Morphogen gradients are used by various organisms to establish polarity along embryonic axes or within organs. In these systems, it is assumed that positional information is provided by the concentration of the morphogen detected by each cell in the target tissue and responsible for the determination of cell identity. The extreme robustness of these processes ensures reproducibility of developmental patterns and emergence of properly proportioned individuals despite varying size and environmental conditions. Most descriptions of developmental regulation assume that highly reproducible transcription programs are directly controlling the mechanisms of differentiation. However, when studied at the single cell level, transcription is frequently observed to be an extremely noisy process, hardly suggestive of such precise control. Understanding how reproducible transcription patterns can robustly emerge from these smooth morphogen gradients given inherent stochastic transcription is an important challenge, and constitutes the general objective of this proposal. Recently, methods to observe the kinetics of the transcription process directly in living cells have been developed. These methodes combine fluorescent labeling of nascent mRNA with live-cell imaging at high spatial and temporal resolution. We have recently adapted these approaches to one of the best characterized model organism, the fruit fly embryo. Our goal was to better understand how cell identity is controlled by the Bicoid (Bcd) morphogen system along the antero-posterior (AP) axis of the embryo. Focusing on the expression of the main Bcd target, hunchback (hb), at the onset of zygotic transcription, we have successfully built an MS2 reporter reproducing endogenous expression of the gene. Despite high nuclei-to-nuclei variability in transcription kinetics, the hb promoter was able to establish a sharp expression boundary along to separate anterior expressing from posterior non expressing nuclei. Surprisingly, it only takes ~3 min at each interphase for the system to measure subtle differences in Bicoid concentration and produce a complete sharp boundary. If one assumes that the only driver for the hb transcription process is the Bcd gradient, and further that Bcd molecules reach their target sites by 3D diffusion, simple statistical mechanics considerations (combined with current estimates of Bcd concentration and mobility) show that a minimum of 25 min should be necessary for the system to produce the observed sharp boundary. The difference between predicted (25 min) and observed (~ 3 min) time-requirement is of 1 order of magnitude and calls for alternative explanations. We will explore the possibility of alternative mechanisms in an unbiased manner by combining genetics and optogenetics, live-imaging, advanced data analysis and modeling. Our goal is to identify mutant or natural variant contexts altering the dynamics of hb expression, characterize the contribution of spatial vs temporal correlations in the Bcd system to address the question of transcriptional memory, revisit the question of Bcd target search with the development of cutting-edge imaging to measure Bcd physical parameters (concentration/mobility) and use quantitative data driven modeling to shed light on the process and its robustness. The strength of our project, relies on a unique expertise in the MS2 approach combined with an established and productive collaboration between biologists, biophysicists and theoreticians.

COSMHIC is a fundamental research project, which aims at exploring how dynamical processes drive star formation and its galactic-scale properties. It will timely strengthen the leadership and synergy the IPAG Grenoble, DAp Paris-Saclay, and LPENS Paris groups have developed over the years, in the framework of first-class observational databases, rich multi-resolution simulations, data-mining tools, and state-of-the-art shock models. Our team is among the few initiating a change of the star formation paradigm, in which highly dynamical processes couple cloud-scale and core-scale properties. We enter an exciting era when it becomes possible to properly constrain the physics involved in dynamical star formation, associated shocks, and their impact on the origin of the stellar initial mass function. Our team aims at exploring the physics and global properties of star formation under the influence of dynamical processes to precise star formation recipes used in many astrophysical fields.

Elucidating the microscopic origin of the entropy of black holes is a key objective of any putative theory of quantum gravity. String theory approached this milestone 25 years ago, with the first quantitative description of the micro-states of supersymmetric black holes (also known as BPS black holes) in terms of bound states of extended solitons (known as D-branes) wrapped around minimal submanifolds in the internal compactification space. The spectacular quantitative agreement between the (logarithm of the) number of micro-states and the Bekenstein-Hawking entropy has sparked an extremely fruitful dialogue between high energy physicists and mathematicians. However, a full accounting of the micro-states of BPS black holes has only be obtained to date in the case of string vacua with maximal or half-maximal supersymmetry. The main objective of this project is to perform a similar exact accounting in the far more challenging case of four-dimensional superstring vacua with N=2 supersymmetry, which is the minimal amount of supersymmetry which allows the very existence of BPS states, and to build new bridges between physics and mathematics in the process. String vacua with N=2 supersymmetry in four dimensions arise primarily by compactifying type IIA strings on a Calabi-Yau threefold (CY3) X. BPS black holes then arise from bound states of D0-branes, D2-branes wrapped on curves, D4-branes wrapped on divisors, and D6-branes wrapped on X. In mathematical terms, they correspond to stable objects in the derived category of coherent sheaves D(X), and are counted by the generalized Donaldson-Thomas (DT) invariants associated to the category D(X). The DT invariants depend sensitively on the Kähler moduli of X,and exhibit a complicated pattern of jumps across walls in Kähler moduli space, reflecting the appearance or disappearance of multi-centered black hole bound states. Fortunately, there exist distinguished choices of the moduli where the problem simplifies. At the attractor point, most bound states are absent and the computation of the resulting attractor index becomes more tractable. Once these attractor invariants are determined, the DT invariants for any other moduli can be deduced using the attractor flow tree formula. At the large radius point, DT invariants are related to the topological string partition function, for which many computational methods have been developped. The main goal of this project will be to derive explicit results and structural properties of generalized Donaldson-Thomas invariants and topological string partition functions of Calabi-Yau threefolds, both in the compact and non-compact cases. In the first case, we shall rely on the equivalence between the category coherent sheaves D(X) and the category D(Q,W) of representations of quiver with potential, which allows to convert the computation of DT invariants into a representation-theoretic problem, related to the combinatorics of molten crystals. In this context, we shall aim to prove the Attractor Conjecture recently put forward by the scientific coordinator and his collaborators, which predicts a very simple structure for the attractor indices associated to toric CY threefolds. We shall also derive the modularity properties of generating series of such invariants, by constructing a suitable Vertex Operator Algebra acting on the cohomology of the moduli space of quiver representations. In the compact case, we shall investigate the relation between the topological string partition function and the spectrum of BPS states at other special points in moduli space such as K-points and rank-two attractor points, and determine generating series of attractor invariants for one-parameter families of CY threefolds by exploiting mock modular properties and string dualities.

Bacterial communities colonize and attach to solid surfaces thanks to adhesive molecules exposed on the bacterial outer envelope. While a substantial number of molecular actors involved in bacterial adhesion have been characterized, their dynamics and their coordination on the bacterial envelope remain out of sight because the secretion machineries interfere with the fluorescence of standard probes. Recently, we showed thanks to mechanical assays that adhesive molecules were enriched at the old pole of bacteria. From this polar localization at single cell level, it results that microcolonies composed of rod-shaped bacteria develop into dense aggregates rather than into chains where bacteria would be highly exposed to their environment. This organization at the level of the community has a large impact in terms of biofilm tolerance to antibiotics and causes major health concerns by generating nosocomial diseases. In this project, we propose to use a new generation of fluorescent reporters, in order to measure the spatial dynamics of adhesive proteins exposed on the cell envelope of E. coli. By comparing physical modeling and experiments, we will aim at understanding the microscopic mechanisms that are responsible for adhesion polarity at the single cell level and how antibiotics could perturb this polarity and thus the structure of bacterial communities.

Quantum field theories (QFT) are known to be a challenging area for mathematicians and physicists with many important questions still left open. Among them, Conformal Field Theories (CFT) are of special interest as they describe most known models of statistical physics at their critical point but their integrable structure makes their solving tractable. For these reasons, CFTs are a topical playground in mathematics/physics nowadays which attracts numerous distinguished scientists and has experienced recent spectacular advances (e.g. critical 3D Ising). This project proposes an interdisciplary team to investigate this topic at the level of both fundamental questions and applications of CFTs to the description of statistical physics models.