: interface motion and subunit-spanning motion. In the former, each subunit of a complex constitutes a rigid body, and the relative movement between subunits occurs at the interface. In the latter, structural parts from distinct subunits constitute a rigid body, providing the relative movement spanning subunits. All structural changes were classified and examined. It was revealed that the complex-specific motions were common in the homodimers, detected in around 40% of families. The dimeric interfaces were likely to be small and flat for interface motion, while large and rugged for subunit-spanning motion. Interface motion was accompanied by a drastic change in contacts at the interface, while the change in the subunit-spanning motion was moderate. These results indicate that the interface properties of homodimers correlated with the type of complex-specific motion. The study demonstrates that the pipeline of SCPC and Motion Tree is useful for the massive analysis of structural change of protein complexes.

Perturbation-Response Scanning Reveals Key Residues for Allosteric Control in Hsp70

Hsp70 molecular chaperones play an important role in maintaining cellular homeostasis, and are implicated in a wide array of cellular processes, including protein recovery from aggregates, cross-membrane protein translocation, and protein biogenesis. Hsp70 consists of two domains, a nucleotide binding domain (NBD) and a substrate binding domain (SBD), each of which communicates via an allosteric mechanism such that the protein interconverts between two functional states, an ATP-bound open conformation and an ADP-bound closed conformation. The exact mechanism for interstate conversion is not as yet fully understood. However, the ligand-bound states of the NBD and SBD as well as interactions with cochaperones such as DnaJ and nucleotide exchange factor are thought to play crucial regulatory roles. In this study, we apply the perturbation-response scanning (PRS) method in combination with molecular dynamics simulations as a computational tool for the identification of allosteric hot residues in the large multidomain Hsp70 protein. We find evidence in support of the hypothesis that substrate binding triggers ATP hydrolysis and that the ADP-substrate complex favors interstate conversion to the closed state. Furthermore, our data are in agreement with the proposal that there is an allosterically active intermediate state between the open and closed states and vice versa, as we find evidence that ATP binding to the closed structure and peptide binding to the open structure allosterically "activate" the respective complexes. We conclude our analysis by showing how our PRS data fit the current opinion on the Hsp70 conformational cycle and present several allosteric hot residues that may provide a platform for further studies to gain additional insight into Hsp70 allostery.

Modeling global changes induced by local perturbations to the HIV-1 capsid

The HIV-1 capsid is a conical protein shell made up of hexamers and pentamers of the capsid protein. The capsid houses the viral genome and replication machinery, and its opening, or uncoating, within the host cell marks a critical step in the HIV-1 lifecycle. Binding of host factors such as TRIM5α and cyclophilin A (CypA) can alter the capsid's stability, accelerating or delaying the onset of uncoating and disrupting infectivity. We employ coarse-grained computational modeling to investigate the effects of point mutations and host factor binding on HIV-1 capsid stability. We find that the largest fluctuations occur in the low-curvature regions of the capsid, and that its structural dynamics are affected by perturbations at the inter-hexamer interfaces and near the CypA binding loop, suggesting roles for these features in capsid stability. Our models show that linking capsid proteins across hexamers attenuates vibration in the low-curvature regions of the capsid, but that linking within hexamers does not. These results indicate a possible mechanism through which CypA binding alters capsid stability and highlight the utility of coarse-grained network modeling for understanding capsid mechanics.

Strain analysis of protein structures and low dimensionality of mechanical allosteric couplings

In many proteins, especially allosteric proteins that communicate regulatory states from allosteric to active sites, structural deformations are functionally important. To understand these deformations, dynamical experiments are ideal but challenging. Using static structural information, although more limited than dynamical analysis, is much more accessible. Underused for protein analysis, strain is the natural quantity for studying local deformations. We calculate strain tensor fields for proteins deformed by ligands or thermal fluctuations using crystal and NMR structure ensembles. Strains-primarily shears-show deformations around binding sites. These deformations can be induced solely by ligand binding at distant allosteric sites. Shears reveal quasi-2D paths of mechanical coupling between allosteric and active sites that may constitute a widespread mechanism of allostery. We argue that strain-particularly shear-is the most appropriate quantity for analysis of local protein deformations. This analysis can reveal mechanical and biological properties of many proteins.

Similarity in Shape Dictates Signature Intrinsic Dynamics Despite No Functional Conservation in TIM Barrel Enzymes

The conservation of the intrinsic dynamics of proteins emerges as we attempt to understand the relationship between sequence, structure and functional conservation. We characterise the conservation of such dynamics in a case where the structure is conserved but function differs greatly. The triosephosphate isomerase barrel fold (TBF), renowned for its 8 β-strand-α-helix repeats that close to form a barrel, is one of the most diverse and abundant folds found in known protein structures. Proteins with this fold have diverse enzymatic functions spanning five of six Enzyme Commission classes, and we have picked five different superfamily candidates for our analysis using elastic network models. We find that the overall shape is a large determinant in the similarity of the intrinsic dynamics, regardless of function. In particular, the β-barrel core is highly rigid, while the α-helices that flank the β-strands have greater relative mobility, allowing for the many possibilities for placement of catalytic residues. We find that these elements correlate with each other via the loops that link them, as opposed to being directly correlated. We are also able to analyse the types of motions encoded by the normal mode vectors of the α-helices. We suggest that the global conservation of the intrinsic dynamics in the TBF contributes greatly to its success as an enzymatic scaffold both through evolution and enzyme design.

Bridging between NMA and Elastic Network Models: Preserving All-Atom Accuracy in Coarse-Grained Models

Dynamics can provide deep insights into the functional mechanisms of proteins and protein complexes. For large protein complexes such as GroEL/GroES with more than 8,000 residues, obtaining a fine-grained all-atom description of its normal mode motions can be computationally prohibitive and is often unnecessary. For this reason, coarse-grained models have been used successfully. However, most existing coarse-grained models use extremely simple potentials to represent the interactions within the coarse-grained structures and as a result, the dynamics obtained for the coarse-grained structures may not always be fully realistic. There is a gap between the quality of the dynamics of the coarse-grained structures given by all-atom models and that by coarse-grained models. In this work, we resolve an important question in protein dynamics computations—how can we efficiently construct coarse-grained models whose description of the dynamics of the coarse-grained structures remains as accurate as that given by all-atom models? Our method takes advantage of the sparseness of the Hessian matrix and achieves a high efficiency with a novel iterative matrix projection approach. The result is highly significant since it can provide descriptions of normal mode motions at an all-atom level of accuracy even for the largest biomolecular complexes. The application of our method to GroEL/GroES offers new insights into the mechanism of this biologically important chaperonin, such as that the conformational transitions of this protein complex in its functional cycle are even more strongly connected to the first few lowest frequency modes than with other coarse-grained models.

Proteins and other biomolecules are not static but are constantly in motion. Moreover, they possess intrinsic collective motion patterns that are tightly linked to their functions. Thus, an accurate and detailed description of their motions can provide deep insights into their functional mechanisms. For large protein complexes with hundreds of thousands of atoms or more, an atomic level description of the motions can be computationally prohibitive, and so coarse-grained models with fewer structural details are often used instead. However, there can be a big gap between the quality of motions derived from atomic models and those from coarse-grained models. In this work, we solve an important problem in protein dynamics studies: how to preserve the atomic-level accuracy in describing molecular motions while using coarse-grained models? We accomplish this by developing a novel iterative matrix projection method that dramatically speeds up the computations. This method is significant since it promises accurate descriptions of protein motions approaching an all-atom level even for the largest biomolecular complexes. Results shown here for a large molecular chaperonin demonstrate how this can provide new insights into its functional process.

Comparison of intrinsic dynamics of cytochrome p450 proteins using normal mode analysis

Cytochrome P450 enzymes are hemeproteins that catalyze the monooxygenation of a wide-range of structurally diverse substrates of endogenous and exogenous origin. These heme monooxygenases receive electrons from NADH/NADPH via electron transfer proteins. The cytochrome P450 enzymes, which constitute a diverse superfamily of more than 8,700 proteins, share a common tertiary fold but < 25% sequence identity. Based on their electron transfer protein partner, cytochrome P450 proteins are classified into six broad classes. Traditional methods of pro are based on the canonical paradigm that attributes proteins' function to their three-dimensional structure, which is determined by their primary structure that is the amino acid sequence. It is increasingly recognized that protein dynamics play an important role in molecular recognition and catalytic activity. As the mobility of a protein is an intrinsic property that is encrypted in its primary structure, we examined if different classes of cytochrome P450 enzymes display any unique patterns of intrinsic mobility. Normal mode analysis was performed to characterize the intrinsic dynamics of five classes of cytochrome P450 proteins. The present study revealed that cytochrome P450 enzymes share a strong dynamic similarity (root mean squared inner product > 55% and Bhattacharyya coefficient > 80%), despite the low sequence identity (< 25%) and sequence similarity (< 50%) across the cytochrome P450 superfamily. Noticeable differences in Cα atom fluctuations of structural elements responsible for substrate binding were noticed. These differences in residue fluctuations might be crucial for substrate selectivity in these enzymes.

Motion Tree Delineates Hierarchical Structure of Protein Dynamics Observed in Molecular Dynamics Simulation

Molecular dynamics (MD) simulations of proteins provide important information to understand their functional mechanisms, which are, however, likely to be hidden behind their complicated motions with a wide range of spatial and temporal scales. A straightforward and intuitive analysis of protein dynamics observed in MD simulation trajectories is therefore of growing significance with the large increase in both the simulation time and system size. In this study, we propose a novel description of protein motions based on the hierarchical clustering of fluctuations in the inter-atomic distances calculated from an MD trajectory, which constructs a single tree diagram, named a “Motion Tree”, to determine a set of rigid-domain pairs hierarchically along with associated inter-domain fluctuations. The method was first applied to the MD trajectory of substrate-free adenylate kinase to clarify the usefulness of the Motion Tree, which illustrated a clear-cut dynamics picture of the inter-domain motions involving the ATP/AMP lid and the core domain together with the associated amplitudes and correlations. The comparison of two Motion Trees calculated from MD simulations of ligand-free and -bound glutamine binding proteins clarified changes in inherent dynamics upon ligand binding appeared in both large domains and a small loop that stabilized ligand molecule. Another application to a huge protein, a multidrug ATP binding cassette (ABC) transporter, captured significant increases of fluctuations upon binding a drug molecule observed in both large scale inter-subunit motions and a motion localized at a transmembrane helix, which may be a trigger to the subsequent structural change from inward-open to outward-open states to transport the drug molecule. These applications demonstrated the capabilities of Motion Trees to provide an at-a-glance view of various sizes of functional motions inherent in the complicated MD trajectory.

Structure-Encoded Global Motions and Their Role in Mediating Protein-Substrate Interactions

Recent structure-based computational studies suggest that, in contrast to the classical description of equilibrium fluctuations as wigglings and jigglings, proteins have access to well-defined spectra of collective motions, called intrinsic dynamics, encoded by their structure under native state conditions. In particular, the global modes of motions (at the low frequency end of the spectrum) are shown by multiple studies to be highly robust to minor differences in the structure or to detailed interactions at the atomic level. These modes, encoded by the overall fold, usually define the mechanisms of interactions with substrates. They can be estimated by low-resolution models such as the elastic network models (ENMs) exclusively based on interresidue contact topology. The ability of ENMs to efficiently assess the global motions intrinsically favored by the overall fold as well as the relevance of these predictions to the dominant changes in structure experimentally observed for a given protein in the presence of different substrates suggest that the intrinsic dynamics plays a role in mediating protein-substrate interactions. These observations underscore the functional significance of structure-encoded dynamics, or the importance of the predisposition to favor functional global modes in the evolutionary selection of structures.

On the relationship between low-frequency normal modes and the large-scale conformational changes of proteins

Normal mode analysis is a computational technique that allows to study the dynamics of biological macromolecules. It was first applied to small protein cases, more than thirty years ago. The interest in this technique then raised when it was realized that it can provide insights about the large-scale conformational changes a protein can experience, for instance upon ligand binding. As it was also realized that studying highly simplified protein models can provide similar insights, meaning that this kind of analysis can be both quick and simple to handle, several applications were proposed, in the context of various structural biology techniques. This review focuses on these applications, as well as on how the functional relevance of the lowest-frequency modes of proteins was established.

Conformational state distributions and catalytically relevant dynamics of a hinge-bending enzyme studied by single-molecule FRET and a coarse-grained simulation

Over the last few decades, a view has emerged showing that multidomain enzymes are biological machines evolved to harness stochastic kicks of solvent particles into highly directional functional motions. These intrinsic motions are structurally encoded, and Nature makes use of them to catalyze chemical reactions by means of ligand-induced conformational changes and states redistribution. Such mechanisms align reactive groups for efficient chemistry and stabilize conformers most proficient for catalysis. By combining single-molecule Förster resonance energy transfer measurements with normal mode analysis and coarse-grained mesoscopic simulations, we obtained results for a hinge-bending enzyme, namely phosphoglycerate kinase (PGK), which support and extend these ideas. From single-molecule Förster resonance energy transfer, we obtained insight into the distribution of conformational states and the dynamical properties of the domains. The simulations allowed for the characterization of interdomain motions of a compact state of PGK. The data show that PGK is intrinsically a highly dynamic system sampling a wealth of conformations on timescales ranging from nanoseconds to milliseconds and above. Functional motions encoded in the fold are performed by the PGK domains already in its ligand-free form, and substrate binding is not required to enable them. Compared to other multidomain proteins, these motions are rather fast and presumably not rate-limiting in the enzymatic reaction. Ligand binding slightly readjusts the orientation of the domains and feasibly locks the protein motions along a preferential direction. In addition, the functionally relevant compact state is stabilized by the substrates, and acts as a prestate to reach active conformations by means of Brownian motions.

Comparing the intrinsic dynamics of multiple protein structures using elastic network models

BACKGROUND

Elastic network models (ENMs) are based on the simple idea that a protein can be described as a set of particles connected by springs, which can then be used to describe its intrinsic flexibility using, for example, normal mode analysis. Since the introduction of the first ENM by Monique Tirion in 1996, several variants using coarser protein models have been proposed and their reliability for the description of protein intrinsic dynamics has been widely demonstrated. Lately an increasing number of studies have focused on the meaning of slow dynamics for protein function and its potential conservation through evolution. This leads naturally to comparisons of the intrinsic dynamics of multiple protein structures with varying levels of similarity.

SCOPE OF REVIEW

We describe computational strategies for calculating and comparing intrinsic dynamics of multiple proteins using elastic network models, as well as a selection of examples from the recent literature.

MAJOR CONCLUSIONS

The increasing interest for comparing dynamics across protein structures with various levels of similarity, has led to the establishment and validation of reliable computational strategies using ENMs. Comparing dynamics has been shown to be a viable way for gaining greater understanding for the mechanisms employed by proteins for their function. Choices of ENM parameters, structure alignment or similarity measures will likely influence the interpretation of the comparative analysis of protein motion.

GENERAL SIGNIFICANCE

Understanding the relation between protein function and dynamics is relevant to the fundamental understanding of protein structure-dynamics-function relationship. This article is part of a Special Issue entitled Recent developments of molecular dynamics.

iMODS: internal coordinates normal mode analysis server

Normal mode analysis (NMA) in internal (dihedral) coordinates naturally reproduces the collective functional motions of biological macromolecules. iMODS facilitates the exploration of such modes and generates feasible transition pathways between two homologous structures, even with large macromolecules. The distinctive internal coordinate formulation improves the efficiency of NMA and extends its applicability while implicitly maintaining stereochemistry. Vibrational analysis, motion animations and morphing trajectories can be easily carried out at different resolution scales almost interactively. The server is versatile; non-specialists can rapidly characterize potential conformational changes, whereas advanced users can customize the model resolution with multiple coarse-grained atomic representations and elastic network potentials. iMODS supports advanced visualization capabilities for illustrating collective motions, including an improved affine-model-based arrow representation of domain dynamics. The generated all-heavy-atoms conformations can be used to introduce flexibility for more advanced modeling or sampling strategies. The server is free and open to all users with no login requirement at http://imods.chaconlab.org.

The joys and perils of flexible fitting

While performing their functions, biological macromolecules often form large, dynamically changing macromolecular assemblies. Only a relatively small number of such assemblies have been accessible to the atomic-resolution techniques X-ray crystallography and NMR. Electron microscopy in conjunction with image reconstruction has become the preferred alternative for revealing the structures of such macromolecular complexes. However, for most assemblies the achievable resolution is too low to allow accurate atomic modeling directly from the data. Yet, useful models often can be obtained by fitting atomic models of individual components into a low-resolution reconstruction of the entire assembly. Several algorithms for achieving optimal fits in this context were developed recently, many allowing considerable degrees of flexibility to account for binding-induced conformational changes of the assembly components. This chapter describes the advantages and potential pitfalls of these methods and puts them into perspective with alternative approaches such as iterative modular fitting of rigid-body domains.

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

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