Regularization of statistical inverse problems and the Bakushinskii veto

In the deterministic context Bakushinskii's theorem excludes the existence of purely data driven convergent regularization for ill-posed problems. We will prove in the present work that in the statistical setting we can either construct a counter example or develop an equivalent formulation depending on the considered class of probability distributions. Hence, Bakushinskii's theorem does not generalize to the statistical context, although this has often been assumed in the past. To arrive at this conclusion, we will deduce from the classic theory new concepts for a general study of statistical inverse problems and perform a systematic clarification of the key ideas of statistical regularization.Comment: 20 page

Statistical analysis of the individual variability of 1D protein profiles as a tool in ecology: an application to parasitoid venom

International audienceUnderstanding the forces that shape eco-evolutionary patterns often requires linking phenotypes to genotypes, allowing characterization of these patterns at the molecular level. DNA-based markers are less informative in this aim compared to markers associated with gene expression and, more specifically, with protein quantities. The characterization of eco-evolutionary patterns also usually requires the analysis of large sample sizes to accurately estimate interindividual variability. However, the methods used to characterize and compare protein samples are generally expensive and time-consuming, which constrains the size of the produced data sets to few individuals. We present here a method that estimates the interindividual variability of protein quantities based on a global, semi-automatic analysis of 1D electrophoretic profiles, opening the way to rapid analysis and comparison of hundreds of individuals. The main original features of the method are the in silico normalization of sample protein quantities using pictures of electrophoresis gels at different staining levels, as well as a new method of analysis of electrophoretic profiles based on a median profile. We demonstrate that this method can accurately discriminate between species and between geographically distant or close populations, based on interindividual variation in venom protein profiles from three endoparasitoid wasps of two different genera (Psyttalia concolor, Psyttalia lounsburyi and Leptopili-na boulardi). Finally, we discuss the experimental designs that would benefit from the use of this method

General regularization schemes for signal detection in inverse problems

The authors discuss how general regularization schemes, in particular linear regularization schemes and projection schemes, can be used to design tests for signal detection in statistical inverse problems. It is shown that such tests can attain the minimax separation rates when the regularization parameter is chosen appropriately. It is also shown how to modify these tests in order to obtain (up to a $\log\log$ factor) a test which adapts to the unknown smoothness in the alternative. Moreover, the authors discuss how the so-called \emph{direct} and \emph{indirect} tests are related via interpolation properties

Signal detection for inverse problems in a multidimensional framework

International audienceThis paper is devoted to multi-dimensional inverse problems. In this setting, we address a goodness-of-fit testing problem. We investigate the separation rates associated to different kinds of smoothness assumptions and different degrees of ill-posedness

Duration learning for analysis of nanopore ionic current blockades

<p>Abstract</p> <p>Background</p> <p>Ionic current blockade signal processing, for use in nanopore detection, offers a promising new way to analyze single molecule properties, with potential implications for DNA sequencing. The alpha-Hemolysin transmembrane channel interacts with a translocating molecule in a nontrivial way, frequently evidenced by a complex ionic flow blockade pattern. Typically, recorded current blockade signals have several levels of blockade, with various durations, all obeying a fixed statistical profile for a given molecule. Hidden Markov Model (HMM) based duration learning experiments on artificial two-level Gaussian blockade signals helped us to identify proper modeling framework. We then apply our framework to the real multi-level DNA hairpin blockade signal.</p> <p>Results</p> <p>The identified upper level blockade state is observed with durations that are geometrically distributed (consistent with an a physical decay process for remaining in any given state). We show that mixture of convolution chains of geometrically distributed states is better for presenting multimodal long-tailed duration phenomena. Based on learned HMM profiles we are able to classify 9 base-pair DNA hairpins with accuracy up to 99.5% on signals from same-day experiments.</p> <p>Conclusion</p> <p>We have demonstrated several implementations for <it>de novo </it>estimation of duration distribution probability density function with HMM framework and applied our model topology to the real data. The proposed design could be handy in molecular analysis based on nanopore current blockade signal.</p

The metaRbolomics Toolbox in Bioconductor and beyond

Metabolomics aims to measure and characterise the complex composition of metabolites in a biological system. Metabolomics studies involve sophisticated analytical techniques such as mass spectrometry and nuclear magnetic resonance spectroscopy, and generate large amounts of high-dimensional and complex experimental data. Open source processing and analysis tools are of major interest in light of innovative, open and reproducible science. The scientific community has developed a wide range of open source software, providing freely available advanced processing and analysis approaches. The programming and statistics environment R has emerged as one of the most popular environments to process and analyse Metabolomics datasets. A major benefit of such an environment is the possibility of connecting different tools into more complex workflows. Combining reusable data processing R scripts with the experimental data thus allows for open, reproducible research. This review provides an extensive overview of existing packages in R for different steps in a typical computational metabolomics workflow, including data processing, biostatistics, metabolite annotation and identification, and biochemical network and pathway analysis. Multifunctional workflows, possible user interfaces and integration into workflow management systems are also reviewed. In total, this review summarises more than two hundred metabolomics specific packages primarily available on CRAN, Bioconductor and GitHub

¹H, ¹⁵N, ¹³C backbone resonance assignments of human phosphoglycerate kinase in a transition state analogue complex with ADP, 3-phosphoglycerate and magnesium trifluoride

Human phosphoglycerate kinase (PGK) is an energy generating glycolytic enzyme that catalyses the transfer of a phosphoryl group from 1,3-bisphosphoglycerate (BPG) to ADP producing 3-phosphoglycerate (3PG) and ATP. PGK is composed of two α/β Rossmann-fold domains linked by a central α-helix and the active site is located in the cleft formed between the N-domain which binds BPG or 3PG, and the C-domain which binds the nucleotides ADP or ATP. Domain closure is required to bring the two substrates into close proximity for phosphoryl transfer to occur, however previous structural studies involving a range of native substrates and substrate analogues only yielded open or partly closed PGK complexes. X-ray crystallography using magnesium trifluoride (MgF3(-)) as a isoelectronic and near-isosteric mimic of the transferring phosphoryl group (PO3(-)), together with 3PG and ADP has been successful in trapping human PGK in a fully closed transition state analogue (TSA) complex. In this work we report the (1)H, (15)N and (13)C backbone resonance assignments of human PGK in the solution conformation of the fully closed PGK:3PG:MgF3:ADP TSA complex. Assignments were obtained by heteronuclear multidimensional NMR spectroscopy. In total, 97% of all backbone resonances were assigned in the complex, with 385 out of a possible 399 residues assigned in the (1)H-(15)N TROSY spectrum. Prediction of solution secondary structure from a chemical shift analysis using the TALOS-N webserver is in good agreement with the published X-ray crystal structure of this complex

Troposphere-to-mesosphere microphysics of carbon dioxide ice clouds in a Mars Global Climate Model

We have implemented full CO ice cloud microphysics into the LMD Mars Global Climate Model (MGCM) and we have conducted the first global simulations. The microphysical model implementation follows the modal scheme used for water ice cloud microphysics in the MGCM, but includes specific aspects that need to be accounted for when dealing with CO ice clouds. These include nucleation of CO on water ice crystals and CO condensation theory adapted for the Martian conditions. The model results are compared to available observations globally, and separately for polar regions and equatorial mesosphere. The observed seasonal and latitudinal variability of the CO ice clouds is in general reproduced. The polar regions are covered by CO ice clouds during the winter as observed. Instead of forming only in the lowest 10–15 km of the atmosphere, they extend up to several tens of kilometers above the surface in the model, dictated by the modeled temperature structure. We have also quantified the contribution of the cloud microphysics to the surface CO ice deposits. Snowfall from these clouds contributes up to 10% of the atmosphere–surface ice flux in the polar regions in our simulations, in the range that has been indirectly deduced from observations. In the mesosphere, notable amounts of CO ice clouds form only when water ice crystals are used as condensation nuclei in addition to dust particles, and their spatial distribution is in agreement with observations. The mesospheric temperature structure, dominated by tides, dictates the longitudinal and seasonal distribution of these clouds. The seasonal and local time variations of the clouds are not fully reproduced by the model. There is a long pause in CO ice cloud formation in the model around the aphelion season, but clouds have been observed during this period, although with a lower apparition frequency. Modeled mesospheric clouds form mainly during the night and in the morning, whereas during the daytime, when most of the cloud observations have been made, the model rarely predicts clouds. These discrepancies could be explained by the strong dependence of the cloud formation process on mesospheric temperatures that are themselves challenging to reproduce and sensitive to the MGCM processes and parameters. The rare possibilities for nighttime observations might also bias the observational climatologies towards daytime detections. Future developments of the model consist in the inclusion of a possible exogenous condensation nucleus source in the mesosphere and the radiative effect of CO ice clouds. © 2022 Elsevier Inc. All rights reserved.This paper presents the results of ten years of development that has been supported by funding from several sources. We thank the Agence National de la Recherche for funding (project MECCOM, ANR-18-CE31-0013). We are also grateful for the financial support by the LabEx (Laboratoire d’Excellence) ESEP, by the French space agency CNES and the European Space Agency ESA. We acknowledge the support of the French national planetology programme (PNP) as well. F.G.-G. is funded by the Spanish Ministerio de Ciencia, Innovación y Universidades, the Agencia Estatal de Investigación and EC FEDER funds under project RTI2018-100920-J-I00, and acknowledges financial support from the State Agency for Research of the Spanish MCIU through the Center of Excellence Severo Ochoa” award to the Instituto de Astrofísica de Andalucía (SEV-2017-0709). This work was performed using HPC computing resources from GENCI-CINES (Grant 2021-A0100110391), and resources at the ESPRI mesocentre of the IPSL institute .Peer reviewe

Expression Profiling of a Genetic Animal Model of Depression Reveals Novel Molecular Pathways Underlying Depressive-Like Behaviours

The Flinders model is a validated genetic rat model of depression that exhibits a number of behavioural, neurochemical and pharmacological features consistent with those observed in human depression.In this study we have used genome-wide microarray expression profiling of the hippocampus and prefrontal/frontal cortex of Flinders Depression Sensitive (FSL) and control Flinders Depression Resistant (FRL) lines to understand molecular basis for the differences between the two lines. We profiled two independent cohorts of Flinders animals derived from the same colony six months apart, each cohort statistically powered to allow independent as well as combined analysis. Using this approach, we were able to validate using real-time-PCR a core set of gene expression differences that showed statistical significance in each of the temporally distinct cohorts, representing consistently maintained features of the model. Small but statistically significant increases were confirmed for cholinergic (chrm2, chrna7) and serotonergic receptors (Htr1a, Htr2a) in FSL rats consistent with known neurochemical changes in the model. Much larger gene changes were validated in a number of novel genes as exemplified by TMEM176A, which showed 35-fold enrichment in the cortex and 30-fold enrichment in hippocampus of FRL animals relative to FSL.These data provide significant insights into the molecular differences underlying the Flinders model, and have potential relevance to broader depression research