Project acronym CASe
Project Combinatorics with an analytic structure
Researcher (PI) Karim ADIPRASITO
Host Institution (HI) THE HEBREW UNIVERSITY OF JERUSALEM
Call Details Starting Grant (StG), PE1, ERC-2016-STG
Summary "Combinatorics, and its interplay with geometry, has fascinated our ancestors as shown by early stone carvings in the Neolithic period. Modern combinatorics is motivated by the ubiquity of its structures in both pure and applied mathematics.
The work of Hochster and Stanley, who realized the relation of enumerative questions to commutative algebra and toric geometry made a vital contribution to the development of this subject. Their work was a central contribution to the classification of face numbers of simple polytopes, and the initial success lead to a wealth of research in which combinatorial problems were translated to algebra and geometry and then solved using deep results such as Saito's hard Lefschetz theorem. As a caveat, this also made branches of combinatorics reliant on algebra and geometry to provide new ideas.
In this proposal, I want to reverse this approach and extend our understanding of geometry and algebra guided by combinatorial methods. In this spirit I propose new combinatorial approaches to the interplay of curvature and topology, to isoperimetry, geometric analysis, and intersection theory, to name a few. In addition, while these subjects are interesting by themselves, they are also designed to advance classical topics, for example, the diameter of polyhedra (as in the Hirsch conjecture), arrangement theory (and the study of arrangement complements), Hodge theory (as in Grothendieck's standard conjectures), and realization problems of discrete objects (as in Connes embedding problem for type II factors).
This proposal is supported by the review of some already developed tools, such as relative Stanley--Reisner theory (which is equipped to deal with combinatorial isoperimetries), combinatorial Hodge theory (which extends the ``K\""ahler package'' to purely combinatorial settings), and discrete PDEs (which were used to construct counterexamples to old problems in discrete geometry)."
Summary
"Combinatorics, and its interplay with geometry, has fascinated our ancestors as shown by early stone carvings in the Neolithic period. Modern combinatorics is motivated by the ubiquity of its structures in both pure and applied mathematics.
The work of Hochster and Stanley, who realized the relation of enumerative questions to commutative algebra and toric geometry made a vital contribution to the development of this subject. Their work was a central contribution to the classification of face numbers of simple polytopes, and the initial success lead to a wealth of research in which combinatorial problems were translated to algebra and geometry and then solved using deep results such as Saito's hard Lefschetz theorem. As a caveat, this also made branches of combinatorics reliant on algebra and geometry to provide new ideas.
In this proposal, I want to reverse this approach and extend our understanding of geometry and algebra guided by combinatorial methods. In this spirit I propose new combinatorial approaches to the interplay of curvature and topology, to isoperimetry, geometric analysis, and intersection theory, to name a few. In addition, while these subjects are interesting by themselves, they are also designed to advance classical topics, for example, the diameter of polyhedra (as in the Hirsch conjecture), arrangement theory (and the study of arrangement complements), Hodge theory (as in Grothendieck's standard conjectures), and realization problems of discrete objects (as in Connes embedding problem for type II factors).
This proposal is supported by the review of some already developed tools, such as relative Stanley--Reisner theory (which is equipped to deal with combinatorial isoperimetries), combinatorial Hodge theory (which extends the ``K\""ahler package'' to purely combinatorial settings), and discrete PDEs (which were used to construct counterexamples to old problems in discrete geometry)."
Max ERC Funding
1 337 200 €
Duration
Start date: 2016-12-01, End date: 2021-11-30
Project acronym CRYOMATH
Project Cryo-electron microscopy: mathematical foundations and algorithms
Researcher (PI) Yoel SHKOLNISKY
Host Institution (HI) TEL AVIV UNIVERSITY
Call Details Consolidator Grant (CoG), PE1, ERC-2016-COG
Summary The importance of understanding the functions of the basic building blocks of life, such as proteins, cannot be overstated (as asserted by two recent Nobel prizes in Chemistry), as this understanding unravels the mechanisms that control all organisms. The critical step towards such an understanding is to reveal the structures of these building blocks. A leading method for resolving such structures is cryo-electron microscopy (cryo-EM), in which the structure of a molecule is recovered from its images taken by an electron microscope, by using sophisticated mathematical algorithms (to which my group has made several key mathematical and algorithmic contributions). Due to hardware breakthroughs in the past three years, cryo-EM has made a giant leap forward, introducing capabilities that until recently were unimaginable, opening an opportunity to revolutionize our biological understanding. As extracting information from cryo-EM experiments completely relies on mathematical algorithms, the method’s deep mathematical challenges that have emerged must be solved as soon as possible. Only then cryo-EM could realize its nearly inconceivable potential. These challenges, for which no adequate solutions exist (or none at all), focus on integrating information from huge sets of extremely noisy images reliability and efficiently. Based on the experience of my research group in developing algorithms for cryo-EM data processing, gained during the past eight years, we will address the three key open challenges of the field – a) deriving reliable and robust reconstruction algorithms from cryo-EM data, b) developing tools to process heterogeneous cryo-EM data sets, and c) devising validation and quality measures for structures determined from cryo-EM data. The fourth goal of the project, which ties all goals together and promotes the broad interdisciplinary impact of the project, is to merge all our algorithms into a software platform for state-of-the-art processing of cryo-EM data.
Summary
The importance of understanding the functions of the basic building blocks of life, such as proteins, cannot be overstated (as asserted by two recent Nobel prizes in Chemistry), as this understanding unravels the mechanisms that control all organisms. The critical step towards such an understanding is to reveal the structures of these building blocks. A leading method for resolving such structures is cryo-electron microscopy (cryo-EM), in which the structure of a molecule is recovered from its images taken by an electron microscope, by using sophisticated mathematical algorithms (to which my group has made several key mathematical and algorithmic contributions). Due to hardware breakthroughs in the past three years, cryo-EM has made a giant leap forward, introducing capabilities that until recently were unimaginable, opening an opportunity to revolutionize our biological understanding. As extracting information from cryo-EM experiments completely relies on mathematical algorithms, the method’s deep mathematical challenges that have emerged must be solved as soon as possible. Only then cryo-EM could realize its nearly inconceivable potential. These challenges, for which no adequate solutions exist (or none at all), focus on integrating information from huge sets of extremely noisy images reliability and efficiently. Based on the experience of my research group in developing algorithms for cryo-EM data processing, gained during the past eight years, we will address the three key open challenges of the field – a) deriving reliable and robust reconstruction algorithms from cryo-EM data, b) developing tools to process heterogeneous cryo-EM data sets, and c) devising validation and quality measures for structures determined from cryo-EM data. The fourth goal of the project, which ties all goals together and promotes the broad interdisciplinary impact of the project, is to merge all our algorithms into a software platform for state-of-the-art processing of cryo-EM data.
Max ERC Funding
1 751 250 €
Duration
Start date: 2017-03-01, End date: 2022-02-28
Project acronym HARMONIC
Project Studies in Harmonic Analysis and Discrete Geometry: Tilings, Spectra and Quasicrystals
Researcher (PI) Nir Lev
Host Institution (HI) BAR ILAN UNIVERSITY
Call Details Starting Grant (StG), PE1, ERC-2016-STG
Summary This proposal is concerned with several themes which lie in the crossroads of Harmonic Analysis and Discrete Geometry. Harmonic Analysis is fundamental in all areas of science and engineering, and has vast applications in most branches of mathematics. Discrete Geometry deals with some of the most natural and beautiful problems in mathematics, which often turn out to be also very deep and difficult in spite of their apparent simplicity. The proposed project deals with some fundamental problems which involve an interplay between these two important disciplines.
One theme of the project deals with tilings of the Euclidean space by translations, and the interaction of this subject with questions in orthogonal harmonic analysis. The PI has recently developed an approach to attack some problems in connection with the famous conjecture due to Fuglede (1974), concerning the characterization of domains which admit orthogonal Fourier bases in terms of their possibility to tile the space by translations, and in relation with the theory of multiple tiling by translates of a convex polytope, or by a function. A main goal of this project is to further develop new methods and extend some promising intermediate results obtained by the PI in these directions.
Another theme of the proposed research lies in the mathematical theory of quasicrystals. This area has received a lot of attention since the experimental discovery in the 1980's of the physical quasicrystals, namely, of non-periodic atomic structures with diffraction patterns consisting of spots. Recently, by a combination of harmonic analytic and discrete combinatorial methods, the PI was able to answer some long-standing questions of Lagarias (2000) concerning the geometry and structure of these rigid point configurations. In the present project, the PI intends to continue the investigation in the mathematical theory of quasicrystals, and to analyze some basic problems which are still open in this field.
Summary
This proposal is concerned with several themes which lie in the crossroads of Harmonic Analysis and Discrete Geometry. Harmonic Analysis is fundamental in all areas of science and engineering, and has vast applications in most branches of mathematics. Discrete Geometry deals with some of the most natural and beautiful problems in mathematics, which often turn out to be also very deep and difficult in spite of their apparent simplicity. The proposed project deals with some fundamental problems which involve an interplay between these two important disciplines.
One theme of the project deals with tilings of the Euclidean space by translations, and the interaction of this subject with questions in orthogonal harmonic analysis. The PI has recently developed an approach to attack some problems in connection with the famous conjecture due to Fuglede (1974), concerning the characterization of domains which admit orthogonal Fourier bases in terms of their possibility to tile the space by translations, and in relation with the theory of multiple tiling by translates of a convex polytope, or by a function. A main goal of this project is to further develop new methods and extend some promising intermediate results obtained by the PI in these directions.
Another theme of the proposed research lies in the mathematical theory of quasicrystals. This area has received a lot of attention since the experimental discovery in the 1980's of the physical quasicrystals, namely, of non-periodic atomic structures with diffraction patterns consisting of spots. Recently, by a combination of harmonic analytic and discrete combinatorial methods, the PI was able to answer some long-standing questions of Lagarias (2000) concerning the geometry and structure of these rigid point configurations. In the present project, the PI intends to continue the investigation in the mathematical theory of quasicrystals, and to analyze some basic problems which are still open in this field.
Max ERC Funding
1 260 625 €
Duration
Start date: 2016-12-01, End date: 2021-11-30
Project acronym MIX-Effectors
Project T6SS MIX-effectors: secretion, activities and use as antibacterial treatment
Researcher (PI) Dor Samuel Salomon
Host Institution (HI) TEL AVIV UNIVERSITY
Call Details Starting Grant (StG), LS6, ERC-2016-STG
Summary Bacteria use various mechanisms to combat competitors and colonize new niches. The Type VI Secretion System (T6SS), a contact-dependent protein delivery apparatus, is a widespread, recently discovered machine used by Gram-negative bacteria to target competitors. Its toxicity is mediated by secreted proteins called effectors, yet the identity of many effectors, the mechanism of secretion of different effector classes, and their toxic activities remain largely unknown. I recently uncovered a widespread class of T6SS effectors that share a domain called MIX. MIX-effectors are polymorphic proteins carrying various toxin domains, many of which with unknown activities.
Many bacterial pathogens have acquired resistance to contemporary antibiotic treatments, becoming a public health threat and necessitating the development of novel antibacterial strategies. Thus, as a relatively untapped antibacterial system, studying the T6SS and its MIX-effectors presents a double incentive: 1) previously uncharacterized antibacterial activities of MIX-effectors can illuminate novel cellular targets for antibacterial drug development; 2) the T6SS machinery can be used as a novel toxin delivery platform to combat multi-drug resistant bacterial infections, using polymorphic MIX-effectors.
In this proposal, I will focus on T6SS MIX-effectors and elucidate their activities, mechanism of secretion, and utilization as antibacterial agents, by combining microbiology, molecular biology, genetic, biochemical, and proteomic approaches. Specifically, the goal of this proposal is to utilize T6SSs and MIX-effectors to develop a novel T6SS-based, antibacterial therapeutic platform in which a nonpathogenic bacterium will be engineered to carry a T6SS that can secrete a diverse repertoire of polymorphic antibacterial MIX-effectors. This innovative platform has several advantages over current antibacterial strategies, and can be used as an adjustable tool to combat multi-drug resistant bacteria.
Summary
Bacteria use various mechanisms to combat competitors and colonize new niches. The Type VI Secretion System (T6SS), a contact-dependent protein delivery apparatus, is a widespread, recently discovered machine used by Gram-negative bacteria to target competitors. Its toxicity is mediated by secreted proteins called effectors, yet the identity of many effectors, the mechanism of secretion of different effector classes, and their toxic activities remain largely unknown. I recently uncovered a widespread class of T6SS effectors that share a domain called MIX. MIX-effectors are polymorphic proteins carrying various toxin domains, many of which with unknown activities.
Many bacterial pathogens have acquired resistance to contemporary antibiotic treatments, becoming a public health threat and necessitating the development of novel antibacterial strategies. Thus, as a relatively untapped antibacterial system, studying the T6SS and its MIX-effectors presents a double incentive: 1) previously uncharacterized antibacterial activities of MIX-effectors can illuminate novel cellular targets for antibacterial drug development; 2) the T6SS machinery can be used as a novel toxin delivery platform to combat multi-drug resistant bacterial infections, using polymorphic MIX-effectors.
In this proposal, I will focus on T6SS MIX-effectors and elucidate their activities, mechanism of secretion, and utilization as antibacterial agents, by combining microbiology, molecular biology, genetic, biochemical, and proteomic approaches. Specifically, the goal of this proposal is to utilize T6SSs and MIX-effectors to develop a novel T6SS-based, antibacterial therapeutic platform in which a nonpathogenic bacterium will be engineered to carry a T6SS that can secrete a diverse repertoire of polymorphic antibacterial MIX-effectors. This innovative platform has several advantages over current antibacterial strategies, and can be used as an adjustable tool to combat multi-drug resistant bacteria.
Max ERC Funding
1 484 375 €
Duration
Start date: 2017-02-01, End date: 2022-01-31
Project acronym MultiLevelLandscape
Project Multilevel Selection for Specificity and Divergence in Bacteria
Researcher (PI) Avigdor Eldar
Host Institution (HI) TEL AVIV UNIVERSITY
Call Details Consolidator Grant (CoG), LS8, ERC-2016-COG
Summary The evolution of specificity between interacting biological molecules underlies the diversification and expansion of biological pathways. A shift in specificity poses a serious theoretical problem; it requires coordinated mutations in the interacting partners, but mutation in one partner may lead to loss of interaction and functional failure. While some theoretical suggestions were proposed to solve this 'specificity valley crossing' problem, it remains a challenge to study this problem empirically at the molecular level. In bacteria, there are numerous divergent evolving pathways. Many of these pathways are involved in mediating conflicts between selfish genes, cells and populations. We and others have speculated that such multilevel selection can facilitate pathway divergence. Here we propose to study this link using the Rap-Phr cell-cell communication system, which has diversified to ~100 specific systems in the B. subtilis lineage. These systems consist of a receptor (Rap) and its cognate peptide pheromone (Phr) that influence multiple levels of selection. They promote their own horizontal transfer, modulate core cellular pathways, and manipulate cooperation between cells. Combining modelling with deep mutational scanning, competition assays and time-lapse microscopy we will quantitatively study all these levels of selection and their implication for diversification on a large fitness landscape. Specifically, we will (1) map the Rap-Phr interaction landscape at unprecedented resolution, constructing and screening libraries of ~106 Phr peptide variants and ~104 Rap variants. (2) Quantify the fitness effects of these systems at multiple levels of selection in biofilms. (3) Theoretically generate and experimentally verify predictions about how Rap-Phr co-evolve and diversify. Our work will pioneer the study of fitness landscapes under multilevel selection and provide a direct, quantitative, and predictive framework for understanding the evolution of specificity.
Summary
The evolution of specificity between interacting biological molecules underlies the diversification and expansion of biological pathways. A shift in specificity poses a serious theoretical problem; it requires coordinated mutations in the interacting partners, but mutation in one partner may lead to loss of interaction and functional failure. While some theoretical suggestions were proposed to solve this 'specificity valley crossing' problem, it remains a challenge to study this problem empirically at the molecular level. In bacteria, there are numerous divergent evolving pathways. Many of these pathways are involved in mediating conflicts between selfish genes, cells and populations. We and others have speculated that such multilevel selection can facilitate pathway divergence. Here we propose to study this link using the Rap-Phr cell-cell communication system, which has diversified to ~100 specific systems in the B. subtilis lineage. These systems consist of a receptor (Rap) and its cognate peptide pheromone (Phr) that influence multiple levels of selection. They promote their own horizontal transfer, modulate core cellular pathways, and manipulate cooperation between cells. Combining modelling with deep mutational scanning, competition assays and time-lapse microscopy we will quantitatively study all these levels of selection and their implication for diversification on a large fitness landscape. Specifically, we will (1) map the Rap-Phr interaction landscape at unprecedented resolution, constructing and screening libraries of ~106 Phr peptide variants and ~104 Rap variants. (2) Quantify the fitness effects of these systems at multiple levels of selection in biofilms. (3) Theoretically generate and experimentally verify predictions about how Rap-Phr co-evolve and diversify. Our work will pioneer the study of fitness landscapes under multilevel selection and provide a direct, quantitative, and predictive framework for understanding the evolution of specificity.
Max ERC Funding
2 000 000 €
Duration
Start date: 2017-03-01, End date: 2022-02-28
Project acronym ThymusTolerance
Project Delineation of molecular mechanisms underlying the establishment and breakdown of immunological tolerance in the thymus
Researcher (PI) Jakub ABRAMSON
Host Institution (HI) WEIZMANN INSTITUTE OF SCIENCE
Call Details Consolidator Grant (CoG), LS6, ERC-2016-COG
Summary Central tolerance is shaped in the thymus, a primary lymphoid organ, where immature T lymphocytes are “educated” into mature cells, capable of recognizing foreign antigens, while tolerating the body’s own components. This process is driven mainly by two separate lineages of thymic epithelial cells (TECs), the cortical (cTEC) and the medullary (mTEC). While cTECs are critical at the early stages of T cell development, mTECs play a pivotal role in negative selection of self-reactive thymocytes and the generation of Foxp3+ regulatory T (Treg) cells. Crucial to the key role of mTECs in the screening of self-reactive T cell clones, is their unique capacity to promiscuously express and present almost all self-antigens, including thousands of tissue-specific antigen (TSA) genes. Strikingly, the expression of most of this TSA repertoire in mTECs is regulated by a single transcriptional regulator called Aire. Indeed, Aire deficiency in mice and human patients results to multi-organ autoimmunity. Although there has been dramatic progress in our understanding of how thymic epithelial cells shape and govern the establishment of adaptive immunity and of immunological self-tolerance, there are still several outstanding questions with no comprehensive answers. Therefore, in the research proposed herein, we wish to provide more comprehensive answers to these still elusive, but very fundamental questions. Specifically we will aim at: 1.) Delineation of molecular mechanisms controlling TEC development and thymus organogenesis; 2.) Delineation of molecular mechanisms underlying promiscuous gene expression in the thymus; 3.) Identification and characterization of molecular determinants responsible for the breakdown of thymus-dependent self-tolerance. To this end, we will build upon our recently published data, as well as unpublished preliminary data and utilize several state-of-the-art and interdisciplinary approaches, which have become an integral part of our lab’s toolbox.
Summary
Central tolerance is shaped in the thymus, a primary lymphoid organ, where immature T lymphocytes are “educated” into mature cells, capable of recognizing foreign antigens, while tolerating the body’s own components. This process is driven mainly by two separate lineages of thymic epithelial cells (TECs), the cortical (cTEC) and the medullary (mTEC). While cTECs are critical at the early stages of T cell development, mTECs play a pivotal role in negative selection of self-reactive thymocytes and the generation of Foxp3+ regulatory T (Treg) cells. Crucial to the key role of mTECs in the screening of self-reactive T cell clones, is their unique capacity to promiscuously express and present almost all self-antigens, including thousands of tissue-specific antigen (TSA) genes. Strikingly, the expression of most of this TSA repertoire in mTECs is regulated by a single transcriptional regulator called Aire. Indeed, Aire deficiency in mice and human patients results to multi-organ autoimmunity. Although there has been dramatic progress in our understanding of how thymic epithelial cells shape and govern the establishment of adaptive immunity and of immunological self-tolerance, there are still several outstanding questions with no comprehensive answers. Therefore, in the research proposed herein, we wish to provide more comprehensive answers to these still elusive, but very fundamental questions. Specifically we will aim at: 1.) Delineation of molecular mechanisms controlling TEC development and thymus organogenesis; 2.) Delineation of molecular mechanisms underlying promiscuous gene expression in the thymus; 3.) Identification and characterization of molecular determinants responsible for the breakdown of thymus-dependent self-tolerance. To this end, we will build upon our recently published data, as well as unpublished preliminary data and utilize several state-of-the-art and interdisciplinary approaches, which have become an integral part of our lab’s toolbox.
Max ERC Funding
2 220 000 €
Duration
Start date: 2017-09-01, End date: 2022-08-31
