A multi-tree approach to compute transition paths on energy landscapes

Exploring the conformational energy landscape of a molecule is an important but challenging problem because of the inherent complexity of this landscape. As part of this theme, various methods have been developed to compute transition paths between stable states of a molecule. Besides the methods classically used in biophysics/biochemistry, a recent approach originating from the robotics community has proven to be an efficient tool for conformational exploration. This approach, called the Transition-based RRT (T-RRT) is based on the combination of an effective path planning algorithm (RRT) with a Monte-Carlo-like transition test. In this paper, we propose an extension to T-RRT based on a multi-tree approach, which we call Multi-T-RRT. It builds several trees rooted at different interesting points of the energy landscape and allows to quickly gain knowledge about possible conformational transition paths. We demonstrate this on the alanine dipeptide

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 paper, 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 very short computing time. Ligand unbinding pathways generated by MoMA-LigPath are a first approximation that can provide very 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

Coarse-grained elastic networks, normal mode analysis and robotics-inspired methods for modeling protein conformational transitions

International audienceThis paper presents a method, inspired by robot motion planning algorithms, to model conformational transitions in proteins. The capacity of normal mode analysis to predict directions of collective large-amplitude motions is exploited to bias the conformational exploration. A coarse-grained elastic network model built on short fragments of three residues is proposed for the rapid computation of normal modes. The accurate reconstruction of the all-atom model from the coarse-grained one is achieved using closed-form inverse kinematics. Results show the capacity of the method to model conformational transitions of proteins within a few hours of computing time on a single processor. Tests on a set of ten proteins demonstrate 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

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

International audienceBackground:Obtaining atomic-scale information about large-amplitude conformational transitions in proteins is achallenging problem for both experimental and computational methods. Such information is, however, importantfor understanding the mechanisms of interaction of many proteins.Methods:This paper presents a computationally efficient approach, combining methods originating from roboticsand computational biophysics, to model protein conformational transitions. The ability of normal mode analysis topredict directions of collective, large-amplitude motions is applied to bias the conformational explorationperformed by a motion planning algorithm. To reduce the dimension of the problem, normal modes arecomputed for a coarse-grained elastic network model built on short fragments of three residues. Nevertheless, thevalidity of intermediate conformations is checked using the all-atom model, which is accurately reconstructed fromthe 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 transitionsof proteins within a few hours of computing time on a single processor. These results also show that thecomputing time scales linearly with the protein size, independently of the protein topology. Further experimentson adenylate kinase show that main features of the transition between the open and closed conformations of thisprotein are well captured in the computed path.Conclusions:The proposed method enables the simulation of large-amplitude conformational transitions inproteins using very few computational resources. The resulting paths are a first approximation that can directlyprovide important information on the molecular mechanisms involved in the conformational transition. Thisapproximation can be subsequently refined and analyzed using state-of-the-art energy models and molecularmodeling methods

Combining System Design and Path Planning

International audienceThis paper addresses the simultaneous design and path planning problem, in which features associated to the bodies of a mobile system have to be selected to find the best design that optimizes its motion between two given configurations. Solving individual path planning problems for all possible designs and selecting the best result would be a straightforward approach for very simple cases. We propose a more efficient approach that combines discrete (design) and continuous (path) optimization in a single stage. It builds on an extension of a sampling-based algorithm, which simultaneously explores the configuration-space costmap of all possible designs aiming to find the best path-design pair. The algorithm filters out unsuitable designs during the path search, which breaks down the combinatorial explosion. Illustrative results are presented for relatively simple (academic) examples. While our work is currently motivated by problems in computational biology, several applications in robotics can also be envisioned

Exhaustive exploration of the conformational landscape of small cyclic peptides using a robotics approach

International audienceSmall cyclic peptides represent a promising class of therapeutic molecules with unique chemical properties. However, the poor knowledge of their structural characteristics makes their computational design and structure prediction a real challenge. In order to better describe their conformational space, we developed a method, named EGSCyP, for the exhaustive exploration of the energy landscape of small head-to-tail cyclic peptides. The method can be summarized by (i) a global exploration of the conformational space based on a mechanistic representation of the peptide and the use of robotics-based algorithms to deal with the closure constraint, (ii) an all-atom refinement of the obtained conformations. EGSCyP can handle D-form residues and N-methylations. Two strategies for the side-chains placement were implemented and compared. To validate our approach, we applied it to a set of three variants of cyclic RGDFV pentapeptides, including the drug candidate Cilengitide. A comparative 1 analysis was made with respect to replica exchange molecular dynamics simulations in implicit solvent. It results that the EGSCyP method provides a very complete characterization of the conformational space of small cyclic pentapeptides

Protein loops with multiple meta-stable conformations: a challenge for sampling and scoring methods

International audienceFlexible regions in proteins, such as loops, cannot be represented by a single conformation. Instead, conformational ensembles are needed to provide a more global picture. In this context, identifying statistically meaningful conforma-tions within an ensemble generated by loop sampling techniques remains an open problem. The difficulty is primarily related to the lack of structural data about these flexible regions. With the majority of structural data coming from X-ray crystallography and ignoring plasticity, the conception and evaluation of loop scoring methods is challenging. In this work, we compare the performance of various scoring methods on a set of 8 protein loops that are known to be flexible. The ability of each method to identify and select all of the known conformations is assessed, and the underlying energy landscapes are produced and projected to visualize the qualitative differences obtained when using the methods. Statistical potentials are found to provide considerable reliability despite their being designed to tradeoff accurac

A Reinforcement-Learning-Based Approach to Enhance Exhaustive Protein Loop Sampling

International audienceMotivation: Loop portions in proteins are involved in many molecular interaction processes. They often exhibit a high degree of flexibility, which can be essential for their function. However, molecular modeling approaches usually represent loops using a single conformation. Although this conformation may correspond to a (meta-)stable state, it does not always provide a realistic representation. Results: In this paper, we propose a method to exhaustively sample the conformational space of protein loops. It exploits structural information encoded in a large library of three-residue fragments, and enforces loop-closure using a closed-form inverse kinematics solver. A novel reinforcement-learning-based approach is applied to accelerate sampling while preserving diversity. The performance of our method is showcased on benchmark datasets involving 9-, 12-and 15-residue loops. In addition, more detailed results presented for streptavidin illustrate the ability of the method to exhaustively sample the conformational space of loops presenting several meta-stable conformations. Availability: We are developing a software package called MoMA (for Molecular Motion Algorithms), which includes modeling tools and algorithms to sample conformations and transition paths of biomolecules, including the application described in this work. The binaries can be provided upon request and a web application will also be implemented in the short future

Combining System Design and Path Planning

International audienceThis paper addresses the simultaneous design and path planning problem, in which features associated to the bodies of a mobile system have to be selected to find the best design that optimizes its motion between two given configurations. Solving individual path planning problems for all possible designs and selecting the best result would be a straightforward approach for very simple cases. We propose a more efficient approach that combines discrete (design) and continuous (path) optimization in a single stage. It builds on an extension of a sampling-based algorithm, which simultaneously explores the configuration-space costmap of all possible designs aiming to find the best path-design pair. The algorithm filters out unsuitable designs during the path search, which breaks down the combinatorial explosion. Illustrative results are presented for relatively simple (academic) examples. While our work is currently motivated by problems in computational biology, several applications in robotics can also be envisioned