Multiscale derivation, analysis and simulation of collective dynamics models: geometrical aspects and applications

This thesis is a contribution to the study of swarming phenomena from the point of view of mathematical kinetic theory. This multiscale approach starts from stochastic individual based (or particle) models and aims at the derivation of partial differential equation models on statistical quantities when the number of particles tends to infinity. This latter class of models is better suited for mathematical analysis in order to reveal and explain large-scale emerging phenomena observed in various biological systems such as flocks of birds or swarms of bacteria. Within this objective, a large part of this thesis is dedicated to the study of a body-attitude coordination model and, through this example, of the influence of geometry on self-organisation. The first part of the thesis deals with the rigorous derivation of partial differential equation models from particle systems with mean-field interactions. After a review of the literature, in particular on the notion of propagation of chaos, a rigorous convergence result is proved for a large class of geometrically enriched piecewise deterministic particle models towards local BGK-type equations. In addition, the method developed is applied to the design and analysis of a new particle-based algorithm for sampling. This first part also addresses the question of the efficient simulation of particle systems using recent GPU routines. The second part of the thesis is devoted to kinetic and fluid models for body-oriented particles. The kinetic model is rigorously derived as the mean-field limit of a particle system. In the spatially homogeneous case, a phase transition phenomenon is investigated which discriminates, depending on the parameters of the model, between a “disordered” dynamics and a self-organised “ordered” dynamics. The fluid (or macroscopic) model was derived as the hydrodynamic limit of the kinetic model a few years ago by Degond et al. The analytical and numerical study of this model reveal the existence of new self-organised phenomena which are confirmed and quantified using particle simulations. Finally a generalisation of this model in arbitrary dimension is presented.Open Acces

Collective proposal distributions for nonlinear MCMC samplers : Mean-field theory and fast implementation

Funding Information: ∗This research was conducted while A.D. was supported by an EPSRC-Roth scholarship co-funded by the Engineering and Physical Sciences Research Council and the Department of Mathematics at Imperial College London. Publisher Copyright: © 2022, Institute of Mathematical Statistics. All rights reserved.Over the last decades, various “non-linear” MCMC methods have arisen. While appealing for their convergence speed and efficiency, their practical implementation and theoretical study remain challenging. In this paper, we introduce a non-linear generalization of the Metropolis-Hastings algorithm to a proposal that depends not only on the current state, but also on its law. We propose to simulate this dynamics as the mean field limit of a system of interacting particles, that can in turn itself be understood as a generalisation of the Metropolis-Hastings algorithm to a population of particles. Under the double limit in number of iterations and number of particles we prove that this algorithm converges. Then, we propose an efficient GPU implementation and illustrate its performance on various examples. The method is particularly stable on multimodal examples and converges faster than the classical methods.Peer reviewe

Parametric study of dielectric barrier discharge excimer UV lamps supplied with controlled square current pulses

A parametric study of a system dedicated to non-coherent UV emission, by means of DBD excilamps, supplied by a controlled square shape current source is proposed. The presentation highlights on the one hand the performances experimentally obtained by combining together a set of 20 different bulbs with different diameters, gap and wall thicknesses (all the bulbs have the same length and are filled with the same Xe-Cl gas mixture), with different electrical power supplying conditions: magnitude, frequency (in the 30 kHz – 200 kHz range) and duty cycle of the square shape current pulses injected into the bulb. The performances concern the average UV power, the efficiency of the bulb conversion (electrical power to UV) and the adjustability of the power. On the second hand, we present design considerations of the power supply which has been especially developed for the purpose of these experiments

Turing Pattern Formation in Reaction-Cross-Diffusion Systems with a Bilayer Geometry

Conditions for self-organisation via Turing’s mechanism in biological systems represented by reaction-diffusion or reaction-cross-diffusion models have been extensively studied. Nonetheless, the impact of tissue stratification in such systems is under-explored, despite its ubiquity in the context of a thin epithelium overlying connective tissue, for instance the epidermis and underlying dermal mesenchyme of embryonic skin. In particular, each layer can be subject to extensively different biochemical reactions and transport processes, with chemotaxis - a special case of cross-diffusion - often present in the mesenchyme, contrasting the solely molecular transport typically found in the epidermal layer. We study Turing patterning conditions for a class of reaction-cross-diffusion systems in bilayered regions, with a thin upper layer and coupled by a linear transport law. In particular, the role of differential transport through the interface is explored together with the presence of asymmetry between the homogeneous equilibria of the two layers. A linear stability analysis is carried out around a spatially homogeneous equilibrium state in the asymptotic limit of weak and strong coupling strengths, where quantitative approximations of the bifurcation curve can be computed. Our theoretical findings, for an arbitrary number of reacting species, reveal quantitative Turing conditions, highlighting when the coupling mechanism between the layered regions can either trigger patterning or stabilize a spatially homogeneous equilibrium regardless of the independent patterning state of each layer. We support our theoretical results through direct numerical simulations, and provide an open source code to explore such systems further

Developmental delay in a Streptomyces venezuelae glgE null mutant is associated with the accumulation of alpha-maltose 1-phosphate

The GlgE pathway is thought to be responsible for the conversion of trehalose into a glycogen-like alpha-glucan polymer in bacteria. Trehalose is first converted to maltose, which is phosphorylated by maltose kinase Pep2 to give alpha-maltose 1-phosphate. This is the donor substrate of the maltosyl transferase GlgE that is known to extend alpha-1,4-linked maltooligosaccharides, which are thought to be branched with alpha-1,6 linkages. The genome of Streptomyces venezuelae contains all the genes coding for the GlgE pathway enzymes but none of those of related pathways, including glgC and glgA of the glycogen pathway. This provides an opportunity to study the GlgE pathway in isolation. The genes of the GlgE pathway were upregulated at the onset of sporulation, consistent with the known timing of a-glucan deposition. A constructed Delta glgE null mutant strain was viable but showed a delayed developmental phenotype when grown on maltose, giving less cell mass and delayed sporulation. Pre-spore cells and spores of the mutant were frequently double the length of those of the wild-type, implying impaired cross-wall formation, and spores showed reduced tolerance to stress. The mutant accumulated alpha-maltose 1-phosphate and maltose but no alpha-glucan. Therefore, the GlgE pathway is necessary and sufficient for polymer biosynthesis. Growth of the Delta glgE mutant on galactose and that of a Delta pep2 mutant on maltose were analysed. In both cases, neither accumulation of alpha-maltose 1-phosphate/alpha-glucan nor a developmental delay was observed. Thus, high levels of alpha-maltose 1-phosphate are responsible for the developmental phenotype of the Delta glgE mutant, rather than the lack of a-glucan

Burden of community-acquired and nosocomial rotavirus gastroenteritis in the pediatric population of Western Europe: a scoping review

<p>Abstract</p> <p>Background</p> <p>Rotavirus affects 95% of children worldwide by age 5 years and is the leading cause of severe dehydrating diarrhea. The objective of this review was to estimate the burden of rotavirus gastroenteritis (RVGE) in the Western European pediatric population.</p> <p>Methods</p> <p>A comprehensive literature search (1999-2010) was conducted in PubMed and other sources (CDC; WHO, others). Data on the epidemiology and burden of RVGE among children < 5 years-old in Western Europe --including hospital-acquired disease--were extracted.</p> <p>Results</p> <p>76 studies from 16 countries were identified. The mean percentage of acute gastroenteritis (AGE) cases caused by rotavirus ranged from 25.3%-63.5% in children < 5 years of age, peaking during winter. Incidence rates of RVGE ranged from 1.33-4.96 cases/100 person- years. Hospitalization rates for RVGE ranged from 7% to 81% among infected children, depending on the country. Nosocomial RVGE accounted for 47%-69% of all hospital-acquired AGE and prolonged hospital stays by 4-12 days. Each year, RVGE incurred $0.54-$53.6 million in direct medical costs and $1.7-$22.4 million in indirect costs in the 16 countries studied. Full serotyping data was available for 8 countries. G1P[8], G2P[4], G9P[8], and G3P[8] were the most prevalent serotypes (cumulative frequency: 57.2%- 98.7%). Serotype distribution in nosocomial RVGE was similar.</p> <p>Conclusions</p> <p>This review confirms that RVGE is a common disease associated with significant morbidity and costs across Western Europe. A vaccine protecting against multiple serotypes may decrease the epidemiological and cost burden of RVGE in Western Europe.</p

Mutational spectrum in a worldwide study of 29,700 families with BRCA1 or BRCA2 mutations.

The prevalence and spectrum of germline mutations in BRCA1 and BRCA2 have been reported in single populations, with the majority of reports focused on White in Europe and North America. The Consortium of Investigators of Modifiers of BRCA1/2 (CIMBA) has assembled data on 18,435 families with BRCA1 mutations and 11,351 families with BRCA2 mutations ascertained from 69 centers in 49 countries on six continents. This study comprehensively describes the characteristics of the 1,650 unique BRCA1 and 1,731 unique BRCA2 deleterious (disease-associated) mutations identified in the CIMBA database. We observed substantial variation in mutation type and frequency by geographical region and race/ethnicity. In addition to known founder mutations, mutations of relatively high frequency were identified in specific racial/ethnic or geographic groups that may reflect founder mutations and which could be used in targeted (panel) first pass genotyping for specific populations. Knowledge of the population-specific mutational spectrum in BRCA1 and BRCA2 could inform efficient strategies for genetic testing and may justify a more broad-based oncogenetic testing in some populations

An original phylogenetic approach identified mitochondrial haplogroup T1a1 as inversely associated with breast cancer risk in BRCA2 mutation carriers

Introduction: Individuals carrying pathogenic mutations in the BRCA1 and BRCA2 genes have a high lifetime risk of breast cancer. BRCA1 and BRCA2 are involved in DNA double-strand break repair, DNA alterations that can be caused by exposure to reactive oxygen species, a main source of which are mitochondria. Mitochondrial genome variations affect electron transport chain efficiency and reactive oxygen species production. Individuals with different mitochondrial haplogroups differ in their metabolism and sensitivity to oxidative stress. Variability in mitochondrial genetic background can alter reactive oxygen species production, leading to cancer risk. In the present study, we tested the hypothesis that mitochondrial haplogroups modify breast cancer risk in BRCA1/2 mutation carriers. Methods: We genotyped 22,214 (11,421 affected, 10,793 unaffected) mutation carriers belonging to the Consortium of Investigators of Modifiers of BRCA1/2 for 129 mitochondrial polymorphisms using the iCOGS array. Haplogroup inference and association detection were performed using a phylogenetic approach. ALTree was applied to explore the reference mitochondrial evolutionary tree and detect subclades enriched in affected or unaffected individuals. Results: We discovered that subclade T1a1 was depleted in affected BRCA2 mutation carriers compared with the rest of clade T (hazard ratio (HR) = 0.55; 95% confidence interval (CI), 0.34 to 0.88; P = 0.01). Compared with the most frequent haplogroup in the general population (that is, H and T clades), the T1a1 haplogroup has a HR of 0.62 (95% CI, 0.40 to 0.95; P = 0.03). We also identified three potential susceptibility loci, including G13708A/rs28359178, which has demonstrated an inverse association with familial breast cancer risk. Conclusions: This study illustrates how original approaches such as the phylogeny-based method we used can empower classical molecular epidemiological studies aimed at identifying association or risk modification effects.Peer reviewe