EROS-DOCK for Pairwise and Multi-body Protein-Protein Docking

International audienceProtein-protein docking algorithms aim to predict the 3D structure of a complex using the structures of the individual proteins. For binary complexes, this involves searching and scoring in a six-dimensional space. Many docking algorithms use FFT techniques to exhaustively cover the search space and to accelerate the scoring calculation. However, the results often depend on the initial protein orientations with respect to the Fourier sampling grid. Furthermore, Fourier-transforming a physics-base force field can involve a serious loss of precision. Here, we present a novel docking algorithm called EROS-DOCK (Exhaustive Rotational Search based Docking) [1] to rigidly dock two proteins using a series of exhaustive 3D rotational searches in which non-clashing orientations are scored using ATTRACT coarse-grained force field (ff) [2]. Initial positions are defined by putting each attractive pair of surface pseudo-atoms at their optimal distance in the ff. Thus, EROS-DOCK retains the exhaustive nature of FFT-based search algorithms while using a sensitive physics-based scoring function. Rather than calculating an O(N M) interaction energy * explicitly at every grid point, we use a quaternion "π-ball" to represent the space of all possible 3D Euler angle rotations [3], and we recursively subdivide the π-ball in order to cover the rotational space systematically, from each initial position. An associated tree-like data structure allows rotations that give steric clashes to be pruned efficiently using a "branch-and-bound" technique. To our knowledge, this is the first time that such a branch-and-bound pruning technique has been applied to the rigid-body protein docking problem. The EROS-DOCK algorithm was tested on 173 target complexes from the Protein Docking Benchmark (v4) [4], and results were compared with those of ATTRACT and ZDOCK [5]. Overall, EROS-DOCK was able to find local minima that were not explored by the ATTRACT gradient-driven atom-based search. After refinement by a short coarse-grained minimization, the EROS-DOCK results were generally better than those of ATTRACT and ZDOCK, according to the standard CAPRI criteria. EROS-DOCK can use contact restraints as an additional pruning criteria. Our results show that using even just one residue-residue restraint in each interaction interface is sufficient to increase the number of cases with acceptable solutions within the top 10 from 51 to 121 out of 173 pairwise docking cases. We used EROS-DOCK with restraints to dock trimeric complexes by combinatorial assembly of pairwise solutions. We expected that all interfaces in a multi-body docking solution should be similar to at least one interface in each lists of pairwise docking solutions. Thus, we used a new fast technique to calculate the RMSD between pairs of transformation matrices [6], and an adaptation of the branch-and-bound rotational search algorithm to accelerate the search for low RMSD docking solutions. By test on a home-made benchmark of 11 three-body cases, 7 obtained at least one acceptable quality solution in the top 50 solutions

EROS: A Protein Docking Algorithm Using a Quaternion pi- Ball Representation for Exhaustive and Accelerated Exploration of 3D Rotational Space

International audienceProteins are involved in many essential cellular processes of living organisms. Proteins form macro complexes joining themselves to other proteins to carry out these processes. Therefore, to know the 3D structures of such complexes is of biomedical interest. Proteinprotein docking algorithms aim to predict how two proteins interact with each other to form a 3D complex. Docking algorithms need to fulfill two main tasks: (1) sampling all the possible relative positions of the two proteins and (2) computing the interaction energy at each position to find the minimum energy (= the best solution). Obtaining the interaction energy is a computationally expensive task. We are developing a new algorithm based on the ATTRACT coarsegrained forcefield [1] and using a quaternion ball representation to accelerate the search of the 3D rotational space

EROS-DOCK for Pairwise and Multi-body Protein-Protein Docking

International audienceProtein-protein docking algorithms aim to predict the 3D structure of a complex using the structures of the individual proteins. For binary complexes, this involves searching and scoring in a six-dimensional space. Many docking algorithms use FFT techniques to exhaustively cover the search space and to accelerate the scoring calculation. However, the results often depend on the initial protein orientations with respect to the Fourier sampling grid. Furthermore, Fourier-transforming a physics-base force field can involve a serious loss of precision. Here, we present a novel docking algorithm called EROS-DOCK (Exhaustive Rotational Search based Docking) [1] to rigidly dock two proteins using a series of exhaustive 3D rotational searches in which non-clashing orientations are scored using ATTRACT coarse-grained force field (ff) [2]. Initial positions are defined by putting each attractive pair of surface pseudo-atoms at their optimal distance in the ff. Thus, EROS-DOCK retains the exhaustive nature of FFT-based search algorithms while using a sensitive physics-based scoring function. Rather than calculating an O(N M) interaction energy * explicitly at every grid point, we use a quaternion "π-ball" to represent the space of all possible 3D Euler angle rotations [3], and we recursively subdivide the π-ball in order to cover the rotational space systematically, from each initial position. An associated tree-like data structure allows rotations that give steric clashes to be pruned efficiently using a "branch-and-bound" technique. To our knowledge, this is the first time that such a branch-and-bound pruning technique has been applied to the rigid-body protein docking problem. The EROS-DOCK algorithm was tested on 173 target complexes from the Protein Docking Benchmark (v4) [4], and results were compared with those of ATTRACT and ZDOCK [5]. Overall, EROS-DOCK was able to find local minima that were not explored by the ATTRACT gradient-driven atom-based search. After refinement by a short coarse-grained minimization, the EROS-DOCK results were generally better than those of ATTRACT and ZDOCK, according to the standard CAPRI criteria. EROS-DOCK can use contact restraints as an additional pruning criteria. Our results show that using even just one residue-residue restraint in each interaction interface is sufficient to increase the number of cases with acceptable solutions within the top 10 from 51 to 121 out of 173 pairwise docking cases. We used EROS-DOCK with restraints to dock trimeric complexes by combinatorial assembly of pairwise solutions. We expected that all interfaces in a multi-body docking solution should be similar to at least one interface in each lists of pairwise docking solutions. Thus, we used a new fast technique to calculate the RMSD between pairs of transformation matrices [6], and an adaptation of the branch-and-bound rotational search algorithm to accelerate the search for low RMSD docking solutions. By test on a home-made benchmark of 11 three-body cases, 7 obtained at least one acceptable quality solution in the top 50 solutions

EROS-DOCK and EROS-DOCK MULTI-BODY Approach

International audienceProtein-protein docking aims to predict the 3D structure of a binary complex using the structures of the individual proteins. This typically involves searching and scoring in a six-dimensional space. Many docking algorithms use FFT techniques to exhaustively cover the search space and to accelerate the scoring calculation. However, the results often depend on the initial protein orientations with respect to the Fourier sampling grid. Furthermore, Fourier-transforming a physics-base force field can involve a serious loss of precision. Here, we present a novel docking algorithm, EROS-DOCK (Exhaustive Rotational Search based Docking) to rigidly dock two proteins using a series of exhaustive 3D rotational searches, in which non-clashing orientations are scored using ATTRACT coarse-grained force field. Eros-DOCK retains the exhaustive nature of FFT-based search algorithms while using a sensitive physics-based scoring function. Rather than calculating an O(N M) interaction energy explicitly at every grid * M) inte point, we use a quaternion :π-ball" to represent the space of all possible 3D Euler angle rotations, and we recursively subdivide the π-ball in order to cover the rotational space in a systematic way. We apply a :branch-and-bound" approach for the efficient pruning of rotations that will give steric clashes. The algorithm was tested on a benchmark of 173 complexes, and results were compared with those of a ATTRACT. Eros was able to find local minima that were not explored by the ATTRACT gradient-driven atom-based search. After refinement by a short coarse-grained minimization, EROS-DOCK results were significantly superior to ATTRACT's results according to the standard CAPRI criteria. This is the first time that a branch-and-bound based rotational search is applied to the 6D rigid-body protein docking problem. Given the first success of EROS-DOCK, we are now applying it to multi-body combinatorial docking. This multi-body approach takes advantage of tools as the fast RMSD proposed in [], to compute in an efficient way the RMSD between two transformation matrices and we use 3D rotational maps to find possible good solutions. Since a multi-body complex can be seen as a graph, we build possible multi-body solutions from pairwise solutions, where a pairwise solution is an edge that connects a node pair to obtain a connected graph. However, It is necessary to know all the edges that remain unknown. It is possible to expect that if the one unknown edge corresponds to a good solution, such solution can be found in the corresponding pairwise solutions list. Our idea is to perform an efficient search applying the :branch-and-bound" approach of the 3D rotational map to detect rotations that lead to pairwise solutions, and using the fast RMSD we can know how similar is the unknown edge to some pairwise solution. For a first stage, we have implemented this approach for three multi-body complexes, and it was tested using several complexes. From the results, we can determine this approach can be used to perform and efficient multi-body docking. For consequent work, we will extend it to deal with more than 3 molecules

EROS: A Protein Docking Algorithm Using a Quaternion pi- Ball Representation for Exhaustive and Accelerated Exploration of 3D Rotational Space

International audienceProteins are involved in many essential cellular processes of living organisms. Proteins form macro complexes joining themselves to other proteins to carry out these processes. Therefore, to know the 3D structures of such complexes is of biomedical interest. Proteinprotein docking algorithms aim to predict how two proteins interact with each other to form a 3D complex. Docking algorithms need to fulfill two main tasks: (1) sampling all the possible relative positions of the two proteins and (2) computing the interaction energy at each position to find the minimum energy (= the best solution). Obtaining the interaction energy is a computationally expensive task. We are developing a new algorithm based on the ATTRACT coarsegrained forcefield [1] and using a quaternion ball representation to accelerate the search of the 3D rotational space

Docking protéique par paire et à plusieurs composants, à l'aide d'une exploration systématique de l'espace tri-dimensionnel des rotations par un algorithme de séparation et évaluation

Determination of tri-dimensional (3D) structures of protein complexes is crucial to increase research advances on biological processes that help, for instance, to understand the development of diseases and their possible prevention or treatment. The difficulties and high costs of experimental methods to determine protein 3D structures and the importance of protein complexes for research have encouraged the use of computer science for developing tools to help filling this gap, such as protein docking algorithms. The protein docking problem has been studied for over 40 years. However, developing accurate and efficient protein docking algorithms remains a challenging problem due to the size of the search space, the approximate nature of the scoring functions used, and often the inherent flexibility of the protein structures to be docked. This thesis presents an algorithm to rigidly dock proteins using a series of exhaustive 3D branch-and-bound rotational searches in which non-clashing orientations are scored using ATTRACT. The rotational space is represented as a quaternion “π-ball”, which is systematically sub-divided in a “branch-and-bound” manner, allowing efficient pruning of rotations that will give steric clashes. The contribution of this thesis can be described in three main parts as follows. 1) The algorithm called EROS-DOCK to assemble two proteins. It was tested on 173 Docking Benchmark complexes. According to the CAPRI quality criteria, EROS-DOCK typically gives more acceptable or medium quality solutions than ATTRACT and ZDOCK. 2)The extension of the EROS-DOCK algorithm to allow the use of atom-atom or residue-residue distance restraints. The results show that using even just one residue-residue restraint in each interaction interface is sufficient to increase the number of cases with acceptable solutions within the top-10 from 51 to 121 out of 173 pairwise docking cases. Hence, EROS-DOCK offers a new improved search strategy to incorporate experimental data, of which a proof-of-principle using data-driven computational restraints is demonstrated in this thesis, and this might be especially important for multi-body complexes. 3)The extension of the algorithm to dock trimeric complexes. Here, the proposed method is based on the premise that all of the interfaces in a multi-body docking solution should be similar to at least one interface in each of the lists of pairwise docking solutions. The algorithm was tested on a home-made benchmark of 11 three-body cases. Seven complexes obtained at least one acceptable quality solution in the top-50. In future, the EROS-DOCK algorithm can evolve by integrating improved scoring functions and other types of restraints. Moreover, it can be used as a component in elaborate workflows to efficiently solve complex problems of multi-protein assemblies.La détermination des structures tri-dimensionnelles (3D) des complexes protéiques est cruciale pour l’avancement des recherches sur les processus biologiques qui permettent, par exemple, de comprendre le développement de certaines maladies et, si possible, de les prévenir ou de les traiter. Face à l’intérêt des complexes protéiques pour la recherche, les difficultés et le coût élevé des méthodes expérimentales de détermination des structures 3D des protéines ont encouragé l’utilisation de l’informatique pour développer des outils capables de combler le fossé, comme par exemple les algorithmes d’amarrage protéiques. Le problème de l’amarrage protéique a été étudié depuis plus de 40 ans. Cependant, le développement d’algorithmes d’amarrages précis et efficaces demeure un défi à cause de la taille de l’espace de recherche, de la nature approximée des fonctions de score utilisées, et souvent de la flexibilité inhérente aux structures de protéines à amarrer. Cette thèse présente un algorithme pour l’amarrage rigide des protéines, qui utilise une série de recherches exhaustives rotationnelles au cours desquelles seules les orientations sans clash sont quantifiées par ATTRACT. L’espace rotationnel est représenté par une hyper-sphère à quaternion, qui est systématiquement subdivisée par séparation et évaluation, ce qui permet un élagage efficace des rotations qui donneraient des clashs stériques entre les deux protéines. Les contributions de cette thèse peuvent être décrites en trois parties principales comme suit. 1) L’algorithme appelé EROS-DOCK, qui permet d’amarrer deux protéines. Il a été testé sur 173 complexes du jeu de données “Docking Benchmark”. Selon les critères de qualité CAPRI, EROS-DOCK renvoie typiquement plus de solutions de qualité acceptable ou moyenne que ATTRACT et ZDOCK. 2) L’extension de l’algorithme EROS-DOCK pour permettre d’utiliser les contraintes de distance entre atomes ou entre résidus. Les résultats montrent que le fait d’utiliser une seule contrainte inter-résidus dans chaque interface d’interaction est suffisant pour faire passer de 51 à 121 le nombre de cas présentant une solution dans le top-10, sur 173 cas d’amarrages protéine-protéine. 3) L’extension de EROSDOCK à l’amarrage de complexes trimériques. Ici, la méthode proposée s’appuie sur l’hypothèse selon laquelle chacune des trois interfaces de la solution finale doit être similaire à au moins l’une des interfaces trouvées dans les solutions des amarrages pris deux-à-deux. L’algorithme a été testé sur un benchmark de 11 complexes à 3 protéines. Sept complexes ont obtenu au moins une solution de qualité acceptable dans le top-50 des solutions. À l’avenir, l’algorithme EROS-DOCK pourra encore évoluer en intégrant des fonctions de score améliorées et d’autres types de contraintes. De plus il pourra être utilisé en tant que composant dans des workflows élaborés pour résoudre des problèmes complexes d’assemblage multi-protéiques