Spherical polar Fourier assembly of protein complexes with arbitrary point group symmetry

International audienceA novel fast Fourier transform-based ab inito docking algorithm called SAM is presented, for building perfectly symmetrical models of protein complexes with arbitrary point group symmetry. The basic approach uses a novel and very fast one-dimensional symmetry-constrained spherical polar Fourier search to assemble cyclic Cn systems from a given protein monomer. Structures with higher-order (Dn, T, O and I) point group symmetries may be built using a subsequent symmetry-constrained Fourier domain search to assemble trimeric sub-units. The results reported here show that the SAM algorithm can correctly assemble monomers of up to around 500 residues to produce a near-native complex structure with the given point group symmetry in 17 out of 18 test cases. The SAM program may be downloaded for academic use at http://sam.loria.fr/

User Guide for NOLB : Non-Linear Normal Mode Analysis

Normal mode analysis (NMA) is an old and well established technique that has recently found many new applications in the field of structural biology and structural bioinformatics. Here we present a user guide for new computational scheme for nonlinear normal mode analysis that extrapolates a motion computed from instantaneous linear and angular velocities to large amplitudes. The method is available at https://team.inria.fr/nano-d/software/nolb-normal-modes/

Docking rigid macrocycles using Convex-PL, AutoDock Vina, and RDKit in the D3R Grand Challenge 4

International audienceThe D3R Grand Challenge 4 provided a brilliant opportunity to test macrocyclic docking protocols on a diverse high-quality experimental data. We participated in both pose and affinity prediction exercises. Overall, we aimed to use an automated structure-based docking pipeline built around a set of tools developed in our team. This exercise again demonstrated a crucial importance of the correct local ligand geometry for the overall success of docking. Starting from the second part of the pose prediction stage, we developed a stable pipeline for sampling macrocycle conformers. This resulted in the subangstrom average precision of our pose predictions. In the affinity prediction exercise we obtained average results. However, we could improve these when using docking poses submitted by the best predictors. Our docking tools including the Convex-PL scoring function are available at https://team.inria.fr/nano-d/software/

PEPSI-Dock: a detailed data-driven protein–protein interaction potential accelerated by polar Fourier correlation

International audienceMotivation: Docking prediction algorithms aim to find the native conformation of a complex of proteins from knowledge of their unbound structures. They rely on a combination of sampling and scoring methods, adapted to different scales. Polynomial Expansion of Protein Structures and Interactions for Docking (PEPSI-Dock) improves the accuracy of the first stage of the docking pipeline , which will sharpen up the final predictions. Indeed, PEPSI-Dock benefits from the precision of a very detailed data-driven model of the binding free energy used with a global and exhaustive rigid-body search space. As well as being accurate, our computations are among the fastest by virtue of the sparse representation of the pre-computed potentials and FFT-accelerated sampling techniques. Overall, this is the first demonstration of a FFT-accelerated docking method coupled with an arbitrary-shaped distance-dependent interaction potential. Results: First, we present a novel learning process to compute data-driven distant-dependent pair-wise potentials, adapted from our previous method used for rescoring of putative protein–protein binding poses. The potential coefficients are learned by combining machine-learning techniques with physically interpretable descriptors. Then, we describe the integration of the deduced potentials into a FFT-accelerated spherical sampling provided by the Hex library. Overall, on a training set of 163 heterodimers, PEPSI-Dock achieves a success rate of 91% mid-quality predictions in the top-10 solutions. On a subset of the protein docking benchmark v5, it achieves 44.4% mid-quality predictions in the top-10 solutions when starting from bound structures and 20.5% when starting from unbound structures. The method runs in 5–15 min on a modern laptop and can easily be extended to other types of interactions. Availability and Implementation: https://team.inria.fr/nano-d/software/PEPSI-Dock. Contact: [email protected]

NOLB: Nonlinear Rigid Block Normal Mode Analysis Method

International audienceWe 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. 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

DeepSymmetry : Using 3D convolutional networks for identification of tandem repeats and internal symmetries in protein structures

International audienceMotivation Thanks to the recent advances in structural biology, nowadays 3D structures of various proteins are solved on a routine basis. A large portion of these structures contain structural repetitions or internal symmetries. To understand the evolution mechanisms of these proteins and how structural repetitions affect the protein function, we need to be able to detect such proteins very robustly. As deep learning is particularly suited to deal with spatially organized data, we applied it to the detection of proteins with structural repetitions.Results We present DeepSymmetry, a versatile method based on 3D convolutional networks that detects structural repetitions in proteins and their density maps. Our method is designed to identify tandem repeat proteins, proteins with internal symmetries, symmetries in the raw density maps, their symmetry order and also the corresponding symmetry axes. Detection of symmetry axes is based on learning 6D Veronese mappings of 3D vectors, and the median angular error of axis determination is less than one degree. We demonstrate the capabilities of our method on benchmarks with tandem-repeated proteins and also with symmetrical assemblies. For example, we have discovered about 7800 putative tandem repeat proteins in the PDB.Availability and implementation The method is available at https://team.inria.fr/nano-d/software/deepsymmetry. It consists of a C++ executable that transforms molecular structures into volumetric density maps, and a Python code based on the TensorFlow framework for applying the DeepSymmetry model to these maps

Rapid determination of RMSDs corresponding to macromolecular rigid body motions

International audienceFinding the root mean sum of squared deviations (RMSDs) between two coordinate vectors that correspond to the rigid body motion of a macromolecule is an important problem in structural bioinformatics, computational chemistry, and molecular modeling. Standard algorithms compute the RMSD with time proportional to the number of atoms in the molecule. Here, we present RigidRMSD, a new algorithm that determines a set of RMSDs corresponding to a set of rigid body motions of a macromolecule in constant time with respect to the number of atoms in the molecule. Our algorithm is particularly useful for rigid body modeling applications, such as rigid body docking, and also for high-throughput analysis of rigid body modeling and simulation results. We also introduce a constant-time rotation RMSD as a similarity measure for rigid molecules. A C++ implementation of our algorithm is available at http://nano-d.inrialpes.fr/software/RigidRMSD

Predicting binding poses and affinities for protein-ligand complexes in the 2015 D3R Grand Challenge using a physical model with a statistical parameter estimation

International audienceThe 2015 D3R Grand Challenge provided an opportunity to test our new model for the binding free energy of small molecules, as well as to assess our protocol to predict binding poses for protein-ligand complexes. Our pose predictions were ranked 3-9 for the HSP90 dataset, depending on the assessment metric. For the MAP4K dataset the ranks are very dispersed and equal to 2-35, depending on the assessment metric, which does not provide any insight into the accuracy of the method. The main success of our pose prediction protocol was the re-scoring stage using the recently developed Convex-PL potential. We make a thorough analysis of our docking predictions made with AutoDock Vina and discuss the effect of the choice of rigid receptor templates, the number of flexible residues in the binding pocket, the binding pocket size, and the benefits of re-scoring. However, the main challenge was to predict experimentally determined binding affinities for two blind test sets. Our affinity prediction model consisted of two terms, a pairwise-additive enthalpy, and a non pairwise-additive entropy. We trained the free parameters of the model with a regularized regression using affinity and structural data from the PDBBind database. Our model performed very well on the training set, however, failed on the two test sets. We explain the drawback and pitfalls of our model, in particular in terms of relative coverage of the test set by the training set and missed dynamical properties from crystal structures, and discuss different routes to improve it