Modeling protein conformational changes by iterative fitting of distance constraints using reoriented normal modes

Protein ensemble modeling and analysis with MMMx

Proteins, especially of eukaryotes, often have disordered domains and may contain multiple folded domains whose relative spatial arrangement is distributed. The MMMx ensemble modeling and analysis toolbox (https://github.com/gjeschke/MMMx) can support the design of experiments to characterize the distributed structure of such proteins, starting from AlphaFold2 predictions or folded domain structures. Weak order can be analyzed with reference to a random coil model or to peptide chains that match the residue-specific Ramachandran angle distribution of the loop regions and are otherwise unrestrained. The deviation of the mean square end-to-end distance of chain sections from their average over sections of the same sequence length reveals localized compaction or expansion of the chain. The shape sampled by disordered chains is visualized by superposition in the principal axes frame of their inertia tensor. Ensembles of different sizes and with weighted conformers can be compared based on a similarity parameter that abstracts from the ensemble width.

Integrative ensemble modeling of proteins and their complexes with distance distribution restraints

Many proteins and protein complexes exhibit regions that are intrinsically disordered. Whereas an arsenal of techniques exists to characterize structured proteins or protein regions, characterization of the vast conformational space occupied by intrinsically disordered regions remains a challenging task due the ensemble-averaging nature of many techniques that provide mean value restraints. More representative information can be gained in the form of distribution restraints, such as EPR-derived distance distributions. Previously we developed the ensemble modeling tool MMM, where we partition the macromolecule into structured and unstructured domains and utilize an integrative structural approach with a focus on EPR-derived distance restraints. Here we present the successor program of MMM: MMMx. All the modeling functionality was ported to MMMx and is now accessed by a uniform script format, allowing to combine the different modules at will to modeling pipelines. During the conception of MMMx many of the tools were improved or updated. We discuss the general functionality of MMMx and its modules, and illustrate some of the modeling tools by application examples.

Two-State Exchange Dynamics in Membrane-Embedded Oligosaccharyltransferase Observed in Real-Time by High-Speed AFM

Oligosaccharyltransferase (OST) is a membrane-bound enzyme that catalyzes the transfer of oligosaccharide chains from lipid-linked oligosaccharides (LLO) to asparagine residues in polypeptide chains. Using high-speed atomic force microscopy (AFM), we investigated the dynamic properties of OST molecules embedded in biomembranes. An archaeal single-subunit OST protein was immobilized on a mica support via biotin-avidin interactions and reconstituted in a lipid bilayer. The distance between the top of the protein molecule and the upper surface of the lipid bilayer was monitored in real-time. The height of the extramembranous part exhibited a two-step variation with a difference of 1.8 nm. The high and low states are designated as state 1 and state 2, respectively. The transition processes between the two states fit well to single exponential functions, suggesting that the observed dynamic exchange is an intrinsic property of the archaeal OST protein. The two sets of cross peaks in the NMR spectra of the protein supported the conformational changes between the two states in detergent-solubilized conditions. Considering the height values measured in the AFM measurements, state 1 is closer to the crystal structure, and state 2 has a more compact form. Subsequent AFM experiments indicated that the binding of the sugar donor LLO decreased the structural fluctuation and shifted the equilibrium almost completely to state 1. This dynamic behavior is likely necessary for efficient catalytic turnover. Presumably, state 2 facilitates the immediate release of the bulky glycosylated polypeptide product, thus allowing OST to quickly prepare for the next catalytic cycle.

Exploring Conformational Space with Thermal Fluctuations Obtained by Normal-Mode Analysis

Proteins in their native states can be represented as ensembles of conformers in dynamical equilibrium. Thermal fluctuations are responsible for transitions between these conformers. Normal-modes analysis (NMA) using elastic network models (ENMs) provides an efficient procedure to explore global dynamics of proteins commonly associated with conformational transitions. In the present work, we present an iterative approach to explore protein conformational spaces by introducing structural distortions according to their equilibrium dynamics at room temperature. The approach can be used either to perform unbiased explorations of conformational space or to explore guided pathways connecting two different conformations, e.g., apo and holo forms. In order to test its performance, four proteins with different magnitudes of structural distortions upon ligand binding have been tested. In all cases, the conformational selection model has been confirmed and the conformational space between apo and holo forms has been encompassed. Different strategies have been tested that impact on the efficiency either to achieve a desired conformational change or to achieve a balanced exploration of the protein conformational multiplicity.

ESR Resolves the C Terminus Structure of the Ligand-free Human Glutathione S-Transferase A1-1

Nitroxide- and Cu²⁺-based electron spin resonance (ESR) are combined to provide insight into the conformational states of the functionally important α-helix of the human glutathione S-transferase A1. Distance measurements on various spin-labeled dimeric human glutathione S-transferase A1-1 all result in bimodal distance distributions, indicating that the C-terminus exists in two distinct conformations in solution, one of which closely matches that found in the crystal structure of the ligand-bound enzyme. These measurements permit the generation of a model of the unliganded conformation. Room temperature ESR indicates that the second conformation has high mobility, potentially enabling the enzyme's high degree of substrate promiscuity. This model is then validated using computational modeling and further Cu²⁺-based ESR distance measurements. Cu²⁺-based ESR also provides evidence that the secondary structure of the second conformation is of helical nature. Addition of S-hexyl glutathione results in a shift in relative populations, favoring the state that is similar to the previously known structure of the ligand-bound enzyme.

The contribution of modern EPR to structural biology

Electron paramagnetic resonance (EPR) spectroscopy combined with site-directed spin labelling is applicable to biomolecules and their complexes irrespective of system size and in a broad range of environments. Neither short-range nor long-range order is required to obtain structural restraints on accessibility of sites to water or oxygen, on secondary structure, and on distances between sites. Many of the experiments characterize a static ensemble obtained by shock-freezing. Compared with characterizing the dynamic ensemble at ambient temperature, analysis is simplified and information loss due to overlapping timescales of measurement and system dynamics is avoided. The necessity for labelling leads to sparse restraint sets that require integration with data from other methodologies for building models. The double electron–electron resonance experiment provides distance distributions in the nanometre range that carry information not only on the mean conformation but also on the width of the native ensemble. The distribution widths are often inconsistent with Anfinsen's concept that a sequence encodes a single native conformation defined at atomic resolution under physiological conditions.

MMM: A toolbox for integrative structure modeling

Structural characterization of proteins and their complexes may require integration of restraints from various experimental techniques. MMM (Multiscale Modeling of Macromolecules) is a Matlab-based open-source modeling toolbox for this purpose with a particular emphasis on distance distribution restraints obtained from electron paramagnetic resonance experiments on spin-labelled proteins and nucleic acids and their combination with atomistic structures of domains or whole protomers, small-angle scattering data, secondary structure information, homology information, and elastic network models. MMM does not only integrate various types of restraints, but also various existing modeling tools by providing a common graphical user interface to them. The types of restraints that can support such modeling and the available model types are illustrated by recent application examples.

Systematic Dissociation Pathway Searches Guided by Principal Component Modes

We introduce a novel method, Pathway Search guided by Internal Motions (PSIM), that efficiently finds molecular dissociation pathways of a ligand-receptor system with guidance from principal component (PC) modes obtained from molecular dynamics (MD) simulations. Modeling ligand-receptor dissociation pathways can provide insights into molecular recognition and has practical applications, including understanding kinetic mechanisms and barriers to binding/unbinding as well as design of drugs with desired kinetic properties. PSIM uses PC modes in multilayer internal coordinates to identify natural molecular motions that guide the search for conformational switches and unbinding pathways. The new multilayer internal coordinates overcome problems with Cartesian and classical internal coordinates that fail to smoothly present dihedral rotation or generate nonphysical distortions. We used HIV-1 protease, which has large-scale flap motions, as an example protein to demonstrate use of the multilayer internal coordinates. We provide examples of algorithms and implementation of PSIM with alanine dipeptide and chemical host-guest systems, 2-naphthyl ethanol-β-cyclodextrin and tetramethylammonium-cryptophane complexes. Tetramethylammonium-cryptophane has slow binding/unbinding kinetics. Its residence time, the length to dissociate tetramethylammonium from the host, is ∼14 s from experiments, and PSIM revealed 4 dissociation pathways in approximately 150 CPU h. We also searched the releasing pathways for the product glyceraldehyde-3-phosphate from tryptophan synthase, and one complete dissociation pathway was constructed after running multiple search iterations in approximately 300 CPU h. With guidance by internal PC modes from MD simulations, the PSIM method has advantages over simulation-based methods to search for dissociation pathways of molecular systems with slow noncovalent kinetic behavior.

Understanding ligand-receptor non-covalent binding kinetics using molecular modeling

Kinetic properties may serve as critical differentiators and predictors of drug efficacy and safety, in addition to the traditionally focused binding affinity. However the quantitative structure-kinetics relationship (QSKR) for modeling and ligand design is still poorly understood. This review provides an introduction to the kinetics of drug binding from a fundamental chemistry perspective. We focus on recent developments of computational tools and their applications to non-covalent binding kinetics.

ClustENM: ENM-Based Sampling of Essential Conformational Space at Full Atomic Resolution

Accurate sampling of conformational space and, in particular, the transitions between functional substates has been a challenge in molecular dynamic (MD) simulations of large biomolecular systems. We developed an Elastic Network Model (ENM)-based computational method, ClustENM, for sampling large conformational changes of biomolecules with various sizes and oligomerization states. ClustENM is an iterative method that combines ENM with energy minimization and clustering steps. It is an unbiased technique, which requires only an initial structure as input, and no information about the target conformation. To test the performance of ClustENM, we applied it to six biomolecular systems: adenylate kinase (AK), calmodulin, p38 MAP kinase, HIV-1 reverse transcriptase (RT), triosephosphate isomerase (TIM), and the 70S ribosomal complex. The generated ensembles of conformers determined at atomic resolution show good agreement with experimental data (979 structures resolved by X-ray and/or NMR) and encompass the subspaces covered in independent MD simulations for TIM, p38, and RT. ClustENM emerges as a computationally efficient tool for characterizing the conformational space of large systems at atomic detail, in addition to generating a representative ensemble of conformers that can be advantageously used in simulating substrate/ligand-binding events.

Ligand Docking to Intermediate and Close-To-Bound Conformers Generated by an Elastic Network Model Based Algorithm for Highly Flexible Proteins

Incorporating receptor flexibility in small ligand-protein docking still poses a challenge for proteins undergoing large conformational changes. In the absence of bound structures, sampling conformers that are accessible by apo state may facilitate docking and drug design studies. For this aim, we developed an unbiased conformational search algorithm, by integrating global modes from elastic network model, clustering and energy minimization with implicit solvation. Our dataset consists of five diverse proteins with apo to complex RMSDs 4.7-15 Å. Applying this iterative algorithm on apo structures, conformers close to the bound-state (RMSD 1.4-3.8 Å), as well as the intermediate states were generated. Dockings to a sequence of conformers consisting of a closed structure and its "parents" up to the apo were performed to compare binding poses on different states of the receptor. For two periplasmic binding proteins and biotin carboxylase that exhibit hinge-type closure of two dynamics domains, the best pose was obtained for the conformer closest to the bound structure (ligand RMSDs 1.5-2 Å). In contrast, the best pose for adenylate kinase corresponded to an intermediate state with partially closed LID domain and open NMP domain, in line with recent studies (ligand RMSD 2.9 Å). The docking of a helical peptide to calmodulin was the most challenging case due to the complexity of its 15 Å transition, for which a two-stage procedure was necessary. The technique was first applied on the extended calmodulin to generate intermediate conformers; then peptide docking and a second generation stage on the complex were performed, which in turn yielded a final peptide RMSD of 2.9 Å. Our algorithm is effective in producing conformational states based on the apo state. This study underlines the importance of such intermediate states for ligand docking to proteins undergoing large transitions.

Features of large hinge-bending conformational transitions. Prediction of closed structure from open state

We performed a detailed analysis of conformational transition pathways for a set of 10 proteins, which undergo large hinge-bending-type motions with 4-12 Å RMSD (root mean-square distance) between open and closed crystal structures. Anisotropic network model-Monte Carlo (ANM-MC) algorithm generates a targeted pathway between two conformations, where the collective modes from the ANM are used for deformation at each iteration and the conformational energy of the deformed structure is minimized via an MC algorithm. The target structure was approached successfully with an RMSD of 0.9-4.1 Å when a relatively low cutoff radius of 10 Å was used in ANM. Even though one predominant mode (first or second) directed the open-to-closed conformational transition, changes in the dominant mode character were observed for most cases along the transition. By imposing radius of gyration constraint during mode selection, it was possible to predict the closed structure for eight out of 10 proteins (with initial 4.1-7.1 Å and final 1.7-2.9 Å RMSD to target). Deforming along a single mode leads to most successful predictions. Based on the previously reported free energy surface of adenylate kinase, deformations along the first mode produced an energetically favorable path, which was interestingly facilitated by a change in mode shape (resembling second and third modes) at key points. Pathway intermediates are provided in our database of conformational transitions (http://safir.prc.boun.edu.tr/anmmc/method/1).

High-resolution modeling of protein structures based on flexible fitting of low-resolution structural data

To circumvent the difficulty of directly solving high-resolution biomolecular structures, low-resolution structural data from Cryo-electron microscopy (EM) and small angle solution X-ray scattering (SAXS) are increasingly used to explore multiple conformational states of biomolecular assemblies. One promising venue to obtain high-resolution structural models from low-resolution data is via data-constrained flexible fitting. To this end, we have developed a new method based on a coarse-grained Cα-only protein representation, and a modified form of the elastic network model (ENM) that allows large-scale conformational changes while maintaining the integrity of local structures including pseudo-bonds and secondary structures. Our method minimizes a pseudo-energy which linearly combines various terms of the modified ENM energy with an EM/SAXS-fitting score and a collision energy that penalizes steric collisions. Unlike some previous flexible fitting efforts using the lowest few normal modes, our method effectively utilizes all normal modes so that both global and local structural changes can be fully modeled with accuracy. This method is also highly efficient in computing time. We have demonstrated our method using adenylate kinase as a test case which undergoes a large open-to-close conformational change. The EM-fitting method is available at a web server (http://enm.lobos.nih.gov), and the SAXS-fitting method is available as a pre-compiled executable upon request.

Double electron-electron resonance reveals cAMP-induced conformational change in HCN channels

Binding of 3',5'-cyclic adenosine monophosphate (cAMP) to hyperpolarization-activated cyclic nucleotide-gated (HCN) ion channels regulates their gating. cAMP binds to a conserved intracellular cyclic nucleotide-binding domain (CNBD) in the channel, increasing the rate and extent of activation of the channel and shifting activation to less hyperpolarized voltages. The structural mechanism underlying this regulation, however, is unknown. We used double electron-electron resonance (DEER) spectroscopy to directly map the conformational ensembles of the CNBD in the absence and presence of cAMP. Site-directed, double-cysteine mutants in a soluble CNBD fragment were spin-labeled, and interspin label distance distributions were determined using DEER. We found motions of up to 10 Å induced by the binding of cAMP. In addition, the distributions were narrower in the presence of cAMP. Continuous-wave electron paramagnetic resonance studies revealed changes in mobility associated with cAMP binding, indicating less conformational heterogeneity in the cAMP-bound state. From the measured DEER distributions, we constructed a coarse-grained elastic-network structural model of the cAMP-induced conformational transition. We find that binding of cAMP triggers a reorientation of several helices within the CNBD, including the C-helix closest to the cAMP-binding site. These results provide a basis for understanding how the binding of cAMP is coupled to channel opening in HCN and related channels.

Structural bioinformatics and protein docking analysis of the molecular chaperone-kinase interactions: towards allosteric inhibition of protein kinases by targeting the hsp90-cdc37 chaperone machinery

A fundamental role of the Hsp90-Cdc37 chaperone system in mediating maturation of protein kinase clients and supporting kinase functional activity is essential for the integrity and viability of signaling pathways involved in cell cycle control and organism development. Despite significant advances in understanding structure and function of molecular chaperones, the molecular mechanisms and guiding principles of kinase recruitment to the chaperone system are lacking quantitative characterization. Structural and thermodynamic characterization of Hsp90-Cdc37 binding with protein kinase clients by modern experimental techniques is highly challenging, owing to a transient nature of chaperone-mediated interactions. In this work, we used experimentally-guided protein docking to probe the allosteric nature of the Hsp90-Cdc37 binding with the cyclin-dependent kinase 4 (Cdk4) kinase clients. The results of docking simulations suggest that the kinase recognition and recruitment to the chaperone system may be primarily determined by Cdc37 targeting of the N-terminal kinase lobe. The interactions of Hsp90 with the C-terminal kinase lobe may provide additional "molecular brakes" that can lock (or unlock) kinase from the system during client loading (release) stages. The results of this study support a central role of the Cdc37 chaperone in recognition and recruitment of the kinase clients. Structural analysis may have useful implications in developing strategies for allosteric inhibition of protein kinases by targeting the Hsp90-Cdc37 chaperone machinery.

Molecular modelling and simulations in cancer research

The complexity of cancer and the vast amount of experimental data available have made computer-aided approaches necessary. Biomolecular modelling techniques are becoming increasingly easier to use, whereas hardware and software are becoming better and cheaper. Cross-talk between theoretical and experimental scientists dealing with cancer-research from a molecular approach, however, is still uncommon. This is in contrast to other fields, such as amyloid-related diseases, where molecular modelling studies are widely acknowledged. The aim of this review paper is therefore to expose some of the more common approaches in molecular modelling to cancer scientists in simple terms, illustrating success stories while also revealing the limitations of computational studies at the molecular level.

Optimization of Algorithms for Modeling Protein Structural Transitions from Sparse Long-Range Spin-Label Distance Constraints

Function-related structural transitions of proteins are often large-scale conformational changes that are related to essential dynamics of a protein, which in turn proceeds along a small number of slow normal modes. Hence, it should be possible to characterize such transitions by an equally small number of distance constraints. These constraints should contain the information how the backbone coordinates move along the active normal modes. Such an approach based on residue-level elastic network models for the protein backbone is optimized with respect to the fit algorithm, constraint selection, and parametrization of the elastic network model. A stable fitting algorithm can be based on energy equipartitioning among the modes in the active space. This stabilization allows for extending active space dimension beyond the number of available constraints, which improves fit quality for transitions with a normal mode spectrum of only slowly increasing frequencies. In constraint selection, discrimination between the active normal modes appears to be more important than achieving large distance changes between initial and final structure. Parametrization of the network model has only a small influence on fit quality, as long as scaling of force constants with the inverse sixth power of the distance between network nodes is maintained. Elastic network models with a uniform force constant below a cutoff distance perform significantly worse. With 50 distance constraints, the optimized approach covers more than 50% of the structural change for 44% of all test cases, between 25 and 50% for 22% of the cases, and it fails for 33%.

Coarse-grained and all-atom modeling of structural states and transitions in hemoglobin

Hemoglobin (Hb), an oxygen-binding protein composed of four subunits (α1, α2, β1, and β2), is a well-known example of allosteric proteins that are capable of cooperative ligand binding. Despite decades of studies, the structural basis of its cooperativity remains controversial. In this study, we have integrated coarse-grained (CG) modeling, all-atom simulation, and structural data from X-ray crystallography and wide-angle X-ray scattering (WAXS), aiming to probe dynamic properties of the two structural states of Hb (T and R state) and the transitions between them. First, by analyzing the WAXS data of unliganded and liganded Hb, we have found that the structural ensemble of T or R state is dominated by one crystal structure of Hb with small contributions from other crystal structures of Hb. Second, we have used normal mode analysis to identify two distinct quaternary rotations between the α1β1 and α2β2 dimer, which drive the transitions between T and R state. We have also identified the hot-spot residues whose mutations are predicted to greatly change these quaternary motions. Third, we have generated a CG transition pathway between T and R state, which predicts a clear order of quaternary and tertiary changes involving α and β subunits in Hb. Fourth, we have used the accelerated molecular dynamics to perform an all-atom simulation starting from the T state of Hb, and we have observed a transition toward the R state of Hb. Further analysis of crystal structural data and the all-atom simulation trajectory has corroborated the order of quaternary and tertiary changes predicted by CG modeling.

Characterization of Protein Conformational Changes with Sparse Spin-Label Distance Constraints

The combination of site-directed spin labeling with pulse EPR distance measurements can provide a moderate number of distance constraints on the nanometer length scale for proteins in different states. By adapting an existing algorithm (Zheng, W.; Brooks, B. R. Biophys. J. 2006, 90, 4327) to the problem, we address the question to what extent conformational change can be characterized when the protein structure is known for one of the states, whereas only a sparse set of distance constraints between spin labels is available for the other state. We find that the type and general direction of the conformational change can be recognized, while the amplitude may be uncertain.

A comparative study of structures and structural transitions of secondary transporters with the LeuT fold

Secondary active transporters from several protein families share a core of two five-helix inverted repeats that has become known as the LeuT fold. The known high-resolution protein structures with this fold were analyzed by structural superposition of the core transmembrane domains (TMDs). Three angle parameters derived from the mean TMD axes correlate with accessibility of the central binding site from the outside or inside. Structural transitions between distinct conformations were analyzed for four proteins in terms of changes in relative TMD arrangement and in internal conformation of TMDs. Collectively moving groups of TMDs were found to be correlated in the covariance matrix of elastic network models. The main features of the structural transitions can be reproduced with the 5 % slowest normal modes of anisotropic elastic network models. These results support the rocking bundle model for the major conformational change between the outward- and inward-facing states of the protein and point to an important role for the independently moving last TMDs of each repeat in occluding access to the central binding site. Occlusion is also supported by flexing of some individual TMDs in the collectively moving bundle and hash motifs.

DEER distance measurements on proteins

Distance distributions between paramagnetic centers in the range of 1.8 to 6 nm in membrane proteins and up to 10 nm in deuterated soluble proteins can be measured by the DEER technique. The number of paramagnetic centers and their relative orientation can be characterized. DEER does not require crystallization and is not limited with respect to the size of the protein or protein complex. Diamagnetic proteins are accessible by site-directed spin labeling. To characterize structure or structural changes, experimental protocols were optimized and techniques for artifact suppression were introduced. Data analysis programs were developed, and it was realized that interpretation of the distance distributions must take into account the conformational distribution of spin labels. First methods have appeared for deriving structural models from a small number of distance constraints. The present scope and limitations of the technique are illustrated.

Accurate flexible fitting of high-resolution protein structures to small-angle x-ray scattering data using a coarse-grained model with implicit hydration shell

Small-angle x-ray scattering (SAXS) is a powerful technique widely used to explore conformational states and transitions of biomolecular assemblies in solution. For accurate model reconstruction from SAXS data, one promising approach is to flexibly fit a known high-resolution protein structure to low-resolution SAXS data by computer simulations. This is a highly challenging task due to low information content in SAXS data. To meet this challenge, we have developed what we believe to be a novel method based on a coarse-grained (one-bead-per-residue) protein representation and a modified form of the elastic network model that allows large-scale conformational changes while maintaining pseudobonds and secondary structures. Our method optimizes a pseudoenergy that combines the modified elastic-network model energy with a SAXS-fitting score and a collision energy that penalizes steric collisions. Our method uses what we consider a new implicit hydration shell model that accounts for the contribution of hydration shell to SAXS data accurately without explicitly adding waters to the system. We have rigorously validated our method using five test cases with simulated SAXS data and three test cases with experimental SAXS data. Our method has successfully generated high-quality structural models with root mean-squared deviation of 1 ∼ 3 Å from the target structures.

Accurate flexible fitting of high-resolution protein structures into cryo-electron microscopy maps using coarse-grained pseudo-energy minimization

Cryo-electron microscopy (cryo-EM) has been widely used to explore conformational states of large biomolecular assemblies. The detailed interpretation of cryo-EM data requires the flexible fitting of a known high-resolution protein structure into a low-resolution cryo-EM map. To this end, we have developed what we believe is a new method based on a two-bead-per-residue protein representation, and a modified form of the elastic network model that allows large-scale conformational changes while maintaining pseudobonds and secondary structures. Our method minimizes a pseudo-energy which linearly combines various terms of the modified elastic network model energy with a cryo-EM-fitting score and a collision energy that penalizes steric collisions. Unlike previous flexible fitting efforts using the lowest few normal modes, our method effectively utilizes all normal modes so that both global and local structural changes can be fully modeled. We have validated our method for a diverse set of 10 pairs of protein structures using simulated cryo-EM maps with a range of resolutions and in the absence/presence of random noise. We have shown that our method is both accurate and efficient compared with alternative techniques, and its performance is robust to the addition of random noise. Our method is also shown to be useful for the flexible fitting of three experimental cryo-EM maps.

Structure modeling from small angle X-ray scattering data with elastic network normal mode analysis

Computational algorithms to construct structural models from SAXS experimental data are reviewed. SAXS data provides a wealth of information to study the structure and dynamics of biological molecules, however it does not provide atomic details of structures. Thus combining the low-resolution data with already known X-ray structure is a common approach to study conformational transitions of biological molecules. This review provides a survey of SAXS modeling approaches. In addition, we will discuss theoretical backgrounds and performance of our approach, in which elastic network normal mode analysis is used to predict reasonable conformational transitions from known X-ray structures, and find alternative conformations that are consistent with SAXS data.

Elucidating the higher-order structure of biopolymers by structural probing and mass spectrometry: MS3D

Chemical probing represents a very versatile alternative for studying the structure and dynamics of substrates that are intractable by established high-resolution techniques. The implementation of MS-based strategies for the characterization of probing products has not only extended the range of applicability to virtually all types of biopolymers but has also paved the way for the introduction of new reagents that would not have been viable with traditional analytical platforms. As the availability of probing data is steadily increasing on the wings of the development of dedicated interpretation aids, powerful computational approaches have been explored to enable the effective utilization of such information to generate valid molecular models. This combination of factors has contributed to making the possibility of obtaining actual 3D structures by MS-based technologies (MS3D) a reality. Although approaches for achieving structure determination of unknown targets or assessing the dynamics of known structures may share similar reagents and development trajectories, they clearly involve distinctive experimental strategies, analytical concerns and interpretation paradigms. This Perspective offers a commentary on methods aimed at obtaining distance constraints for the modeling of full-fledged structures while highlighting common elements, salient distinctions and complementary capabilities exhibited by methods used in dynamics studies. We discuss critical factors to be addressed for completing effective structural determinations and expose possible pitfalls of chemical methods. We survey programs developed for facilitating the interpretation of experimental data and discuss possible computational strategies for translating sparse spatial constraints into all-atom models. Examples are provided to illustrate how the concerted application of very diverse probing techniques can lead to the solution of actual biological systems.

Comparative study of various normal mode analysis techniques based on partial Hessians

Standard normal mode analysis becomes problematic for complex molecular systems, as a result of both the high computational cost and the excessive amount of information when the full Hessian matrix is used. Several partial Hessian methods have been proposed in the literature, yielding approximate normal modes. These methods aim at reducing the computational load and/or calculating only the relevant normal modes of interest in a specific application. Each method has its own (dis)advantages and application field but guidelines for the most suitable choice are lacking. We have investigated several partial Hessian methods, including the Partial Hessian Vibrational Analysis (PHVA), the Mobile Block Hessian (MBH), and the Vibrational Subsystem Analysis (VSA). In this article, we focus on the benefits and drawbacks of these methods, in terms of the reproduction of localized modes, collective modes, and the performance in partially optimized structures. We find that the PHVA is suitable for describing localized modes, that the MBH not only reproduces localized and global modes but also serves as an analysis tool of the spectrum, and that the VSA is mostly useful for the reproduction of the low frequency spectrum. These guidelines are illustrated with the reproduction of the localized amine-stretch, the spectrum of quinine and a bis-cinchona derivative, and the low frequency modes of the LAO binding protein.

Large-scale evaluation of dynamically important residues in proteins predicted by the perturbation analysis of a coarse-grained elastic model

Backgrounds

It is increasingly recognized that protein functions often require intricate conformational dynamics, which involves a network of key amino acid residues that couple spatially separated functional sites. Tremendous efforts have been made to identify these key residues by experimental and computational means.

Results

We have performed a large-scale evaluation of the predictions of dynamically important residues by a variety of computational protocols including three based on the perturbation and correlation analysis of a coarse-grained elastic model. This study is performed for two lists of test cases with >500 pairs of protein structures. The dynamically important residues predicted by the perturbation and correlation analysis are found to be strongly or moderately conserved in >67% of test cases. They form a sparse network of residues which are clustered both in 3D space and along protein sequence. Their overall conservation is attributed to their dynamic role rather than ligand binding or high network connectivity.

Conclusion

By modeling how the protein structural fluctuations respond to residue-position-specific perturbations, our highly efficient perturbation and correlation analysis can be used to dissect the functional conformational changes in various proteins with a residue level of detail. The predictions of dynamically important residues serve as promising targets for mutational and functional studies.

Coupling between normal modes drives protein conformational dynamics: illustrations using allosteric transitions in myosin II

Structure-based elastic network models (ENMs) have been remarkably successful in describing conformational transitions in a variety of biological systems. Low-frequency normal modes are usually calculated from the ENM that characterizes elastic interactions between residues in contact in a given protein structure with a uniform force constant. To explore the dynamical effects of nonuniform elastic interactions, we calculate the robustness and coupling of the low-frequency modes in the presence of nonuniform variations in the ENM force constant. The variations in the elastic interactions, approximated here by Gaussian noise, approximately account for perturbation effects of heterogeneous residue-residue interactions or evolutionary sequence changes within a protein family. First-order perturbation theory provides an efficient and qualitatively correct estimate of the mode robustness and mode coupling for finite perturbations to the ENM force constant. The mode coupling analysis and the mode robustness analysis identify groups of strongly coupled modes that encode for protein functional motions. We illustrate the new concepts using myosin II motor protein as an example. The biological implications of mode coupling in tuning the allosteric couplings among the actin-binding site, the nucleotide-binding site, and the force-generating converter and lever arm in myosin isoforms are discussed. We evaluate the robustness of the correlation functions that quantify the allosteric couplings among these three key structural motifs.

Iterative cluster-NMA: A tool for generating conformational transitions in proteins

Computational models provide insight into the structure-function relationship in proteins. These approaches, especially those based on normal mode analysis, can identify the accessible motion space around a given equilibrium structure. The large magnitude, collective motions identified by these methods are often well aligned with the general direction of the expected conformational transitions. However, these motions cannot realistically be extrapolated beyond the local neighborhood of the starting conformation. In this article, the iterative cluster-NMA (icNMA) method is presented for traversing the energy landscape from a starting conformation to a desired goal conformation. This is accomplished by allowing the evolving geometry of the intermediate structures to define the local accessible motion space, and thus produce an appropriate displacement. Following the derivation of the icNMA method, a set of sample simulations are performed to probe the robustness of the model. A detailed analysis of beta1,4-galactosyltransferase-T1 is also given, to highlight many of the capabilities of icNMA. Remarkably, during the transition, a helix is seen to be extended by an additional turn, emphasizing a new unknown role for secondary structures to absorb slack during transitions. The transition pathway for adenylate kinase, which has been frequently studied in the literature, is also discussed.

Conformational transition pathways explored by Monte Carlo simulation integrated with collective modes

Conformational transitions between open/closed or free/bound states in proteins possess functional importance. We propose a technique in which the collective modes obtained from an anisotropic network model (ANM) are used in conjunction with a Monte Carlo (MC) simulation approach, to investigate conformational transition pathways and pathway intermediates. The ANM-MC technique is applied to adenylate kinase (AK) and hemoglobin. The iterative method, in which normal modes are continuously updated during the simulation, proves successful in accomplishing the transition between open-closed conformations of AK and tense-relaxed forms of hemoglobin (C(alpha)-root mean square deviations between two end structures of 7.13 A and 3.55 A, respectively). Target conformations are reached by root mean-square deviations of 2.27 A and 1.90 A for AK and hemoglobin, respectively. The intermediate conformations overlap with crystal structures from the AK family within a 3.0-A root mean-square deviation. In the case of hemoglobin, the transition of tense-to-relaxed passes through the relaxed state. In both cases, the lowest-frequency modes are effective during transitions. The targeted Monte Carlo approach is used without the application of collective modes. Both the ANM-MC and targeted Monte Carlo techniques can explore sequences of events in transition pathways with an efficient yet realistic conformational search.

A unification of the elastic network model and the Gaussian network model for optimal description of protein conformational motions and fluctuations

Coarse-grained elastic models with a C(alpha)-only representation and harmonic interactions have been increasingly used to describe the conformational motions and flexibility of various proteins. In this work, we will unify two complementary elastic models--the elastic network model (ENM) and the Gaussian network model (GNM), in the framework of a generalized anisotropic network model (G-ANM) with a new anisotropy parameter, f(anm). The G-ANM is reduced to GNM at f(anm) = 1, and ENM at f(anm) = 0. By analyzing a list of protein crystal structure pairs using G-ANM, we have attained optimal descriptions of both the isotropic thermal fluctuations and the crystallographically observed conformational changes with a small f(anm) (f(anm) < or = 0.1) and a physically realistic cutoff distance, R(c) approximately 8 A. Thus, the G-ANM improves the performance of GNM and ENM while preserving their simplicity. The properly parameterized G-ANM will enable more accurate and realistic modeling of protein conformational motions and flexibility.

The intrinsic dynamics and function of nickel-binding regulatory protein: insights from elastic network analysis

Nickel-responsive protein NikR regulates the nickel uptake in nickel-dependent bacteria by interacting with the operator of nikABCDE and subsequently repressing the transcription of NikABCDE, an ABC-type nickel transporter system. The function of NikR and its affinity for the operator DNA is highly conformation-dependent, which has been confirmed by three independent crystallographic studies on NikR proteins from different bacteria. Depending on the intracellular nickel concentration, NikR is able to adopt either the open form or one of the two closed forms (cis and trans) that differ in the domain-domain arrangement. Only the closed cis form is optimal for DNA binding. We examined the low-resolution vibrational spectrum of NikR in each conformational form using the elastic network model and observed large-scale domain-domain vibrations that are closely related to the conformational transitions required for function, particularly the symmetric bending mode and the asymmetric twisting mode. This analysis on the intrinsic dynamics coded in the three-dimensional molecular construct allows us to examine the proposed mechanisms of NikR regulation from the standpoint of protein collective motions. Our findings further support the three-state equilibrium hypothesis proposed by others, and imply that an isolated closed cis form may be dynamically unstable but can be stabilized by DNA binding. However, we also found that the simple C(alpha)-model used in the current analysis is insufficient to capture the impact of nickel binding on the protein dynamics, for which an all-atom model with detailed atom typing is more appropriate.