ERC FUNDED PROJECTS

The Virtual Element Method (VEM) is a novel technology for the discretization of partial differential equations (PDEs), that shares the same variational background as the Finite Element Method. First but not only, the VEM responds to the strongly increasing interest in using general polyhedral and polygonal meshes in the approximation of PDEs without the limit of using tetrahedral or hexahedral grids. By avoiding the explicit integration of the shape functions that span the discrete space and introducing an innovative construction of the stiffness matrixes, the VEM acquires very interesting properties and advantages with respect to more standard Galerkin methods, yet still keeping the same coding complexity. For instance, the VEM easily allows for polygonal/polyhedral meshes (even non-conforming) with non-convex elements and possibly with curved faces; it allows for discrete spaces of arbitrary C^k regularity on unstructured meshes. The main scope of the project is to address the recent theoretical challenges posed by VEM and to assess whether this promising technology can achieve a breakthrough in applications. First, the theoretical and computational foundations of VEM will be made stronger. A deeper theoretical insight, supported by a wider numerical experience on benchmark problems, will be developed to gain a better understanding of the method's potentials and set the foundations for more applicative purposes. Second, we will focus our attention on two tough and up-to-date problems of practical interest: large deformation elasticity (where VEM can yield a dramatically more efficient handling of material inclusions, meshing of the domain and grid adaptivity, plus a much stronger robustness with respect to large grid distortions) and the cardiac bidomain model (where VEM can lead to a more accurate domain approximation through MRI data, a flexible refinement/de-refinement procedure along the propagation front, to an exact satisfaction of conservation laws).

980 634 €

Start date: 2016-07-01, End date: 2021-06-30

Cell fusion is critical for fertilization and development, for instance underlying muscle or bone formation. Cell fusion may also play important roles in regeneration and cancer. A conceptual understanding is emerging that cell fusion requires cell-cell communication, polarization of the cells towards each other, and assembly of a fusion machinery, in which an actin-based structure promotes membrane juxtaposition and fusogenic factors drive membrane fusion. However, in no single system have the molecular nature of all these parts been described, and thus the molecular basis of cell fusion remains poorly understood. This proposal aims to depict the complete fusion process in a single organism, using the simple yeast model Schizosaccharomyces pombe, which has a long track record of discoveries in fundamental cellular processes. These haploid cells, which fuse to generate a diploid zygote, use highly conserved mechanisms of cell-cell communication (through pheromones and GPCR signaling), cell polarization (centred around the small GTPase Cdc42) and fusion. Indeed, we recently showed that these cells assemble an actin-based fusion structure, dubbed the actin fusion focus. Our five aims probe the molecular nature of, and the links between, signaling, polarization and the fusion machinery from initiation to termination of the process. These are: 1: To define the roles and feedback regulation of Cdc42 during cell fusion 2: To understand the molecular mechanisms of actin fusion focus formation 3: To identify the fusogen(s) promoting membrane fusion 4: To probe the GPCR signal for fusion initiation 5: To define the mechanism of fusion termination By combining genetic, optogenetic, biochemical, live-imaging, synthetic and modeling approaches, this project will bring a molecular and conceptual understanding of cell fusion. This work will have far-ranging relevance for cell polarization, cytoskeletal organization, cell signalling and communication, and cell fate regulation.

1 999 956 €

Start date: 2016-10-01, End date: 2021-09-30

During the human lifetime 10000 trillion cell divisions take place to ensure tissue homeostasis and several vital functions in the organism. Mitosis is the process that ensures that dividing cells preserve the chromosome number of their progenitors, while deviation from this, a condition known as aneuploidy, represents the most common feature in human cancers. Here we will test two original concepts with strong implications for chromosome segregation fidelity. The first concept is based on the “tubulin code” hypothesis, which predicts that molecular motors “read” tubulin post-translational modifications on spindle microtubules. Our proof-of-concept experiments demonstrate that tubulin detyrosination works as a navigation system that guides chromosomes towards the cell equator. Thus, in addition to regulating the motors required for chromosome motion, the cell might regulate the tracks in which they move on. We will combine proteomic, super-resolution and live-cell microscopy, with in vitro reconstitutions, to perform a comprehensive survey of the tubulin code and the respective implications for motors involved in chromosome motion, mitotic spindle assembly and correction of kinetochore-microtubule attachments. The second concept is centered on the recently uncovered chromosome separation checkpoint mediated by a midzone-associated Aurora B gradient, which delays nuclear envelope reformation in response to incompletely separated chromosomes. We aim to identify Aurora B targets involved in the spatiotemporal regulation of the anaphase-telophase transition. We will establish powerful live-cell microscopy assays and a novel mammalian model system to dissect how this checkpoint allows the detection and correction of lagging/long chromosomes and DNA bridges that would otherwise contribute to genomic instability. Overall, this work will establish a paradigm shift in our understanding of how spatial information is conveyed to faithfully segregate chromosomes during mitosis.

2 323 468 €

Start date: 2016-07-01, End date: 2021-06-30

The activities of the Polycomb group (PcG) of repressive chromatin modifiers are required to maintain correct transcriptional identity during development and differentiation. These activities are altered in a variety of tumours by gain- or loss-of-function mutations, whose mechanistic aspects still remain unclear. PcGs can be classified in two major repressive complexes (PRC1 and PRC2) with common pathways but distinct biochemical activities. PRC1 catalyses histone H2A ubiquitination of lysine 119, and PRC2 tri-methylation of histone H3 lysine 27. However, PRC1 has a more heterogeneous composition than PRC2, with six mutually exclusive PCGF subunits (PCGF1–6) essential for assembling distinct PRC1 complexes that differ in subunit composition but share the same catalytic core. While up to six different PRC1 forms can co-exist in a given cell, the molecular mechanisms regulating their activities and their relative contributions to general PRC1 function in any tissue/cell type remain largely unknown. In line with this biochemical heterogeneity, PRC1 retains broader biological functions than PRC2. Critically, however, no molecular analysis has yet been published that dissects the contribution of each PRC1 complex in regulating transcriptional identity. We will take advantage of newly developed reagents and unpublished genetic models to target each of the six Pcgf genes in either embryonic stem cells or mouse adult tissues. This will systematically dissect the contributions of the different PRC1 complexes to chromatin profiles, gene expression programs, and cellular phenotypes during stem cell self-renewal, differentiation and adult tissue homeostasis. Overall, this will elucidate some of the fundamental mechanisms underlying the establishment and maintenance of cellular identity and will allow us to further determine the molecular links between PcG deregulation and cancer development in a tissue- and/or cell type–specific manner.

2 000 000 €

Start date: 2017-11-01, End date: 2022-10-31

Epigenetic mechanisms heritably maintain gene expression states and chromosome organization across cell division. These include chromatin-based factors that are propagated independent of local DNA sequence elements, and are critical for normal development and prevent reprogramming, e.g. during induction of pluripotency. We focus on the role of nucleosomes, the histone-DNA complexes that make up chromatin. While prominently implicated in epigenetic memory, how histones and their local modifications can actually be inherited is largely unknown. We take aim at three fundamental aspects that we argue are central to this problem: stability of the epigenetic mark, self-templated duplication, and cell cycle coupling. We developed a unique pulse-labeling strategy to determine whether silent and active chromatin can be inherited and how this relates to transcription, both in cancer cells and in vitro differentiating stem cells. By coupling this strategy to an imaging-based RNAi screen we aim to identify components controlling nucleosome assembly and heritability. We achieve this by focusing on the human centromere, the chromosome locus essential for chromosome segregation which serves as an ideal model for epigenetic memory. This locus is specified by nucleosomes carrying the histone H3 variant, CENP-A that we have previously shown to be highly stable in cycling cells and to be replicated in a strict cell cycle coupled manner. We build on our previous successes to uncover the molecular mechanism and cellular consequences of the coupling between CENP-A propagation and the cell cycle which we postulate, ensures proper centromere size and mitotic fidelity. Furthermore, by genome engineering we developed a strategy to delete an endogenous centromere to determine how centromeres can form de novo and how CENP-A chromatin, once formed, can template its own duplication. With this multi-facetted approach we aim to uncover general mechanistic principles of chromatin-based memory.

1 621 400 €

Start date: 2014-06-01, End date: 2019-05-31

The goal of this proposal is to leverage and significantly extend techniques from the field of Combinatorial Optimization to address some fundamental open algorithmic questions in other, related areas, namely Integer Programming and Online Optimization. More precisely, we focus on the following three thrusts, which share many combinatorial features: - Integer programming with bounded subdeterminants. - Expressive power of mixed-integer linear formulations. - The matroid secretary conjecture, a key online selection problem. Recent significant progress, in which the PI played a central role, combined with new ideas, give hope to obtain breakthrough results in these fields. Many of the questions we consider are long-standing open problems in their respective area, and any progress is thus likely to be a significant contribution to Mathematical Optimization and Theoretical Computer Science. However, equally importantly, if progress can be achieved through the suggested methodologies, then this would create intriguing new links between different fields, which was a key driver in the selection of the above research thrusts.

1 443 422 €

Start date: 2019-11-01, End date: 2024-10-31

"This project focuses on several problems in Partial Differential Equations (PDEs) and the Calculus of Variations. These include: - Optimal transport and Monge-Ampère equations. In the last 30 years, the optimal transport problem has been found to be useful to several areas of mathematics. In particular, this problem is related to Monge-Ampère type equations, and understanding the regularity properties of solutions to such equations is an important question with applications to several other fields. - Stability in functional and geometric inequalities. Whether a minimizer of some inequality is ""stable'' in some suitable sense is an important issue in order to understand and/or predict the evolution in time of a physical phenomenon. For instance, quantitative stability results allow one to quantify the rate of convergence of a physical system to some steady state, and they can also be used to understand how much the system changes under the influence of exterior factors. - Di Perna-Lions theory and PDEs. The study of transport equations with rough coefficients is a very active research area. In particular, recent developments have been used to obtain new results on the semiclassical limit for the Schr\""odinger equation and on the Lagrangian structure of transport equations with singular vector-fields (for instance, the Vlasov-Poisson equation). These problems, although apparently different, are actually deeply interconnected. The PI aims to use his expertise in partial differential equations and geometric measure theory to introduce ideas and techniques that will lead to new groundbreaking results. "

1 742 428 €

Start date: 2017-02-01, End date: 2022-01-31

Neural stem/progenitor cells (NSPCs) continue to generate new neurons throughout life in distinct regions of the mammalian brain. Adult neurogenesis has been implicated in brain function and altered neurogenesis has been associated with a number of neuropsychiatric diseases such as depression and cognitive ageing. A key feature of somatic stem cell division is the ability to divide asymmetrically and symmetrically for neurogenic and self-renewing cell division, respectively. However, it remains unknown how age is segregated in the context of somatic stem cell division, i.e., if the cellular history and the replicative age of the mother stem cell is passed onto its progeny. Thus, we hypothesized that – similar to the previously described barrier that exists in budding yeast – somatic stem cells, and more specifically NSPCs, form a diffusion barrier during cell division to retain aging or senescence factors within the stem cell, generating a mechanism for how age is asymmetrically distributed. Indeed, we found the existence of a diffusion barrier that is established during NSPC division, identifying a new mechanism of cellular segregation and asymmetry. With the program proposed here I aim i) to study the effects of the barrier on asymmetric segregation of aging factors and to develop novel tools to visualize the mammalian diffusion barrier, ii) to characterize the presence of a diffusion barrier in endogenous NSPCs in relation to cell division history, iii) to analyse the mechanisms underlying age-associated weakening of the NSPC diffusion barrier, and iv) to evaluate if genetic and pharmacological rescue of the barrier is sufficient to ameliorate the age-dependent decline of neurogenesis. The insights gained from the studies proposed here have the potential to substantially advance our understanding of NSPC biology, to identify a new mechanism underlying the neurogenic process, and to reshape our understanding of asymmetric cell division of somatic stem cells.

2 000 000 €

Start date: 2016-09-01, End date: 2021-08-31