SUMMARY Full-waveform inversion (FWI) has emerged as the state-of-the art high resolution seismic imaging technique, both in seismology for global and regional scale imaging and in the industry for exploration purposes. While gaining in popularity, FWI, at an operational level, remains a heavy computational process involving the repeated solution of large-scale 3-D wave propagation problems. For this reason it is a common practice to focus the interpretation of the results on the final estimated model. This is forgetting FWI is an ill-posed inverse problem in a high dimensional space for which the solution is intrinsically non-unique. This is the reason why being able to qualify and quantify the uncertainty attached to a model estimated by FWI is key. To this end, we propose to extend at an operational level the concepts introduced in a previous study related to the coupling between ensemble Kalman filters (EnKFs) and FWI. These concepts had been developed for 2-D frequency-domain FWI. We extend it here to the case of 3-D time-domain FWI, relying on a source subsampling strategy to assimilate progressively the data within the Kalman filter. We apply our strategy to an ocean bottom cable field data set from the North Sea to illustrate its feasibility. We explore the convergence of the filter in terms of number of elements, and extract variance and covariance information showing which part of the model are well constrained and which are not. Analysing the variance helps to gain insight on how well the final estimated model is constrained by the whole FWI workflow. The variance maps appears as the superposition of a smooth trend related to the geometrical spreading and a high resolution trend related to reflectors. Mapping lines of the covariance (or correlation matrix) to the model space helps to gain insight on the local resolution. Through a wave propagation analysis, we are also able to relate variance peaks in the model space to variance peaks in the data space. Compared to other posterior-covariance approximation scheme, our combination between EnKF and FWI is intrinsically scalable, making it a good candidate for exploiting the recent exascale high performance computing machines.

Regularization is a central topic in the study of the solutions of ill-posed inverse problems. High-resolution seismic imaging using full-waveform inversion (FWI) belongs to this category of problems. Regularization through anisotropic diffusion, a technique that emerged in the field of image processing, is an interesting alternative to conventional regularization strategies. Exploiting the structural information of a given image, it has the capability to smooth this image along its main structures. The main difficulty is how to design the anisotropic diffusion operator. The concept of coherence enhancing proposed in 2D is extended in 3D and applied so as to filter and enhance the structural coherence of the model updates within an FWI algorithm. The benefits of this strategy are investigated on a 2D synthetic experiment before considering the multiparameter inversion of a 3D field data set from the North Sea up to 10 Hz. From this data, the vertical velocity and the density are simultaneously reconstructed. Compared with a conventional nonstationary Gaussian regularization strategy, the models obtained using the coherence-enhancing anisotropic diffusion strategy indicate an enhanced resolution, especially for the density model. The high-resolution reflectivity image computed from the impedance volume clearly illustrates the benefit this filtering approach can deliver in terms of structural interpretation.

Inverse wave problems (IWPs) amount in non-linear optimization problems where a certain distance between a state variable and some observations of a wavefield is to be minimized. Additionally, we require the state variable to be the solution of a model equation that involves a set of parameters to be optimized. Typical approaches to solve IWPs includes the adjoint method, which generates a sequence of parameters and strictly enforces the model equation at each iteration, and, the wavefield reconstruction inversion (WRI) method, which jointly generates a sequence of parameters and state variable but does not strictly enforce the model. WRI is considered to be an interesting approach because, by virtue of not enforcing the model at each iteration, it expands the search space, and can thus find solutions that may not be found by a typical adjoint method. However, WRI techniques generally requires the tuning of a penalty parameter until the model equation is considered satisfied. Alternatively, a fixed penalty parameter can be chosen but, in such case, it is impossible for the algorithm to find a solution that satisfies the model equation exactly. In the present work, we present a, to our knowledge, novel technique of WRI type which jointly generates a sequence of parameters and state variable, and which loosely enforces the model. The method is based on a TR-SQP method which aims at minimizing, at each iteration, both the residual relative to the linearized model and a quadratic approximation of the cost functional. Our method approximately solves a sequence of quadratic subproblems by using a Krylov method. The Hessian-vector product is computed using the second-order adjoint method. The method is demonstrated on a synthetic case, with a configuration relevant to medical imaging.

Large macromolecules, including proteins and their complexes, very often adopt multiple conformations. Some of them can be seen experimentally, for example with x-ray crystallography or cryo-electron microscopy. This structural heterogeneity is not occasional and is frequently linked with specific biological function. Thus, the accurate description of macromolecular conformational transitions is crucial for understanding fundamental mechanisms of life's machinery. We report on a real-time method to predict such transitions by extrapolating from instantaneous eigen motions, computed using the normal mode analysis, to a series of twists. We demonstrate the applicability of our approach to the prediction of a wide range of motions, including large collective opening-closing transitions and conformational changes induced by partner binding. We also highlight particularly difficult cases of very small transitions between crystal and solution structures. Our method guarantees preservation of the protein structure during the transition and allows accessing conformations that are unreachable with classical normal mode analysis. We provide practical solutions to describe localized motions with a few low-frequency modes and to relax some geometrical constraints along the predicted transitions. This work opens the way to the systematic description of protein motions, whatever their degree of collectivity. Our method is freely available as a part of the NOn-Linear rigid Block (NOLB) package.

Files and metadata associated with the EMDataBank/Unified Data Resource for 3DEM 2015/2016 Models Challenge hosted at challenges.emdatabank.org are deposited. All members of the Scientific Community--at all levels of experience--were invited to participate as Challengers, and/or as Assessors. Eight recently determined target structures were selected for the challenge. All of the maps were archived in the EM Data Bank (EMDB; http://emdatabank.org). In total 16 Challengers created 106 models and uploaded their results with associated details. In the zip files, each entry is represented in a folder containing the original deposition upload (deposited_EM.pdb), initial processing at RCSB/Rutgers (deposited_EM_edited.pdb, maxit.cif, maxit.cif.pdb) and final model version evaluated (model-compare.pdb) at UC Davis (http://model-compare.emdatabank.org). This model challenge was one of two community-wide challenges sponsored by EMDataBank in 2015/2016 to critically evaluate 3DEM methods that are coming into use, with the ultimate goal of developing validation criteria associated with every 3DEM map and map-derived model.

Motivation The root mean square deviation (RMSD) is one of the most used similarity criteria in structural biology and bioinformatics. Standard computation of the RMSD has a linear complexity with respect to the number of atoms in a molecule, making RMSD calculations time-consuming for the large-scale modeling applications, such as assessment of molecular docking predictions or clustering of spatially proximate molecular conformations. Previously, we introduced the RigidRMSD algorithm to compute the RMSD corresponding to the rigid-body motion of a molecule. In this study, we go beyond the limits of the rigid-body approximation by taking into account conformational flexibility of the molecule. We model the flexibility with a reduced set of collective motions computed with e.g. normal modes or principal component analysis. Results The initialization of our algorithm is linear in the number of atoms and all the subsequent evaluations of RMSD values between flexible molecular conformations depend only on the number of collective motions that are selected to model the flexibility. Therefore, our algorithm is much faster compared to the standard RMSD computation for large-scale modeling applications. We demonstrate the efficiency of our method on several clustering examples, including clustering of flexible docking results and molecular dynamics (MD) trajectories. We also demonstrate how to use the presented formalism to generate pseudo-random constant-RMSD structural molecular ensembles and how to use these in cross-docking. Availability and implementation We provide the algorithm written in C++ as the open-source RapidRMSD library governed by the BSD-compatible license, which is available at http://team.inria.fr/nano-d/software/RapidRMSD/. The constant-RMSD structural ensemble application and clustering of MD trajectories is available at http://team.inria.fr/nano-d/software/nolb-normal-modes/. Supplementary information Supplementary data are available at Bioinformatics online.

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 .

This paper presents a novel fast Fourier transform (FFT)-based exhaustive search method extended to off-grid translational and rotational degrees of freedom. The method combines the advantages of the FFT-based exhaustive search, which samples all the conformations of a system under study on a grid, with a local optimization technique that guarantees to find the nearest optimal off-grid conformation. The method is demonstrated on a fitting problem and can be readily applied to a docking problem. The algorithm first samples a scoring function on a six-dimensional grid of size N-6 using the FFT. This operation has an asymptotic complexity of O(N-6 logN). Then, the method performs the off-grid search using a local quadratic approximation of the cost function and the trust-region optimization algorithm. The computation of the quadratic approximation is also accelerated by FFT at the same additional asymptotic cost of O(N-6 logN). The method is demonstrated by fitting atomic protein models into several simulated and experimental maps from cryo-electron microscopy. The method is available at https://team. inria. fr/nano-d/software/offgridfit.