Adaptive Scattered Data Fitting with Tensor Product Spline-Wavelets

The core of the work we present here is an algorithm that constructs a least squares approximation to a given set of unorganized points. The approximation is expressed as a linear combination of particular B-spline wavelets. It implies a multiresolution setting which constructs a hierarchy of approximations to the data with increasing level of detail, proceeding from coarsest to finest scales. It allows for an efficient selection of the degrees of freedom of the problem and avoids the introduction of an artificial uniform grid. In fact, an analysis of the data can be done at each of the scales of the hierarchy, which can be used to select adaptively a set of wavelets that can represent economically the characteristics of the cloud of points in the next level of detail. The data adaption of our method is twofold, as it takes into account both horizontal distribution and vertical irregularities of data. This strategy can lead to a striking reduction of the problem complexity. Furthermore, among the possible ways to achieve a multiscale formulation, the wavelet approach shows additional advantages, based on good conditioning properties and level-wise orthogonality. We exploit these features to enhance the efficiency of iterative solution methods for the system of normal equations of the problem. The combination of multiresolution adaptivity with the numerical properties of the wavelet basis gives rise to an algorithm well suited to cope with problems requiring fast solution methods. We illustrate this by means of numerical experiments that compare the performance of the method on various data sets working with different multi-resolution bases. Afterwards, we use the equivalence relation between wavelets and Besov spaces to formulate the problem of data fitting with regularization. We find that the multiscale formulation allows for a flexible and efficient treatment of some aspects of this problem. Moreover, we study the problem known as robust fitting, in which the data is assumed to be corrupted by wrong measurements or outliers. We compare classical methods based on re-weighting of residuals to our setting in which the wavelet representation of the data computed by our algorithm is used to locate the outliers. As a final application that couples two of the main applications of wavelets (data analysis and operator equations), we propose the use of this least squares data fitting method to evaluate the non-linear term in the wavelet-Galerkin formulation of non-linear PDE problems. At the end of this thesis we discuss efficient implementation issues, with a special interest in the interplay between solution methods and data structures

Protocols for Subtomogram Averaging of Membrane Proteins in the Dynamo Software Package

Cryo-electron tomography allows low-resolution three-dimensional (3D) viewing of cellular organelles and macromolecular complexes present as multiple copies within a tomogram. These structures are computationally extracted and averaged in order to obtain high-resolution 3D structures, and provide a map of their spatial distribution and interaction with their biological microenvironment. To do so, we apply the user-friendly Dynamo software package on a tomographic data set. Dynamo acts as a modular toolbox adaptable to different biological scenarios, allowing a custom designed pipeline for subtomogram averaging. Here, we use as a textbook example the mitochondrial docking site of the positive-strand RNA Flock house nodavirus (FHV) to describe how Dynamo coordinates several basic steps in the subtomogram averaging workflow. Our framework covers specific strategies to deal with additional issues in subtomogram averaging as tomographic data management, 3D surface visualization, automatic assignment of asymmetry and inherent loss of Fourier information in presence of preferential views

Radiation dose reduction and image enhancement in biological imaging through equally-sloped tomography

Electron tomography is currently the highest resolution imaging modality available to study the 3D structures of pleomorphic macromolecular assemblies, viruses, organelles and cells. Unfortunately, the resolution is currently limited to 3–5 nm by several factors including the dose tolerance of biological specimens and the inaccessibility of certain tilt angles. Here we report the first experimental demonstration of equally-sloped tomography (EST) to alleviate these problems. As a proof of principle, we applied EST to reconstructing frozen-hydrated keyhole limpet hemocyanin molecules from a tilt-series taken with constant slope increments. In comparison with weighted back-projection (WBP), the algebraic reconstruction technique (ART) and the simultaneous algebraic reconstruction technique (SART), EST reconstructions exhibited higher contrast, less peripheral noise, more easily detectable molecular boundaries and reduced missing wedge effects. More importantly, EST reconstructions including only two-thirds the original images appeared to have the same resolution as full WBP reconstructions, suggesting that EST can either reduce the dose required to reach a given resolution or allow higher resolutions to be achieved with a given dose. EST was also applied to reconstructing a frozen-hydrated bacterial cell from a tilt-series taken with constant angular increments. The results confirmed similar benefits when standard tilts are utilized

A Bayesian approach to single-particle electron cryo-tomography in RELION-4.0

We present a new approach for macromolecular structure determination from multiple particles in electron cryo-tomography (cryo-ET) data sets. Whereas existing subtomogram averaging approaches are based on 3D data models, we propose to optimise a regularised likelihood target that approximates a function of the 2D experimental images. In addition, analogous to Bayesian polishing and contrast transfer function (CTF) refinement in single-particle analysis, we describe the approaches that exploit the increased signal-to-noise ratio in the averaged structure to optimise tilt-series alignments, beam-induced motions of the particles throughout the tilt-series acquisition, defoci of the individual particles, as well as higher-order optical aberrations of the microscope. Implementation of our approaches in the open-source software package RELION aims to facilitate their general use, particularly for those researchers who are already familiar with its single-particle analysis tools. We illustrate for three applications that our approaches allow structure determination from cryo-ET data to resolutions sufficient for de novo atomic modelling.This work was funded by the UK Research and Innovation (UKRI) Medical Research Council (MC_UP_A025_1013 to SHWS; and MC_UP_1201/16 to JAGB), the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (ERC-CoG-2014, grant 648432, MEMBRANEFUSION to JAGB and ERC StG-2019, grant 852915 CRYTOCOP to GZ); the Swiss National Science Foundation (grant 205321_179041/1 to DC-D), the Max Planck Society (to JAGB) and the UKRI Biotechnology and Biological Sciences Research Council (grant BB/T002670/1 to GZ). TAMB is a recipient of a Sir Henry Dale Fellowship, jointly funded by the Wellcome Trust and the Royal Society (202231/Z/16/Z). JZ was partially funded by the European Union’s Horizon 2020 research and innovation program (ERC-ADG-2015, grant 692726, GlobalBioIm to Michael Unser)

Architecture of the ESCPE-1 membrane coat

Recycling of membrane proteins enables the reuse of receptors, ion channels and transporters. A key component of the recycling machinery is the endosomal sorting complex for promoting exit 1 (ESCPE-1), which rescues transmembrane proteins from the endolysosomal pathway for transport to the trans-Golgi network and the plasma membrane. This rescue entails the formation of recycling tubules through ESCPE-1 recruitment, cargo capture, coat assembly and membrane sculpting by mechanisms that remain largely unknown. Herein, we show that ESCPE-1 has a single-layer coat organization and suggest how synergistic interactions between ESCPE-1 protomers, phosphoinositides and cargo molecules result in a global arrangement of amphipathic helices to drive tubule formation. Our results thus define a key process of tubule-based endosomal sorting.This work was funded by MCIN/AEI/10.13039/501100011033 (PID2020- 119132GB-I00, CEX2021-001136-S) (to A.H.), the Intramural Program of NICHD, NIH (ZIA HD001607 to J.S.B.), the Swiss National Science Foundation grant 205321 179041 (to D.C.-D.), the Human Frontiers Science Program grant RGP0017/2020 (to D.C.-D.) and the PID2021- 127309NB-I00 funded by AEI/10.13039/501100011033/ FEDER, UE (to D.C.-D.). This study made use of the Diamond Light Source proposal MX20113, ALBA synchrotron beamline BL13-XALOC, the cryo-EM facilities at the UK Electron Bio-Imaging Centre, proposals EM17171- 6 and EM17171, and the Midlands Regional Cryo-EM Facility at the Leicester Institute of Structural and Chemical Biology (LISCB). We thank C. Savva (LISCB, University of Leicester) for his help in cryo-EM data collection. With funding from the Spanish government through the Severo Ochoa Centre of Excellence’ accreditation (CEX2021-001136-S

dose reduction and image enhancement in biological imaging through equally-sloped tomography [J

a b s t r a c t Electron tomography is currently the highest resolution imaging modality available to study the 3D structures of pleomorphic macromolecular assemblies, viruses, organelles and cells. Unfortunately, the resolution is currently limited to 3-5 nm by several factors including the dose tolerance of biological specimens and the inaccessibility of certain tilt angles. Here we report the first experimental demonstration of equally-sloped tomography (EST) to alleviate these problems. As a proof of principle, we applied EST to reconstructing frozen-hydrated keyhole limpet hemocyanin molecules from a tilt-series taken with constant slope increments. In comparison with weighted back-projection (WBP), the algebraic reconstruction technique (ART) and the simultaneous algebraic reconstruction technique (SART), EST reconstructions exhibited higher contrast, less peripheral noise, more easily detectable molecular boundaries and reduced missing wedge effects. More importantly, EST reconstructions including only twothirds the original images appeared to have the same resolution as full WBP reconstructions, suggesting that EST can either reduce the dose required to reach a given resolution or allow higher resolutions to be achieved with a given dose. EST was also applied to reconstructing a frozen-hydrated bacterial cell from a tilt-series taken with constant angular increments. The results confirmed similar benefits when standard tilts are utilized

European LeukemiaNet 2017 risk stratification for acute myeloid leukemia: validation in a risk-adapted protocol

The 2017 European LeukemiaNet (ELN 2017) guidelines for the diagnosis and management of acute myeloid leukemia (AML) have become fundamental guidelines to assess the prognosis and postremission therapy of patients. However, they have been retrospectively validated in few studies with patients included in different treatment protocols. We analyzed 861 patients included in the Cooperativo Para el Estudio y Tratamiento de las Leucemias Agudas y Mielodisplasias-12 risk-adapted protocol, which indicates cytarabine-based consolidation for patients allocated to the ELN 2017 favorable-risk group, whereas it recommends allogeneic stem cell transplantation (alloSCT) as a postremission strategy for the ELN 2017 intermediateand adverse-risk groups. We retrospectively classified patients according to the ELN 2017, with 327 (48%), 109 (16%), and 245 (36%) patients allocated to the favorable-, intermediate-, and adverse-risk group, respectively. The 2- and 5-year overall survival (OS) rates were 77% and 70% for favorable-risk patients, 52% and 46% for intermediate-risk patients, and 33% and 23% for adverse-risk patients, respectively. Furthermore, we identified a subgroup of patients within the adverse group (inv(3)/t(3;3), complex karyotype, and/or TP53 mutation/17p abnormality) with a particularly poor outcome, with a 2-year OS of 15%. Our study validates the ELN 2017 risk stratification in a large cohort of patients treated with an ELN-2017 risk-adapted protocol based on alloSCT after remission for nonfavorable ELN subgroups and identifies a genetic subset with a very poor outcome that warrants investigation of novel strategies

The Dynamo package for tomography and subtomogram averaging: components for MATLAB, GPU computing and EC2 Amazon Web Services

Dynamo is a package for the processing of tomographic data. As a tool for subtomogram averaging, it includes different alignment and classification strategies. Furthermore, its data-management module allows experiments to be organized in groups of tomograms, while offering specialized three-dimensional tomographic browsers that facilitate visualization, location of regions of interest, modelling and particle extraction in complex geometries. Here, a technical description of the package is presented, focusing on its diverse strategies for optimizing computing performance. Dynamo is built upon mbtools (middle layer toolbox), a general-purpose MATLAB library for object-oriented scientific programming specifically developed to underpin Dynamo but usable as an independent tool. Its structure intertwines a flexible MATLAB codebase with precompiled C++ functions that carry the burden of numerically intensive operations. The package can be delivered as a precompiled standalone ready for execution without a MATLAB license. Multicore parallelization on a single node is directly inherited from the high-level parallelization engine provided for MATLAB, automatically imparting a balanced workload among the threads in computationally intense tasks such as alignment and classification, but also in logistic-oriented tasks such as tomogram binning and particle extraction. Dynamo supports the use of graphical processing units (GPUs), yielding considerable speedup factors both for native Dynamo procedures (such as the numerically intensive subtomogram alignment) and procedures defined by the user through its MATLAB-based GPU library for three-dimensional operations. Cloud-based virtual computing environments supplied with a pre-installed version of Dynamo can be publicly accessed through the Amazon Elastic Compute Cloud (EC2), enabling users to rent GPU computing time on a pay-as-you-go basis, thus avoiding upfront investments in hardware and longterm software maintenance