Frustration‐guided motion planning reveals conformational transitions in proteins

Proteins exist as conformational ensembles, exchanging between substates to perform their function. Advances in experimental techniques yield unprecedented access to structural snapshots of their conformational landscape. However, computationally modeling how proteins use collective motions to transition between substates is challenging owing to a rugged landscape and large energy barriers. Here, we present a new, robotics‐inspired motion planning procedure called dCC‐RRT that navigates the rugged landscape between substates by introducing dynamic, interatomic constraints to modulate frustration. The constraints balance non‐native contacts and flexibility, and instantaneously redirect the motion towards sterically favorable conformations. On a test set of eight proteins determined in two conformations separated by, on average, 7.5 Å root mean square deviation (RMSD), our pathways reduced the Cα atom RMSD to the goal conformation by 78%, outperforming peer methods. We then applied dCC‐RRT to examine how collective, small‐scale motions of four side‐chains in the active site of cyclophilin A propagate through the protein. dCC‐RRT uncovered a spatially contiguous network of residues linked by steric interactions and collective motion connecting the active site to a recently proposed, non‐canonical capsid binding site 25 Å away, rationalizing NMR and multi‐temperature crystallography experiments. In all, dCC‐RRT can reveal detailed, all‐atom molecular mechanisms for small and large amplitude motions. Source code and binaries are freely available at https://github.com/ExcitedStates/KGS/ .     

Simulating protein motions with rigidity analysis.

Protein motions, ranging from molecular flexibility to large-scale conformational change, play an essential role in many biochemical processes. Despite the explosion in our knowledge of structural and functional data, our understanding of protein movement is still very limited. In previous work, we developed and validated a motion planning based method for mapping protein folding pathways from unstructured conformations to the native state. In this paper, we propose a novel method based on rigidity theory to sample conformation space more effectively, and we describe extensions of our framework to automate the process and to map transitions between specified conformations. Our results show that these additions both improve the accuracy of our maps and enable us to study a broader range of motions for larger proteins. For example, we show that rigidity-based sampling results in maps that capture subtle folding differences between protein G and its mutants, NuG1 and NuG2, and we illustrate how our technique can be used to study large-scale conformational changes in calmodulin, a 148 residue signaling protein known to undergo conformational changes when binding to Ca(2+). Finally, we announce our web-based protein folding server which includes a publicly available archive of protein motions: (http://parasol.tamu.edu/foldingserver/).     

Characterization of Protein Flexibility Using Small-Angle X-Ray Scattering and Amplified Collective Motion Simulations

Large-scale flexibility within a multidomain protein often plays an important role in its biological function. Despite its inherent low resolution, small-angle x-ray scattering (SAXS) is well suited to investigate protein flexibility and determine, with the help of computational modeling, what kinds of protein conformations would coexist in solution. In this article, we develop a tool that combines SAXS data with a previously developed sampling technique called amplified collective motions (ACM) to elucidate structures of highly dynamic multidomain proteins in solution. We demonstrate the use of this tool in two proteins, bacteriophage T4 lysozyme and tandem WW domains of the formin-binding protein 21. The ACM simulations can sample the conformational space of proteins much more extensively than standard molecular dynamics (MD) simulations. Therefore, conformations generated by ACM are significantly better at reproducing the SAXS data than are those from MD simulations.     

Characterization of Protein Flexibility Using Small-Angle X-Ray Scattering and Amplified Collective Motion Simulations

Large-scale flexibility within a multidomain protein often plays an important role in its biological function. Despite its inherent low resolution, small-angle x-ray scattering (SAXS) is well suited to investigate protein flexibility and determine, with the help of computational modeling, what kinds of protein conformations would coexist in solution. In this article, we develop a tool that combines SAXS data with a previously developed sampling technique called amplified collective motions (ACM) to elucidate structures of highly dynamic multidomain proteins in solution. We demonstrate the use of this tool in two proteins, bacteriophage T4 lysozyme and tandem WW domains of the formin-binding protein 21. The ACM simulations can sample the conformational space of proteins much more extensively than standard molecular dynamics (MD) simulations. Therefore, conformations generated by ACM are significantly better at reproducing the SAXS data than are those from MD simulations.     

Modeling correlated main-chain motions in proteins for flexible molecular recognition

We describe a new method for modeling protein and ligand main-chain flexibility, and show its ability to model flexible molecular recognition. The goal is to sample the full conformational space, including large-scale motions that typically cannot be reached in molecular dynamics simulations due to the computational intensity, as well as conformations that have not been observed yet by crystallography or NMR. A secondary goal is to assess the degree of flexibility consistent with protein-ligand recognition. Flexibility analysis of the target protein is performed using the graph-theoretic algorithm FIRST, which also identifies coupled networks of covalent and noncovalent bonds within the protein. The available conformations of the flexible regions are then explored with ROCK by random-walk sampling of the rotatable bonds. ROCK explores correlated motions by only sampling dihedral angles that preserve the coupled bond networks in the protein and generates conformers with good stereochemistry, without using a computationally expensive potential function. A representative set of the conformational ensemble generated this way can be used as targets for docking with SLIDE, which handles the flexibility of protein and ligand side-chains. The realism of this protein main-chain conformational sampling is assessed by comparison with time-resolved NMR studies of cyclophilin A motions. ROCK is also effective for modeling the flexibility of large cyclic and polycyclic ligands, as demonstrated for cyclosporin and zearalenol. The use of this combined approach to perform docking with main-chain flexibility is illustrated for the cyclophilin A-cyclosporin complex and the estrogen receptor in complex with zearalenol, while addressing the question of how much flexibility is allowed without hindering molecular recognition.     

A methodology for efficiently sampling the conformation space of molecular structures

Motivated by recently developed computational techniques for studying protein flexibility, and their potential applications in docking, we propose an efficient method for sampling the conformational space of complex molecular structures. We focus on the loop closure problem, identified in the work of Thorpe and Lei (2004 Phil. Mag. 84 1323-31) as a primary bottleneck in the fast simulation of molecular motions. By modeling a molecular structure as a branching robot, we use an intuitive method in which the robot holds onto itself for maintaining loop constraints. New conformations are generated by applying random external forces, while internal, attractive forces pull the loops closed. Our implementation, tested on several model molecules with low number of degrees of freedom but many interconnected loops, gives promising results that show an almost four times speed-up on the benchmark cube-molecule of Thorpe and Lei.     

Dead‐end elimination with perturbations (DEEPer): A provable protein design algorithm with continuous sidechain and backbone flexibility

Computational protein and drug design generally require accurate modeling of protein conformations. This modeling typically starts with an experimentally determined protein structure and considers possible conformational changes due to mutations or new ligands. The DEE/A* algorithm provably finds the global minimum‐energy conformation (GMEC) of a protein assuming that the backbone does not move and the sidechains take on conformations from a set of discrete, experimentally observed conformations called rotamers. DEE/A* can efficiently find the overall GMEC for exponentially many mutant sequences. Previous improvements to DEE/A* include modeling ensembles of sidechain conformations and either continuous sidechain or backbone flexibility. We present a new algorithm, DEEPer (D ead‐E nd E limination with Per turbations), that combines these advantages and can also handle much more extensive backbone flexibility and backbone ensembles. DEEPer provably finds the GMEC or, if desired by the user, all conformations and sequences within a specified energy window of the GMEC. It includes the new abilities to handle arbitrarily large backbone perturbations and to generate ensembles of backbone conformations. It also incorporates the shear, an experimentally observed local backbone motion never before used in design. Additionally, we derive a new method to accelerate DEE/A*‐based calculations, indirect pruning, that is particularly useful for DEEPer. In 67 benchmark tests on 64 proteins, DEEPer consistently identified lower‐energy conformations than previous methods did, indicating more accurate modeling. Additional tests demonstrated its ability to incorporate larger, experimentally observed backbone conformational changes and to model realistic conformational ensembles. These capabilities provide significant advantages for modeling protein mutations and protein–ligand interactions. Proteins 2013. © 2012 Wiley Periodicals, Inc.     

PABMB Lecture. Protein dynamics, folding and misfolding: from basic physical chemistry to human conformational diseases.

Proteins exhibit a variety of motions ranging from amino acid side-chain rotations to the motions of large domains. Recognition of their conformational flexibility has led to the view that protein molecules undergo fast dynamic interconversion between different conformational substates. This proposal has received support from a wide variety of experimental techniques and from computer simulations of protein dynamics. More recently, studies of the subunit dissociation of oligomeric proteins induced by hydrostatic pressure have shown that the characteristic times for subunit exchange between oligomers and for interconversion between different conformations may be rather slow (hours or days). In such cases, proteins cannot be treated as an ensemble of rapidly interconverting conformational substates, but rather as a persistently heterogeneous population of different long-lived conformers. This is reminiscent of the deterministic behavior exhibited by macroscopic bodies, and may have important implications for our understanding of protein folding and biological functions. Here, we propose that the deterministic behavior of proteins may be closely related to the genesis of conformational diseases, a class of pathological conditions that includes transmissible spongiform encephalopathies, Alzheimer's disease and other amyloidosis.     

A simple model of backbone flexibility improves modeling of side-chain conformational variability

The considerable flexibility of side-chains in folded proteins is important for protein stability and function, and may have a role in mediating allosteric interactions. While sampling side-chain degrees of freedom has been an integral part of several successful computational protein design methods, the predictions of these approaches have not been directly compared to experimental measurements of side-chain motional amplitudes. In addition, protein design methods frequently keep the backbone fixed, an approximation that may substantially limit the ability to accurately model side-chain flexibility. Here, we describe a Monte Carlo approach to modeling side-chain conformational variability and validate our method against a large dataset of methyl relaxation order parameters derived from nuclear magnetic resonance (NMR) experiments (17 proteins and a total of 530 data points). We also evaluate a model of backbone flexibility based on Backrub motions, a type of conformational change frequently observed in ultra-high-resolution X-ray structures that accounts for correlated side-chain backbone movements. The fixed-backbone model performs reasonably well with an overall rmsd between computed and predicted side-chain order parameters of 0.26. Notably, including backbone flexibility leads to significant improvements in modeling side-chain order parameters for ten of the 17 proteins in the set. Greater accuracy of the flexible backbone model results from both increases and decreases in side-chain flexibility relative to the fixed-backbone model. This simple flexible-backbone model should be useful for a variety of protein design applications, including improved modeling of protein-protein interactions, design of proteins with desired flexibility or rigidity, and prediction of correlated motions within proteins.     

Backrub-like backbone simulation recapitulates natural protein conformational variability and improves mutant side-chain prediction

Incorporation of effective backbone sampling into protein simulation and design is an important step in increasing the accuracy of computational protein modeling. Recent analysis of high-resolution crystal structures has suggested a new model, termed backrub, to describe localized, hinge-like alternative backbone and side-chain conformations observed in the crystal lattice. The model involves internal backbone rotations about axes between C-alpha atoms. Based on this observation, we have implemented a backrub-inspired sampling method in the Rosetta structure prediction and design program. We evaluate this model of backbone flexibility using three different tests. First, we show that Rosetta backrub simulations recapitulate the correlation between backbone and side-chain conformations in the high-resolution crystal structures upon which the model was based. As a second test of backrub sampling, we show that backbone flexibility improves the accuracy of predicting point-mutant side-chain conformations over fixed backbone rotameric sampling alone. Finally, we show that backrub sampling of triosephosphate isomerase loop 6 can capture the millisecond/microsecond oscillation between the open and closed states observed in solution. Our results suggest that backrub sampling captures a sizable fraction of localized conformational changes that occur in natural proteins. Application of this simple model of backbone motions may significantly improve both protein design and atomistic simulations of localized protein flexibility.     

SPEACH_AF: Sampling protein ensembles and conformational heterogeneity with Alphafold2

The unprecedented performance of Deepmind’s Alphafold2 in predicting protein structure in CASP XIV and the creation of a database of structures for multiple proteomes and protein sequence repositories is reshaping structural biology. However, because this database returns a single structure, it brought into question Alphafold’s ability to capture the intrinsic conformational flexibility of proteins. Here we present a general approach to drive Alphafold2 to model alternate protein conformations through simple manipulation of the multiple sequence alignment via in silico mutagenesis. The approach is grounded in the hypothesis that the multiple sequence alignment must also encode for protein structural heterogeneity, thus its rational manipulation will enable Alphafold2 to sample alternate conformations. A systematic modeling pipeline is benchmarked against canonical examples of protein conformational flexibility and applied to interrogate the conformational landscape of membrane proteins. This work broadens the applicability of Alphafold2 by generating multiple protein conformations to be tested biologically, biochemically, biophysically, and for use in structure-based drug design.     

Side-chain flexibility in protein-ligand binding: the minimal rotation hypothesis

The goal of this work is to learn from nature about the magnitudes of side-chain motions that occur when proteins bind small organic molecules, and model these motions to improve the prediction of protein-ligand complexes. Following analysis of protein side-chain motions upon ligand binding in 63 complexes, we tested the ability of the docking tool SLIDE to model these motions without being restricted to rotameric transitions or deciding which side chains should be considered as flexible. The model tested is that side-chain conformational changes involving more atoms or larger rotations are likely to be more costly and less prevalent than small motions due to energy barriers between rotamers and the potential of large motions to cause new steric clashes. Accordingly, SLIDE adjusts the protein and ligand side groups as little as necessary to achieve steric complementarity. We tested the hypothesis that small motions are sufficient to achieve good dockings using 63 ligands and the apo structures of 20 different proteins and compared SLIDE side-chain rotations to those experimentally observed. None of these proteins undergoes major main-chain conformational change upon ligand binding, ensuring that side-chain flexibility modeling is not required to compensate for main-chain motions. Although more frugal in the number of side-chain rotations performed, this model substantially mimics the experimentally observed motions. Most side chains do not shift to a new rotamer, and small motions are both necessary and sufficient to predict the correct binding orientation and most protein-ligand interactions for the 20 proteins analyzed.     

Binding of U1A protein changes RNA dynamics as observed by 13C NMR relaxation studies

Recognition of RNA by proteins and small molecules often involves large changes in RNA structure and dynamics, yet very few studies have so far characterized these motional changes. Here we extend to the protein-bound RNA recent 13C relaxation studies of motions in the RNA recognized by human U1A protein, a well-known model for protein-RNA recognition. Changes in relaxation observed upon complex formation demonstrate that the protein-binding site becomes rigid in the complex, but the upper stem-loop that defines the secondary structure of this RNA experiences unexpected motional freedom. By using a helix elongation strategy, we observe that the upper stem-loop moves independently of the remainder of the structure also in the absence of U1A. Surprisingly, RNA residues making important intermolecular contacts in the structure of the complex exhibit increased flexibility in the presence of the protein. Both of these results support the hypothesis that RNA-binding proteins select a structure that optimizes intermolecular contacts in the manifold of conformations sampled by the free RNA and that protein binding quenches these motions. Together with previous studies of the RNA-bound protein, they also demonstrate that protein-RNA interfaces experience complex motions that modulate the strength of individual interactions.     

Local motions in a benchmark of allosteric proteins

Allosteric proteins have been studied extensively in the last 40 years, but so far, no systematic analysis of conformational changes between allosteric structures has been carried out. Here, we compile a set of 51 pairs of known inactive and active allosteric protein structures from the Protein Data Bank. We calculate local conformational differences between the two structures of each protein using simple metrics, such as backbone and side-chain Cartesian displacement, and torsion angle change and rearrangement in residue-residue contacts. Thresholds for each metric arise from distributions of motions in two control sets of pairs of protein structures in the same biochemical state. Statistical analysis of motions in allosteric proteins quantifies the magnitude of allosteric effects and reveals simple structural principles about allostery. For example, allosteric proteins exhibit substantial conformational changes comprising about 20% of the residues. In addition, motions in allosteric proteins show strong bias toward weakly constrained regions such as loops and the protein surface. Correlation functions show that motions communicate through protein structures over distances averaging 10-20 residues in sequence space and 10-20 A in Cartesian space. Comparison of motions in the allosteric set and a set of 21 nonallosteric ligand-binding proteins shows that nonallosteric proteins also exhibit bias of motion toward weakly constrained regions and local correlation of motion. However, allosteric proteins exhibit twice as much percent motion on average as nonallosteric proteins with ligand-induced motion. These observations may guide efforts to design flexibility and allostery into proteins.     

Gaussian-weighted RMSD superposition of proteins: a structural comparison for flexible proteins and predicted protein structures

Many proteins contain flexible structures such as loops and hinged domains. A simple root mean square deviation (RMSD) alignment of two different conformations of the same protein can be skewed by the difference between the mobile regions. To overcome this problem, we have developed a novel method to overlay two protein conformations by their atomic coordinates using a Gaussian-weighted RMSD (wRMSD) fit. The algorithm is based on the Kabsch least-squares method and determines an optimal transformation between two molecules by calculating the minimal weighted deviation between the two coordinate sets. Unlike other techniques that choose subsets of residues to overlay, all atoms are included in the wRMSD overlay. Atoms that barely move between the two conformations will have a greater weighting than those that have a large displacement. Our superposition tool has produced successful alignments when applied to proteins for which two conformations are known. The transformation calculation is heavily weighted by the coordinates of the static region of the two conformations, highlighting the range of flexibility in the overlaid structures. Lastly, we show how wRMSD fits can be used to evaluate predicted protein structures. Comparing a predicted fold to its experimentally determined target structure is another case of comparing two protein conformations of the same sequence, and the degree of alignment directly reflects the quality of the prediction.     

Modeling of the structure of protein–DNA complexes using the data from FRET and footprinting experiments

We discuss the question of constructing three-dimensional models of DNA in complex with proteins using computer modeling and indirect methods of studying the conformation of macromolecules. We consider the methods of interpreting the experimental data obtained by indirect methods of studying the three-dimensional structure of biomolecules. We discuss some aspects of integrating such data into the process of constructing the molecular models of DNA–protein complexes based on the geometric characteristics of DNA. We propose an algorithm for estimating conformations of such complexes based on the information about the local flexibility of DNA and on the experimental data obtained by Forster resonance energy transfer (FRET) and hydroxyl footprinting. Finally, we use this algorithm to predict the hypothetical configuration of DNA in a nucleosome bound with histone H1.     

Relating protein conformational changes to packing efficiency and disorder

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

Large-scale rotational motions of proteins detected by electron paramagnetic resonance and fluorescence.

Direct spectroscopic measurements of rotational motions of proteins and large protein segments are crucial to understanding the molecular dynamics of protein function. Fluorescent probes and spin labels attached to proteins have proved to be powerful tools in the study of large-scale protein motions. Fluorescence depolarization and conventional electron paramagnetic resonance (EPR) are applicable to the study of rotational motions in the nanosecond-to-microsecond time range, and have been used to demonstrate segmental flexibility in an antibody and in myosin. Very slow rotational motions, occurring in the microsecond-to-millisecond time range, are particularly important in supramolecular assemblies, where protein motions are restricted by association with other molecules. Saturation transfer spectroscopy (ST-EPR), a recently developed electron paramagnetic resonance (EPR) technique that permits the detection of rotational correlation times as long as 1 ms, has been used to detect large-scale rotational motions of spin-labeled proteins in muscle filaments and in membranes, providing valuable insights into energy transduction mechanisms in these assemblies.     

Rotamer Dynamics: Analysis of Rotamers in Molecular Dynamics Simulations of Proteins

Given by χ torsional angles, rotamers describe the side-chain conformations of amino acid residues in a protein based on the rotational isomers (hence the word rotamer). Constructed rotamer libraries, based on either protein crystal structures or dynamics studies, are the tools for classifying rotamers (torsional angles) in a way that reflect their frequency in nature. Rotamer libraries are routinely used in structure modeling and evaluation. In this perspective article, we would like to encourage researchers to apply rotamer analyses beyond their traditional use. Molecular dynamics (MD) of proteins highlight the in silico behavior of molecules in solution and thus can identify favorable side-chain conformations. In this article, we used simple computational tools to study rotamer dynamics (RD) in MD simulations. First, we isolated each frame in the MD trajectories in separate Protein Data Bank files via the cpptraj module in AMBER. Then, we extracted torsional angles via the Bio3D module in R language. The classification of torsional angles was also done in R according to the penultimate rotamer library. RD analysis is useful for various applications such as protein folding, study of rotamer-rotamer relationship in protein-protein interaction, real-time correlation between secondary structures and rotamers, study of flexibility of side chains in binding site for molecular docking preparations, use of RD as guide in functional analysis and study of structural changes caused by mutations, providing parameters for improving coarse-grained MD accuracy and speed, and many others. Major challenges facing RD to emerge as a new scientific field involve the validation of results via easy, inexpensive wet-lab methods. This realm is yet to be explored.