Cette thèse s’intéresse à la création de nouvelles approches algorithmiques pour la résolution du problème inverse en biophysiques. Dans un premier temps, on vise l’application RMN de type DOSY: une nouvelle approche de régularisation hybride a été proposée avec un nouvel algorithme PALMA (http://palma.labo.igbmc.fr/). Cet algorithme permet d’analyser des données réelles DOSY avec une précision importante quelque soit leur type. Dans un deuxième temps, notre intérêt s’est tourné vers l’application de spectrométrie de masse. Nous avons proposé une nouvelle approche par dictionnaire dédiée à l’analyse protéomique en utilisant le modèle averagine et une stratégie de minimisation sous contraintes d'une pénalité de parcimonie. Afin d’améliorer la précision de l’information obtenue, nous avons proposé une nouvelle méthode SPOQ, basée sur une nouvelle fonction de pénalisation, résolue par un nouvel algorithme Forward-Backward à métrique variable localement ajustée. Tous nos algorithmes bénéficient de garanties théoriques de convergence, et ont été validés expérimentalement sur des spectres synthétisés et des données réelles / This thesis aims at proposing new approaches to solve the inverse problem in biophysics. Firstly, we study the DOSY NMR experiment: a new hybrid regularization approach has been proposed with a novel PALMA algorithm (http://palma.labo.igbmc.fr/). This algorithm ensures the efficient analysis of real DOSY data with a high precision for all different type. In a second time, we study the mass spectrometry application. We have proposed a new dictionary based approach dedicated to proteomic analysis using the averagine model and the constrained minimization approach associated with a sparsity inducing penalty. In order to improve the accuracy of the information, we proposed a new SPOQ method based on a new penalization, solved with a new Forward-Backward algorithm with a variable metric locally adjusted. All our algorithms benefit from sounded convergence guarantees, and have been validated experimentally on synthetics and real data.

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Synopsis My research work is focused on: (i) development of novel Fast NMR methods in solution state and their application to metabolomics and small molecules. (ii) NMR based metabolic study of human IVF to assess embryo viability for implantation. The major components of the embryo growth media were identified for evaluating the embryo quality. Described below are the projects carried out towards the dissertation of my PhD. Chapter 1 describes NMR methods which are the foundation stones for new Fast NMR methods developed. Typical 1D and 2D NMR experiments used in metabolomics and statistical methods for analysis are described. A few applications of metabolomics are also covered in the chapter. Chapter 2 describes a new Fast NMR method based on polarization sharing and parallel acquisition using the dual receiver system. The method developed helps in acquiring simultaneously three 2D NMR spectra: 2D [13C-1H] HETCOR, 2D [1H-1H] TOCSY and 2D [13C-1H] HSQC-TOCSY in a single data set. This method achieves a time saving of about two fold. All the experiments are acquired on molecules with natural abundance of 13C. The method was used to assign the side chain atoms (1H and 13C) of two important peptides. i) 12 amino acid residue peptide, which is a part of central linker domain of Human Insulin like Growth Factor Binding Protein-2 known to play a vital role in the IGF system and ii) a 18 amino acid residue peptide which acts as an antimicrobial agent. Chapter 3 describes extension of the Fast NMR method described in chapter 2. The method is combined with G-matrix Fourier Transform NMR spectroscopy. In this method we have acquire simultaneously two 2D NMR experiments and one reduced dimensional 3D experiment. The three experiments are 2D [13C-1H] HETCOR, 2D [1H-1H] TOCSY and GFT (3,2)D [13C-1H] HSQC-TOCSY, which provide complementary information for rapid assignments. GFT (3,2)D [13C-1H] HSQC-TOCSY gives 3D correlations in a 2D manner facilitating high resolution and unambiguous assignments. The experiments were applied for complete assignment of 21 unlabeled metabolite mixtures corresponding to the Innovative Sequential medium (ISM1) used for culturing human embryos for IVF. Further, a 13C multiplicity edition block is added to the method to simplify the resonances assignment in GFT (3,2)D [13C-1H] HSQC-TOCSY. Taken together, experiments provide time gain of order of magnitudes compared to conventional data acquisition. Chapter 4 of the thesis describes a metabolomics study of Human in-vitro fertilization to assess viable embryos of implantation potential using NMR as non-invasive tool. NMR study included the analysis of 127 embryo culture media (Innovative Sequential Media-1) and 29 controls (culture media without embryo) of both day-2 and day-3 transferred. The embryos were divided into 3 categories 1) implanted (successful) 2) transferred not-implanted (unsuccessful) 3) not transferred based on morphological studies. All NMR experiments were acquired with CPMG (T2 filter) incorporated in 1D 1H presaturation pulse scheme. The study was based on estimation of lactate, pyruvate and alanine levels in the embryo culture media (ISM1). The study reveals higher uptake of pyruvate and high pyruvate/alanine ratios in case of implanted embryos compared to one which failed to implant. Present study provides pyruvate/alanine ratio as a biomarker to select the embryos with high implantation potential. The method combined with morphology based assessment or with other biomarkers can be serve as a powerful tool to assess the embryo quality. Chapter 5 describes a novel NMR method for rapid characterization of translation diffusion of molecules in solution either in mixture or pure form. Unlike acquisition of several 2D [13C-1H] HSQC experiments with varying gradients to get diffusion measurement, a single 2D [13C-1H] HSQC is sufficient to measure the diffusion coefficients which is in the linewidths of peaks. The method uses the idea of accordion NMR spectroscopy, wherein gradients are linearly co-incremented with 13C chemical shift evolution period during t1. The methodology speeds up the acquisition by replacing series of 2D [13C-1H] HSQC with single 2D constant time [13C-1H] HSQC. The method was used to monitor the diffusion of metabolites in a time-resolved manner during polymerization of SDS-PAGE gel. Using this method, it was possible to detect the presence of oligomers of diphenylalanine (FF) during its self assembly to form nanotubular structures.