Modeling protein conformational transitions by a combination of coarse-grained normal mode analysis and robotics-inspired methods

Leveraging algorithmic search in quantum chemical reaction path finding

Reaction path finding methods construct a graph connecting reactants and products in a quantum chemical energy landscape. They are useful in elucidating various reactions and provide footsteps for designing new reactions. Their enormous computational cost, however, limits their application to relatively simple reactions. This paper engages in accelerating reaction path finding by introducing the principles of algorithmic search. A new method called RRT/SC-AFIR is devised by combining rapidly exploring random tree (RRT) and single component artificial force induced reaction (SC-AFIR). Using 96 cores, our method succeeded in constructing a reaction graph for Fritsch-Buttenberg-Wiechell rearrangement within a time limit of 3 days, while the conventional methods could not. Our results illustrate that the algorithm theory provides refreshing and beneficial viewpoints on quantum chemical methodologies.

Low-Frequency Harmonic Perturbations Drive Protein Conformational Changes

Protein dynamics has been investigated since almost half a century, as it is believed to constitute the fundamental connection between structure and function. Elastic network models (ENMs) have been widely used to predict protein dynamics, flexibility and the biological mechanism, from which remarkable results have been found regarding the prediction of protein conformational changes. Starting from the knowledge of the reference structure only, these conformational changes have been usually predicted either by looking at the individual mode shapes of vibrations (i.e., by considering the free vibrations of the ENM) or by applying static perturbations to the protein network (i.e., by considering a linear response theory). In this paper, we put together the two previous approaches and evaluate the complete protein response under the application of dynamic perturbations. Harmonic forces with random directions are applied to the protein ENM, which are meant to simulate the single frequency-dependent components of the collisions of the surrounding particles, and the protein response is computed by solving the dynamic equations in the underdamped regime, where mass, viscous damping and elastic stiffness contributions are explicitly taken into account. The obtained motion is investigated both in the coordinate space and in the sub-space of principal components (PCs). The results show that the application of perturbations in the low-frequency range is able to drive the protein conformational change, leading to remarkably high values of direction similarity. Eventually, this suggests that protein conformational change might be triggered by external collisions and favored by the inherent low-frequency dynamics of the protein structure.

Integrating Rigidity Analysis into the Exploration of Protein Conformational Pathways Using RRT* and MC

To understand how proteins function on a cellular level, it is of paramount importance to understand their structures and dynamics, including the conformational changes they undergo to carry out their function. For the aforementioned reasons, the study of large conformational changes in proteins has been an interest to researchers for years. However, since some proteins experience rapid and transient conformational changes, it is hard to experimentally capture the intermediate structures. Additionally, computational brute force methods are computationally intractable, which makes it impossible to find these pathways which require a search in a high-dimensional, complex space. In our previous work, we implemented a hybrid algorithm that combines Monte-Carlo (MC) sampling and RRT*, a version of the Rapidly Exploring Random Trees (RRT) robotics-based method, to make the conformational exploration more accurate and efficient, and produce smooth conformational pathways. In this work, we integrated the rigidity analysis of proteins into our algorithm to guide the search to explore flexible regions. We demonstrate that rigidity analysis dramatically reduces the run time and accelerates convergence.

ART-RRT: As-Rigid-As-Possible search for protein conformational transition paths

The possible functions of a protein are strongly related to its structural rearrangements in the presence of other molecules or environmental changes. Hence, the evaluation of transition paths of proteins, which encodes conformational changes between stable states, is important since it may reveal the underlying mechanisms of the biochemical processes related to these motions. During the last few decades, different geometry-based methods have been proposed to predict such transition paths. However, in the cases where the solution requires complex motions, these methods, which typically constrain only locally the molecular structures, could produce physically irrelevant solutions involving self-intersection. Recently, we have proposed ART-RRT, an efficient method for finding ligand-unbinding pathways. It relies on the exploration of energy valleys in low-dimensional spaces, taking advantage of some mechanisms inspired from computer graphics to ensure the consistency of molecular structures. This article extends ART-RRT to the problem of finding probable conformational transition between two stable states for proteins. It relies on a bidirectional exploration rooted on the two end states and introduces an original strategy to attempt connections between the explored regions. The resulting method is able to produce at low computational cost biologically realistic paths free from self-intersection. These paths can serve as valuable input to other advanced methods for the study of proteins. A better understanding of conformational changes of proteins is important since it may reveal the underlying mechanisms of the biochemical processes related to such motions. Recently, the ART-RRT method has been introduced for finding ligand-unbinding pathways. This article presents an adaptation of the method for finding probable conformational transition between two stable states of a protein. The method is not only computationally cost-effective but also able to produce biologically realistic paths which are free from self-intersection.

Attenuating dependence on structural data in computing protein energy landscapes

Background

Nearly all cellular processes involve proteins structurally rearranging to accommodate molecular partners. The energy landscape underscores the inherent nature of proteins as dynamic molecules interconverting between structures with varying energies. In principle, reconstructing a protein’s energy landscape holds the key to characterizing the structural dynamics and its regulation of protein function. In practice, the disparate spatio-temporal scales spanned by the slow dynamics challenge both wet and dry laboratories. However, the growing number of deposited structures for proteins central to human biology presents an opportunity to infer the relevant dynamics via exploitation of the information encoded in such structures about equilibrium dynamics.

Results

Recent computational efforts using extrinsic modes of motion as variables have successfully reconstructed detailed energy landscapes of several medium-size proteins. Here we investigate the extent to which one can reconstruct the energy landscape of a protein in the absence of sufficient, wet-laboratory structural data. We do so by integrating intrinsic modes of motion extracted off a single structure in a stochastic optimization framework that supports the plug-and-play of different variable selection strategies. We demonstrate that, while knowledge of more wet-laboratory structures yields better-reconstructed landscapes, precious information can be obtained even when only one structural model is available.

Conclusions

The presented work shows that it is possible to reconstruct the energy landscape of a protein with reasonable detail and accuracy even when the structural information about the protein is limited to one structure. By attenuating the dependence on structural data of methods designed to compute protein energy landscapes, the work opens up interesting venues of research on structure-based inference of dynamics. Of particular interest are directions of research that will extend such inference to proteins with no experimentally-characterized structures.

Ligand binding effects on the activation of the EGFR extracellular domain

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

Survey of the analysis of continuous conformational variability of biological macromolecules by electron microscopy

Single-particle analysis by electron microscopy is a well established technique for analyzing the three-dimensional structures of biological macromolecules. Besides its ability to produce high-resolution structures, it also provides insights into the dynamic behavior of the structures by elucidating their conformational variability. Here, the different image-processing methods currently available to study continuous conformational changes are reviewed.

Collision-free poisson motion planning in ultra high-dimensional molecular conformation spaces

The function of protein, RNA, and DNA is modulated by fast, dynamic exchanges between three-dimensional conformations. Conformational sampling of biomolecules with exact and nullspace inverse kinematics, using rotatable bonds as revolute joints and noncovalent interactions as holonomic constraints, can accurately characterize these native ensembles. However, sampling biomolecules remains challenging owing to their ultra-high dimensional configuration spaces, and the requirement to avoid (self-) collisions, which results in low acceptance rates. Here, we present two novel mechanisms to overcome these limitations. First, we introduce temporary constraints between near-colliding links. The resulting constraint varieties instantaneously redirect the search for collision-free conformations, and couple motions between distant parts of the linkage. Second, we adapt a randomized Poisson-disk motion planner, which prevents local oversampling and widens the search, to ultra-high dimensions. Tests on several model systems show that the sampling acceptance rate can increase from 16% to 70%, and that the conformational coverage in loop modeling measured as average closeness to existing loop conformations doubled. Correlated protein motions identified with our algorithm agree with those from MD simulations. © 2018 Wiley Periodicals, Inc.

Maintaining and Enhancing Diversity of Sampled Protein Conformations in Robotics-Inspired Methods

The ability to efficiently sample structurally diverse protein conformations allows one to gain a high-level view of a protein's energy landscape. Algorithms from robot motion planning have been used for conformational sampling, and several of these algorithms promote diversity by keeping track of "coverage" in conformational space based on the local sampling density. However, large proteins present special challenges. In particular, larger systems require running many concurrent instances of these algorithms, but these algorithms can quickly become memory intensive because they typically keep previously sampled conformations in memory to maintain coverage estimates. In addition, robotics-inspired algorithms depend on defining useful perturbation strategies for exploring the conformational space, which is a difficult task for large proteins because such systems are typically more constrained and exhibit complex motions. In this article, we introduce two methodologies for maintaining and enhancing diversity in robotics-inspired conformational sampling. The first method addresses algorithms based on coverage estimates and leverages the use of a low-dimensional projection to define a global coverage grid that maintains coverage across concurrent runs of sampling. The second method is an automatic definition of a perturbation strategy through readily available flexibility information derived from B-factors, secondary structure, and rigidity analysis. Our results show a significant increase in the diversity of the conformations sampled for proteins consisting of up to 500 residues when applied to a specific robotics-inspired algorithm for conformational sampling. The methodologies presented in this article may be vital components for the scalability of robotics-inspired approaches.

Detecting intermediate protein conformations using algebraic topology

Background

Understanding protein structure and dynamics is essential for understanding their function. This is a challenging task due to the high complexity of the conformational landscapes of proteins and their rugged energy levels. In particular, it is important to detect highly populated regions which could correspond to intermediate structures or local minima.

Results

We present a hierarchical clustering and algebraic topology based method that detects regions of interest in protein conformational space. The method is based on several techniques. We use coarse grained protein conformational search, efficient robust dimensionality reduction and topological analysis via persistent homology as the main tools. We use two dimensionality reduction methods as well, robust Principal Component Analysis (PCA) and Isomap, to generate a reduced representation of the data while preserving most of the variance in the data.

Conclusions

Our hierarchical clustering method was able to produce compact, well separated clusters for all the tested examples.

Computing energy landscape maps and structural excursions of proteins

BACKGROUND

Structural excursions of a protein at equilibrium are key to biomolecular recognition and function modulation. Protein modeling research is driven by the need to aid wet laboratories in characterizing equilibrium protein dynamics. In principle, structural excursions of a protein can be directly observed via simulation of its dynamics, but the disparate temporal scales involved in such excursions make this approach computationally impractical. On the other hand, an informative representation of the structure space available to a protein at equilibrium can be obtained efficiently via stochastic optimization, but this approach does not directly yield information on equilibrium dynamics.

METHODS

We present here a novel methodology that first builds a multi-dimensional map of the energy landscape that underlies the structure space of a given protein and then queries the computed map for energetically-feasible excursions between structures of interest. An evolutionary algorithm builds such maps with a practical computational budget. Graphical techniques analyze a computed multi-dimensional map and expose interesting features of an energy landscape, such as basins and barriers. A path searching algorithm then queries a nearest-neighbor graph representation of a computed map for energetically-feasible basin-to-basin excursions.

RESULTS

Evaluation is conducted on intrinsically-dynamic proteins of importance in human biology and disease. Visual statistical analysis of the maps of energy landscapes computed by the proposed methodology reveals features already captured in the wet laboratory, as well as new features indicative of interesting, unknown thermodynamically-stable and semi-stable regions of the equilibrium structure space. Comparison of maps and structural excursions computed by the proposed methodology on sequence variants of a protein sheds light on the role of equilibrium structure and dynamics in the sequence-function relationship.

CONCLUSIONS

Applications show that the proposed methodology is effective at locating basins in complex energy landscapes and computing basin-basin excursions of a protein with a practical computational budget. While the actual temporal scales spanned by a structural excursion cannot be directly obtained due to the foregoing of simulation of dynamics, hypotheses can be formulated regarding the impact of sequence mutations on protein function. These hypotheses are valuable in instigating further research in wet laboratories.

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.

Adaptive local learning in sampling based motion planning for protein folding

BACKGROUND

Simulating protein folding motions is an important problem in computational biology. Motion planning algorithms, such as Probabilistic Roadmap Methods, have been successful in modeling the folding landscape. Probabilistic Roadmap Methods and variants contain several phases (i.e., sampling, connection, and path extraction). Most of the time is spent in the connection phase and selecting which variant to employ is a difficult task. Global machine learning has been applied to the connection phase but is inefficient in situations with varying topology, such as those typical of folding landscapes.

RESULTS

We develop a local learning algorithm that exploits the past performance of methods within the neighborhood of the current connection attempts as a basis for learning. It is sensitive not only to different types of landscapes but also to differing regions in the landscape itself, removing the need to explicitly partition the landscape. We perform experiments on 23 proteins of varying secondary structure makeup with 52-114 residues. We compare the success rate when using our methods and other methods. We demonstrate a clear need for learning (i.e., only learning methods were able to validate against all available experimental data) and show that local learning is superior to global learning producing, in many cases, significantly higher quality results than the other methods.

CONCLUSIONS

We present an algorithm that uses local learning to select appropriate connection methods in the context of roadmap construction for protein folding. Our method removes the burden of deciding which method to use, leverages the strengths of the individual input methods, and it is extendable to include other future connection methods.

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.

Influence of model resolution on geometric simulations of antibody aggregation

It is estimated that allergies afflict up to 40% of the world's population. A primary mediator for allergies is the aggregation of antigens and IgE antibodies bound to cell-surface receptors, FcεRI. Antibody/antigen aggregate formation causes stimulation of mast cells and basophils, initiating cellular degranulation and releasing immune mediators which produce an allergic or anaphylactic response. Understanding the shape and structure of these aggregates can provide critical insights into the allergic response. We have previously developed methods to geometrically model, simulate and analyze antibody aggregation inspired by rigid body robotic motion simulations. Our technique handles the large size and number of molecules involved in aggregation, providing an advantage over traditional simulations such as molecular dynamics (MD) and coarse-grained energetic models. In this paper, we study the impact of model resolution on simulations of geometric structures using both our previously developed Monte Carlo simulation and a novel application of rule-based modeling. These methods complement each other, the former providing explicit geometric detail and the latter providing a generic representation where multiple resolutions can be captured. Our exploration is focused on two antigens, a man-made antigen with three binding sites, DF3, and a common shrimp allergen (antigen), Pen a 1. We find that impact of resolution is minimal for DF3, a small globular antigen, but has a larger impact on Pen a 1, a rod-shaped molecule. The volume reduction caused by the loss in resolution allows more binding site accessibility, which can be quantified using a rule-based model with implicit geometric input. Clustering analysis of our simulation shows good correlation when compared with available experimental results. Moreover, collisions in all-atom reconstructions are negligible, at around 0.2% at 90% reduction.

Probing RNA Native Conformational Ensembles with Structural Constraints

Noncoding ribonucleic acids (RNA) play a critical role in a wide variety of cellular processes, ranging from regulating gene expression to post-translational modification and protein synthesis. Their activity is modulated by highly dynamic exchanges between three-dimensional conformational substates, which are difficult to characterize experimentally and computationally. Here, we present an innovative, entirely kinematic computational procedure to efficiently explore the native ensemble of RNA molecules. Our procedure projects degrees of freedom onto a subspace of conformation space defined by distance constraints in the tertiary structure. The dimensionality reduction enables efficient exploration of conformational space. We show that the conformational distributions obtained with our method broadly sample the conformational landscape observed in NMR experiments. Compared to normal mode analysis-based exploration, our procedure diffuses faster through the experimental ensemble while also accessing conformational substates to greater precision. Our results suggest that conformational sampling with a highly reduced but fully atomistic representation of noncoding RNA expresses key features of their dynamic nature.

A General, Adaptive, Roadmap-Based Algorithm for Protein Motion Computation

Precious information on protein function can be extracted from a detailed characterization of protein equilibrium dynamics. This remains elusive in wet and dry laboratories, as function-modulating transitions of a protein between functionally-relevant, thermodynamically-stable and meta-stable structural states often span disparate time scales. In this paper we propose a novel, robotics-inspired algorithm that circumvents time-scale challenges by drawing analogies between protein motion and robot motion. The algorithm adapts the popular roadmap-based framework in robot motion computation to handle the more complex protein conformation space and its underlying rugged energy surface. Given known structures representing stable and meta-stable states of a protein, the algorithm yields a time- and energy-prioritized list of transition paths between the structures, with each path represented as a series of conformations. The algorithm balances computational resources between a global search aimed at obtaining a global view of the network of protein conformations and their connectivity and a detailed local search focused on realizing such connections with physically-realistic models. Promising results are presented on a variety of proteins that demonstrate the general utility of the algorithm and its capability to improve the state of the art without employing system-specific insight.

Enhanced conformational sampling technique provides an energy landscape view of large-scale protein conformational transitions

A novel in silico approach (NMA–ITS) is introduced to rapidly and effectively sample the configuration space and give quantitative data for exploring the conformational changes of proteins.

A stochastic roadmap method to model protein structural transitions

Evidence is emerging that the role of protein structure in disease needs to be rethought. Sequence mutations in proteins are often found to affect the rate at which a protein switches between structures. Modeling structural transitions in wildtype and variant proteins is central to understanding the molecular basis of disease. This paper investigates an efficient algorithmic realization of the stochastic roadmap simulation framework to model structural transitions in wildtype and variants of proteins implicated in human disorders. Our results indicate that the algorithm is able to extract useful information on the impact of mutations on protein structure and function.

Carbohydrate-protein interactions: molecular modeling insights

The article reviews the significant contributions to, and the present status of, applications of computational methods for the characterization and prediction of protein-carbohydrate interactions. After a presentation of the specific features of carbohydrate modeling, along with a brief description of the experimental data and general features of carbohydrate-protein interactions, the survey provides a thorough coverage of the available computational methods and tools. At the quantum-mechanical level, the use of both molecular orbitals and density-functional theory is critically assessed. These are followed by a presentation and critical evaluation of the applications of semiempirical and empirical methods: QM/MM, molecular dynamics, free-energy calculations, metadynamics, molecular robotics, and others. The usefulness of molecular docking in structural glycobiology is evaluated by considering recent docking- validation studies on a range of protein targets. The range of applications of these theoretical methods provides insights into the structural, energetic, and mechanistic facets that occur in the course of the recognition processes. Selected examples are provided to exemplify the usefulness and the present limitations of these computational methods in their ability to assist in elucidation of the structural basis underlying the diverse function and biological roles of carbohydrates in their dialogue with proteins. These test cases cover the field of both carbohydrate biosynthesis and glycosyltransferases, as well as glycoside hydrolases. The phenomenon of (macro)molecular recognition is illustrated for the interactions of carbohydrates with such proteins as lectins, monoclonal antibodies, GAG-binding proteins, porins, and viruses.