An NMA-guided path planning approach for computing large-amplitude conformational changes in proteins

Tackling Hysteresis in Conformational Sampling: How to Be Forgetful with MEMENTO

The structure of proteins has long been recognized to hold the key to understanding and engineering their function, and rapid advances in structural biology and protein structure prediction are now supplying researchers with an ever-increasing wealth of structural information. Most of the time, however, structures can only be determined in free energy minima, one at a time. While conformational flexibility may thus be inferred from static end-state structures, their interconversion mechanisms─a central ambition of structural biology─are often beyond the scope of direct experimentation. Given the dynamical nature of the processes in question, many studies have attempted to explore conformational transitions using molecular dynamics (MD). However, ensuring proper convergence and reversibility in the predicted transitions is extremely challenging. In particular, a commonly used technique to map out a path from a starting to a target conformation called steered MD (SMD) can suffer from starting-state dependence (hysteresis) when combined with techniques such as umbrella sampling (US) to compute the free energy profile of a transition. Here, we study this problem in detail on conformational changes of increasing complexity. We also present a new, history-independent approach that we term "MEMENTO" (Morphing End states by Modelling Ensembles with iNdependent TOpologies) to generate paths that alleviate hysteresis in the construction of conformational free energy profiles. MEMENTO utilizes template-based structure modelling to restore physically reasonable protein conformations based on coordinate interpolation (morphing) as an ensemble of plausible intermediates, from which a smooth path is picked. We compare SMD and MEMENTO on well-characterized test cases (the toy peptide deca-alanine and the enzyme adenylate kinase) before discussing its use in more complicated systems (the kinase P38α and the bacterial leucine transporter LeuT). Our work shows that for all but the simplest systems SMD paths should not in general be used to seed umbrella sampling or related techniques, unless the paths are validated by consistent results from biased runs in opposite directions. MEMENTO, on the other hand, performs well as a flexible tool to generate intermediate structures for umbrella sampling. We also demonstrate that extended end-state sampling combined with MEMENTO can aid the discovery of collective variables on a case-by-case basis.

Modular representation and control of floppy networks

Geometric graph models of systems as diverse as proteins, DNA assemblies, architected materials and robot swarms are useful abstract representations of these objects that also unify ways to study their properties and control them in space and time. While much work has been done in the context of characterizing the behaviour of these networks close to critical points associated with bond and rigidity percolation, isostaticity, etc., much less is known about floppy, underconstrained networks that are far more common in nature and technology. Here, we combine geometric rigidity and algebraic sparsity to provide a framework for identifying the zero energy floppy modes via a representation that illuminates the underlying hierarchy and modularity of the network and thence the control of its nestedness and locality. Our framework allows us to demonstrate a range of applications of this approach that include robotic reaching tasks with motion primitives, and predicting the linear and nonlinear response of elastic networks based solely on infinitesimal rigidity and sparsity, which we test using physical experiments. Our approach is thus likely to be of use broadly in dissecting the geometrical properties of floppy networks using algebraic sparsity to optimize their function and performance.

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.

Normal-mode driven exploration of protein domain motions

Domain motions involved in the function of proteins can often be well described as a combination of motions along a handfull of low-frequency modes, that is, with the values of a few normal coordinates. This means that, when the functional motion of a protein is unknown, it should prove possible to predict it, since it amounts to guess a few values. However, without the help of additional experimental data, using normal coordinates for generating accurate conformers far away from the initial one is not so straightforward. To do so, a new approach is proposed: instead of building conformers directly with the values of a subset of normal coordinates, they are built in two steps, the conformer built with normal coordinates being just used for defining a set of distance constraints, the final conformer being built so as to match them. Note that this approach amounts to transform the problem of generating accurate protein conformers using normal coordinates into a better known one: the distance-geometry problem, which is herein solved with the help of the ROSETTA software. In the present study, this approach allowed to rebuild accurately six large amplitude conformational changes, using at most six low-frequency normal coordinates. As a consequence of the low-dimensionality of the corresponding subspace, random exploration also proved enough for generating low-energy conformers close to the known end-point of the conformational change of the LAO binding protein, lysozyme T4 and adenylate kinase.

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.

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.

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.

Structure-Guided Protein Transition Modeling with a Probabilistic Roadmap Algorithm

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

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.

Elastic network model of learned maintained contacts to predict protein motion

We present a novel elastic network model, lmcENM, to determine protein motion even for localized functional motions that involve substantial changes in the protein's contact topology. Existing elastic network models assume that the contact topology remains unchanged throughout the motion and are thus most appropriate to simulate highly collective function-related movements. lmcENM uses machine learning to differentiate breaking from maintained contacts. We show that lmcENM accurately captures functional transitions unexplained by the classical ENM and three reference ENM variants, while preserving the simplicity of classical ENM. We demonstrate the effectiveness of our approach on a large set of proteins covering different motion types. Our results suggest that accurately predicting a "deformation-invariant" contact topology offers a promising route to increase the general applicability of ENMs. We also find that to correctly predict this contact topology a combination of several features seems to be relevant which may vary slightly depending on the protein. Additionally, we present case studies of two biologically interesting systems, Ferric Citrate membrane transporter FecA and Arachidonate 15-Lipoxygenase.

NOLB: Nonlinear Rigid Block Normal-Mode Analysis Method

We present a new conceptually simple and computationally efficient method for nonlinear normal-mode analysis called NOLB. It relies on the rotations-translations of blocks (RTB) theoretical basis developed by Y.-H. Sanejouand and colleagues [ Durand et al. Biopolymers 1994 , 34 , 759 - 771 . Tama et al. Proteins: Struct., Funct., Bioinf . 2000 , 41 , 1 - 7 ]. We demonstrate how to physically interpret the eigenvalues computed in the RTB basis in terms of angular and linear velocities applied to the rigid blocks and how to construct a nonlinear extrapolation of motion out of these velocities. The key observation of our method is that the angular velocity of a rigid block can be interpreted as the result of an implicit force, such that the motion of the rigid block can be considered as a pure rotation about a certain center. We demonstrate the motions produced with the NOLB method on three different molecular systems and show that some of the lowest frequency normal modes correspond to the biologically relevant motions. For example, NOLB detects the spiral sliding motion of the TALE protein, which is capable of rapid diffusion along its target DNA. Overall, our method produces better structures compared to the standard approach, especially at large deformation amplitudes, as we demonstrate by visual inspection, energy, and topology analyses and also by the MolProbity service validation. Finally, our method is scalable and can be applied to very large molecular systems, such as ribosomes. Standalone executables of the NOLB normal-mode analysis method are available at https://team.inria.fr/nano-d/software/nolb-normal-modes/ . A graphical user interface created for the SAMSON software platform will be made available at https://www.samson-connect.net .

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.

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.

Prediction and clarification of structures of (bio)molecules on surfaces

The design of future materials for biotechnological applications via deposition of molecules on surfaces will require not only exquisite control of the deposition procedure, but of equal importance will be our ability to predict the shapes and stability of individual molecules on various surfaces. Furthermore, one will need to be able to predict the structure patterns generated during the self-organization of whole layers of (bio)molecules on the surface. In this review, we present an overview over the current state of the art regarding the prediction and clarification of structures of biomolecules on surfaces using theoretical and computational methods.

Evolutionary Conserved Positions Define Protein Conformational Diversity

Conformational diversity of the native state plays a central role in modulating protein function. The selection paradigm sustains that different ligands shift the conformational equilibrium through their binding to highest-affinity conformers. Intramolecular vibrational dynamics associated to each conformation should guarantee conformational transitions, which due to its importance, could possibly be associated with evolutionary conserved traits. Normal mode analysis, based on a coarse-grained model of the protein, can provide the required information to explore these features. Herein, we present a novel procedure to identify key positions sustaining the conformational diversity associated to ligand binding. The method is applied to an adequate refined dataset of 188 paired protein structures in their bound and unbound forms. Firstly, normal modes most involved in the conformational change are selected according to their corresponding overlap with structural distortions introduced by ligand binding. The subspace defined by these modes is used to analyze the effect of simulated point mutations on preserving the conformational diversity of the protein. We find a negative correlation between the effects of mutations on these normal mode subspaces associated to ligand-binding and position-specific evolutionary conservations obtained from multiple sequence-structure alignments. Positions whose mutations are found to alter the most these subspaces are defined as key positions, that is, dynamically important residues that mediate the ligand-binding conformational change. These positions are shown to be evolutionary conserved, mostly buried aliphatic residues localized in regular structural regions of the protein like β-sheets and α-helix.

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.

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.

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).

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

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

Insights into mechanism kinematics for protein motion simulation

Background

The high demanding computational requirements necessary to carry out protein motion simulations make it difficult to obtain information related to protein motion. On the one hand, molecular dynamics simulation requires huge computational resources to achieve satisfactory motion simulations. On the other hand, less accurate procedures such as interpolation methods, do not generate realistic morphs from the kinematic point of view. Analyzing a protein’s movement is very similar to serial robots; thus, it is possible to treat the protein chain as a serial mechanism composed of rotational degrees of freedom. Recently, based on this hypothesis, new methodologies have arisen, based on mechanism and robot kinematics, to simulate protein motion. Probabilistic roadmap method, which discretizes the protein configurational space against a scoring function, or the kinetostatic compliance method that minimizes the torques that appear in bonds, aim to simulate protein motion with a reduced computational cost.

Results

In this paper a new viewpoint for protein motion simulation, based on mechanism kinematics is presented. The paper describes a set of methodologies, combining different techniques such as structure normalization normalization processes, simulation algorithms and secondary structure detection procedures. The combination of all these procedures allows to obtain kinematic morphs of proteins achieving a very good computational cost-error rate, while maintaining the biological meaning of the obtained structures and the kinematic viability of the obtained motion.

Conclusions

The procedure presented in this paper, implements different modules to perform the simulation of the conformational change suffered by a protein when exerting its function. The combination of a main simulation procedure assisted by a secondary structure process, and a side chain orientation strategy, allows to obtain a fast and reliable simulations of protein motion.

Elucidating the ensemble of functionally-relevant transitions in protein systems with a robotics-inspired method

Background

Many proteins tune their biological function by transitioning between different functional states, effectively acting as dynamic molecular machines. Detailed structural characterization of transition trajectories is central to understanding the relationship between protein dynamics and function. Computational approaches that build on the Molecular Dynamics framework are in principle able to model transition trajectories at great detail but also at considerable computational cost. Methods that delay consideration of dynamics and focus instead on elucidating energetically-credible conformational paths connecting two functionally-relevant structures provide a complementary approach. Effective sampling-based path planning methods originating in robotics have been recently proposed to produce conformational paths. These methods largely model short peptides or address large proteins by simplifying conformational space.

Methods

We propose a robotics-inspired method that connects two given structures of a protein by sampling conformational paths. The method focuses on small- to medium-size proteins, efficiently modeling structural deformations through the use of the molecular fragment replacement technique. In particular, the method grows a tree in conformational space rooted at the start structure, steering the tree to a goal region defined around the goal structure. We investigate various bias schemes over a progress coordinate for balance between coverage of conformational space and progress towards the goal. A geometric projection layer promotes path diversity. A reactive temperature scheme allows sampling of rare paths that cross energy barriers.

Results and conclusions

Experiments are conducted on small- to medium-size proteins of length up to 214 amino acids and with multiple known functionally-relevant states, some of which are more than 13Å apart of each-other. Analysis reveals that the method effectively obtains conformational paths connecting structural states that are significantly different. A detailed analysis on the depth and breadth of the tree suggests that a soft global bias over the progress coordinate enhances sampling and results in higher path diversity. The explicit geometric projection layer that biases the exploration away from over-sampled regions further increases coverage, often improving proximity to the goal by forcing the exploration to find new paths. The reactive temperature scheme is shown effective in increasing path diversity, particularly in difficult structural transitions with known high-energy barriers.

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

BACKGROUND

Obtaining atomic-scale information about large-amplitude conformational transitions in proteins is a challenging problem for both experimental and computational methods. Such information is, however, important for understanding the mechanisms of interaction of many proteins.

METHODS

This paper presents a computationally efficient approach, combining methods originating from robotics and computational biophysics, to model protein conformational transitions. The ability of normal mode analysis to predict directions of collective, large-amplitude motions is applied to bias the conformational exploration performed by a motion planning algorithm. To reduce the dimension of the problem, normal modes are computed for a coarse-grained elastic network model built on short fragments of three residues. Nevertheless, the validity of intermediate conformations is checked using the all-atom model, which is accurately reconstructed from the coarse-grained one using closed-form inverse kinematics.

RESULTS

Tests on a set of ten proteins demonstrate the ability of the method to model conformational transitions of proteins within a few hours of computing time on a single processor. These results also show that the computing time scales linearly with the protein size, independently of the protein topology. Further experiments on adenylate kinase show that main features of the transition between the open and closed conformations of this protein are well captured in the computed path.

CONCLUSIONS

The proposed method enables the simulation of large-amplitude conformational transitions in proteins using very few computational resources. The resulting paths are a first approximation that can directly provide important information on the molecular mechanisms involved in the conformational transition. This approximation can be subsequently refined and analyzed using state-of-the-art energy models and molecular modeling methods.

SIMS: a hybrid method for rapid conformational analysis

Proteins are at the root of many biological functions, often performing complex tasks as the result of large changes in their structure. Describing the exact details of these conformational changes, however, remains a central challenge for computational biology due the enormous computational requirements of the problem. This has engendered the development of a rich variety of useful methods designed to answer specific questions at different levels of spatial, temporal, and energetic resolution. These methods fall largely into two classes: physically accurate, but computationally demanding methods and fast, approximate methods. We introduce here a new hybrid modeling tool, the Structured Intuitive Move Selector (sims), designed to bridge the divide between these two classes, while allowing the benefits of both to be seamlessly integrated into a single framework. This is achieved by applying a modern motion planning algorithm, borrowed from the field of robotics, in tandem with a well-established protein modeling library. sims can combine precise energy calculations with approximate or specialized conformational sampling routines to produce rapid, yet accurate, analysis of the large-scale conformational variability of protein systems. Several key advancements are shown, including the abstract use of generically defined moves (conformational sampling methods) and an expansive probabilistic conformational exploration. We present three example problems that sims is applied to and demonstrate a rapid solution for each. These include the automatic determination of “active” residues for the hinge-based system Cyanovirin-N, exploring conformational changes involving long-range coordinated motion between non-sequential residues in Ribose-Binding Protein, and the rapid discovery of a transient conformational state of Maltose-Binding Protein, previously only determined by Molecular Dynamics. For all cases we provide energetic validations using well-established energy fields, demonstrating this framework as a fast and accurate tool for the analysis of a wide range of protein flexibility problems.

Molecular dynamics studies on the conformational transitions of adenylate kinase: a computational evidence for the conformational selection mechanism

Escherichia coli adenylate kinase (ADK) is a monomeric phosphotransferase enzyme that catalyzes reversible transfer of phosphoryl group from ATP to AMP with a large-scale domain motion. The detailed mechanism for this conformational transition remains unknown. In the current study, we performed long time-scale molecular dynamics simulations on both open and closed states of ADK. Based on the structural analyses of the simulation trajectories, we detected over 20 times conformational transitions between the open and closed states of ADK and identified two novel conformations as intermediate states in the catalytic processes. With these findings, we proposed a possible mechanism for the large-scale domain motion of Escherichia coli ADK and its catalytic process: (1) the substrate free ADK adopted an open conformation; (2) ATP bound with LID domain closure; (3) AMP bound with NMP domain closure; (4) phosphoryl transfer occurred with ATP, and AMP converted into two ADPs, and no conformational transition was detected in the enzyme; (5) LID domain opened with one ADP released; (6) another ADP released with NMP domain open. As both open and closed states sampled a wide range of conformation transitions, our simulation strongly supported the conformational selection mechanism for Escherichia coli ADK.

MoMA-LigPath: a web server to simulate protein-ligand unbinding

Protein–ligand interactions taking place far away from the active site, during ligand binding or release, may determine molecular specificity and activity. However, obtaining information about these interactions with experimental or computational methods remains difficult. The computational tool presented in this article, MoMA-LigPath, is based on a mechanistic representation of the molecular system, considering partial flexibility, and on the application of a robotics-inspired algorithm to explore the conformational space. Such a purely geometric approach, together with the efficiency of the exploration algorithm, enables the simulation of ligand unbinding within short computing time. Ligand unbinding pathways generated by MoMA-LigPath are a first approximation that can provide useful information about protein–ligand interactions. When needed, this approximation can be subsequently refined and analyzed using state-of-the-art energy models and molecular modeling methods. MoMA-LigPath is available at http://moma.laas.fr. The web server is free and open to all users, with no login requirement.

Protein flexibility and conformational states of Leishmania antigen eIF-4A: identification of a novel plausible protein adjuvant using comparative genomics and molecular modeling

Recent homology modeling studies have identified specific residues (epitope) of the Leishmania RNA helicase protein (LmeIF) that stimulates production of IL-12 cytokine. However, question remains concerning how LmeIF's N-terminal moiety initiates adjuvant effects. Extensive molecular modeling combining the normal mode analysis (NMA) and molecular dynamics simulations, in the present study, has demonstrated that the LmeIF structure may exist in two different forms corresponding to the extended and collapsed (closed) states of the entire structure. The computational results showed that the two domains of the LmeIF structure tend to undergo large fluctuations in a concerted fashion and have strong effect on the solvent accessible surface of the epitope situated on the N-terminal structure. The conformational freedom of the C-terminal domains may explain why the entire LmeIF protein is not as active as the N-terminal moiety. Thereafter, a comparative genome analysis with subsequent homology modeling and molecular electrostatic potential (MEP) techniques allowed us to predict a novel and plausible RNA helicase (LI-helicase) from the Listeria source with adjuvant property as observed for the Leishmania eIF-4A protein. The structural folding and MEP maps revealed similar topologies of the epitope of both LmeIF and LI-helicase proteins and striking identity in the local disposition of the charged groups. An animated Interactive 3D Complement (I3DC) is available in Proteopedia at http://proteopedia.org/w/Journal:JBSD:7.

Thumb-loops up for catalysis: a structure/function investigation of a functional loop movement in a GH11 xylanase

Dynamics is a key feature of enzyme catalysis. Unfortunately, current experimental and computational techniques do not yet provide a comprehensive understanding and description of functional macromolecular motions. In this work, we have extended a novel computational technique, which combines molecular modeling methods and robotics algorithms, to investigate functional motions of protein loops. This new approach has been applied to study the functional importance of the so-called thumb-loop in the glycoside hydrolase family 11 xylanase from Thermobacillus xylanilyticus (Tx-xyl). The results obtained provide new insight into the role of the loop in the glycosylation/deglycosylation catalytic cycle, and underline the key importance of the nature of the residue located at the tip of the thumb-loop. The effect of mutations predicted in silico has been validated by in vitro site-directed mutagenesis experiments. Overall, we propose a comprehensive model of Tx-xyl catalysis in terms of substrate and product dynamics by identifying the action of the thumb-loop motion during catalysis.

Flexible protein docking refinement using pose-dependent normal mode analysis

Modeling conformational changes in protein docking calculations is challenging. To make the calculations tractable, most current docking algorithms typically treat proteins as rigid bodies and use soft scoring functions that implicitly accommodate some degree of flexibility. Alternatively, ensembles of structures generated from molecular dynamics (MD) may be cross-docked. However, such combinatorial approaches can produce many thousands or even millions of docking poses, and require fast and sensitive scoring functions to distinguish them. Here, we present a novel approach called "EigenHex," which is based on normal mode analyses (NMAs) of a simple elastic network model of protein flexibility. We initially assume that the proteins to be docked are rigid, and we begin by performing conventional soft docking using the Hex polar Fourier correlation algorithm. We then apply a pose-dependent NMA to each of the top 1000 rigid body docking solutions, and we sample and re-score multiple perturbed docking conformations generated from linear combinations of up to 20 eigenvectors using a multi-threaded particle swarm optimization algorithm. When applied to the 63 "rigid body" targets of the Protein Docking Benchmark version 2.0, our results show that sampling and re-scoring from just one to three eigenvectors gives a modest but consistent improvement for these targets. Thus, pose-dependent NMA avoids the need to sample multiple eigenvectors and it offers a promising alternative to combinatorial cross-docking.

A normal mode-based geometric simulation approach for exploring biologically relevant conformational transitions in proteins

A three-step approach for multiscale modeling of protein conformational changes is presented that incorporates information about preferred directions of protein motions into a geometric simulation algorithm. The first two steps are based on a rigid cluster normal-mode analysis (RCNMA). Low-frequency normal modes are used in the third step (NMSim) to extend the recently introduced idea of constrained geometric simulations of diffusive motions in proteins by biasing backbone motions of the protein, whereas side-chain motions are biased toward favorable rotamer states. The generated structures are iteratively corrected regarding steric clashes and stereochemical constraint violations. The approach allows performing three simulation types: unbiased exploration of conformational space; pathway generation by a targeted simulation; and radius of gyration-guided simulation. When applied to a data set of proteins with experimentally observed conformational changes, conformational variabilities are reproduced very well for 4 out of 5 proteins that show domain motions, with correlation coefficients r > 0.70 and as high as r = 0.92 in the case of adenylate kinase. In 7 out of 8 cases, NMSim simulations starting from unbound structures are able to sample conformations that are similar (root-mean-square deviation = 1.0-3.1 Å) to ligand bound conformations. An NMSim generated pathway of conformational change of adenylate kinase correctly describes the sequence of domain closing. The NMSim approach is a computationally efficient alternative to molecular dynamics simulations for conformational sampling of proteins. The generated conformations and pathways of conformational transitions can serve as input to docking approaches or as starting points for more sophisticated sampling techniques.

Encoding molecular motions in voxel maps

This paper builds on the combination of robotic path planning algorithms and molecular modeling methods for computing large-amplitude molecular motions, and introduces voxel maps as a computational tool to encode and to represent such motions. We investigate several applications and show results that illustrate the interest of such representation.

Protein folding pathways and state transitions described by classical equations of motion of an elastic network model

Protein topology defined by the matrix of residue contacts has proved to be a fruitful basis for the study of protein dynamics. The widely implemented coarse-grained elastic network model of backbone fluctuations has been used to describe crystallographic temperature factors, allosteric couplings, and some aspects of the folding pathway. In the present study, we develop a model of protein dynamics based on the classical equations of motion of a damped network model (DNM) that describes the folding path from a completely unfolded state to the native conformation through a single-well potential derived purely from the native conformation. The kinetic energy gained through the collapse of the protein chain is dissipated through a friction term in the equations of motion that models the water bath. This approach is completely general and sufficiently fast that it can be applied to large proteins. Folding pathways for various proteins of different classes are described and shown to correlate with experimental observations and molecular dynamics and Monte Carlo simulations. Allosteric transitions between alternative protein structures are also modeled within the DNM through an asymmetric double-well potential.

Simulating ligand-induced conformational changes in proteins using a mechanical disassembly method

Simulating protein conformational changes induced or required by the internal diffusion of a ligand is important for the understanding of their interaction mechanisms. Such simulations are challenging for currently available computational methods. In this paper, the problem is formulated as a mechanical disassembly problem where the protein and the ligand are modeled like articulated mechanisms, and an efficient method for computing molecular disassembly paths is described. The method extends recent techniques developed in the framework of robot motion planning. Results illustrating the capacities of the approach are presented on two biologically interesting systems involving ligand-induced conformational changes: lactose permease (LacY), and the beta(2)-adrenergic receptor.

Instantaneous normal modes as an unforced reaction coordinate for protein conformational transitions

We present a novel sampling approach to explore large protein conformational transitions by determining unique substates from instantaneous normal modes calculated from an elastic network model, and applied to a progression of atomistic molecular dynamics snapshots. This unbiased sampling scheme allows us to direct the path sampling between the conformational end states over simulation timescales that are greatly reduced relative to the known experimental timescales. We use adenylate kinase as a test system to show that instantaneous normal modes can be used to identify substates that drive the structural fluctuations of adenylate kinase from its closed to open conformations, in which we observe 16 complete transitions in 4 mus of simulation time, reducing the timescale over conventional simulation timescales by two orders of magnitude. Analysis shows that the unbiased determination of substates is consistent with known pathways determined experimentally.

Tracing conformational changes in proteins

Background

Many proteins undergo extensive conformational changes as part of their functionality. Tracing these changes is important for understanding the way these proteins function. Traditional biophysics-based conformational search methods require a large number of calculations and are hard to apply to large-scale conformational motions.

Results

In this work we investigate the application of a robotics-inspired method, using backbone and limited side chain representation and a coarse grained energy function to trace large-scale conformational motions. We tested the algorithm on four well known medium to large proteins and we show that even with relatively little information we are able to trace low-energy conformational pathways efficiently. The conformational pathways produced by our methods can be further filtered and refined to produce more useful information on the way proteins function under physiological conditions.

Conclusions

The proposed method effectively captures large-scale conformational changes and produces pathways that are consistent with experimental data and other computational studies. The method represents an important first step towards a larger scale modeling of more complex biological systems.

Guiding the Search for Native-like Protein Conformations with an Ab-initio Tree-based Exploration

In this paper we propose a robotics-inspired method to enhance sampling of native-like conformations when employing only aminoacid sequence information for a protein at hand. Computing such conformations, essential to associating structural and functional information with gene sequences, is challenging due to the high-dimensionality and the rugged energy surface of the protein conformational space. The contribution of this paper is a novel two-layered method to enhance the sampling of geometrically distinct low-energy conformations at a coarse-grained level of detail. The method grows a tree in conformational space reconciling two goals: (i) guiding the tree towards lower energies; and (ii) not oversampling geometrically similar conformations. Discretizations of the energy surface and a low-dimensional projection space are employed to select more often for expansion low-energy conformations in under-explored regions of the conformational space. The tree is expanded with low-energy conformations through a Metropolis Monte Carlo framework that uses a move set of physical fragment configurations. Testing on sequences of eight small-to-medium structurally diverse proteins shows that the method rapidly samples native-like conformations in a few hours on a single CPU. Analysis shows that computed conformations are good candidates for further detailed energetic refinements by larger studies in protein engineering and design.

Control of lipase enantioselectivity by engineering the substrate binding site and access channel

Lipase from Burkholderia cepacia (BCL) has proven to be a very useful biocatalyst for the resolution of 2-substituted racemic acid derivatives, which are important chiral building blocks. Our previous work showed that enantioselectivity of the wild-type BCL could be improved by chemical engineering of the substrate's molecular structure. From this earlier study, three amino acids (L17, V266 and L287) were proposed as targets for mutagenesis aimed at tailoring enzyme enantioselectivity. In the present work, a small library of 57 BCL single mutants targeted on these three residues was constructed and screened for enantioselectivity towards (R,S)-2-chloro ethyl 2-bromophenylacetate. This led to the fast isolation of three single mutants with a remarkable tenfold enhanced or reversed enantioselectivity. Analysis of substrate docking and access trajectories in the active site was then performed. From this analysis, the construction of 13 double mutants was proposed. Among them, an outstanding improved mutant of BCL was isolated that showed an E value of 178 and a 15-fold enhanced specific activity compared to the parental enzyme; thus, this study demonstrates the efficiency of the semirational engineering strategy.

A force field for virtual atom molecular mechanics of proteins

Activities of many biological macromolecules involve large conformational transitions for which crystallography can specify atomic details of alternative end states, but the course of transitions is often beyond the reach of computations based on full-atomic potential functions. We have developed a coarse-grained force field for molecular mechanics calculations based on the virtual interactions of C alpha atoms in protein molecules. This force field is parameterized based on the statistical distribution of the energy terms extracted from crystallographic data, and it is formulated to capture features dependent on secondary structure and on residue-specific contact information. The resulting force field is applied to energy minimization and normal mode analysis of several proteins. We find robust convergence in minimizations to low energies and energy gradients with low degrees of structural distortion, and atomic fluctuations calculated from the normal mode analyses correlate well with the experimental B-factors obtained from high-resolution crystal structures. These findings suggest that the virtual atom force field is a suitable tool for various molecular mechanics applications on large macromolecular systems undergoing large conformational changes.

Computation of conformational transitions in proteins by virtual atom molecular mechanics as validated in application to adenylate kinase

Many proteins function through conformational transitions between structurally disparate states, and there is a need to explore transition pathways between experimentally accessible states by computation. The sizes of systems of interest and the scale of conformational changes are often beyond the scope of full atomic models, but appropriate coarse-grained approaches can capture significant features. We have designed a comprehensive knowledge-based potential function based on a C alpha representation for proteins that we call the virtual atom molecular mechanics (VAMM) force field. Here, we describe an algorithm for using the VAMM potential to describe conformational transitions, and we validate this algorithm in application to a transition between open and closed states of adenylate kinase (ADK). The VAMM algorithm computes normal modes for each state and iteratively moves each structure toward the other through a series of intermediates. The move from each side at each step is taken along that normal mode showing greatest engagement with the other state. The process continues to convergence of terminal intermediates to within a defined limit--here, a root-mean-square deviation of 1 A. Validations show that the VAMM algorithm is highly effective, and the transition pathways examined for ADK are compatible with other structural and biophysical information. We expect that the VAMM algorithm can address many biological systems.

Principles of flexible protein-protein docking

Treating flexibility in molecular docking is a major challenge in cell biology research. Here we describe the background and the principles of existing flexible protein-protein docking methods, focusing on the algorithms and their rational. We describe how protein flexibility is treated in different stages of the docking process: in the preprocessing stage, rigid and flexible parts are identified and their possible conformations are modeled. This preprocessing provides information for the subsequent docking and refinement stages. In the docking stage, an ensemble of pre-generated conformations or the identified rigid domains may be docked separately. In the refinement stage, small-scale movements of the backbone and side-chains are modeled and the binding orientation is improved by rigid-body adjustments. For clarity of presentation, we divide the different methods into categories. This should allow the reader to focus on the most suitable method for a particular docking problem.

Rapid sampling of molecular motions with prior information constraints

Proteins are active, flexible machines that perform a range of different functions. Innovative experimental approaches may now provide limited partial information about conformational changes along motion pathways of proteins. There is therefore a need for computational approaches that can efficiently incorporate prior information into motion prediction schemes. In this paper, we present PathRover, a general setup designed for the integration of prior information into the motion planning algorithm of rapidly exploring random trees (RRT). Each suggested motion pathway comprises a sequence of low-energy clash-free conformations that satisfy an arbitrary number of prior information constraints. These constraints can be derived from experimental data or from expert intuition about the motion. The incorporation of prior information is very straightforward and significantly narrows down the vast search in the typically high-dimensional conformational space, leading to dramatic reduction in running time. To allow the use of state-of-the-art energy functions and conformational sampling, we have integrated this framework into Rosetta, an accurate protocol for diverse types of structural modeling. The suggested framework can serve as an effective complementary tool for molecular dynamics, Normal Mode Analysis, and other prevalent techniques for predicting motion in proteins. We applied our framework to three different model systems. We show that a limited set of experimentally motivated constraints may effectively bias the simulations toward diverse predicates in an outright fashion, from distance constraints to enforcement of loop closure. In particular, our analysis sheds light on mechanisms of protein domain swapping and on the role of different residues in the motion.