Project acronym 20SComplexity
Project An integrative approach to uncover the multilevel regulation of 20S proteasome degradation
Researcher (PI) Michal Sharon
Host Institution (HI) WEIZMANN INSTITUTE OF SCIENCE
Call Details Starting Grant (StG), LS1, ERC-2014-STG
Summary For many years, the ubiquitin-26S proteasome degradation pathway was considered the primary route for proteasomal degradation. However, it is now becoming clear that proteins can also be targeted for degradation by a ubiquitin-independent mechanism mediated by the core 20S proteasome itself. Although initially believed to be limited to rare exceptions, degradation by the 20S proteasome is now understood to have a wide range of substrates, many of which are key regulatory proteins. Despite its importance, little is known about the mechanisms that control 20S proteasomal degradation, unlike the extensive knowledge acquired over the years concerning degradation by the 26S proteasome. Our overall aim is to reveal the multiple regulatory levels that coordinate the 20S proteasome degradation route.
To achieve this goal we will carry out a comprehensive research program characterizing three distinct levels of 20S proteasome regulation:
Intra-molecular regulation- Revealing the intrinsic molecular switch that activates the latent 20S proteasome.
Inter-molecular regulation- Identifying novel proteins that bind the 20S proteasome to regulate its activity and characterizing their mechanism of function.
Cellular regulatory networks- Unraveling the cellular cues and multiple pathways that influence 20S proteasome activity using a novel systematic and unbiased screening approach.
Our experimental strategy involves the combination of biochemical approaches with native mass spectrometry, cross-linking and fluorescence measurements, complemented by cell biology analyses and high-throughput screening. Such a multidisciplinary approach, integrating in vitro and in vivo findings, will likely provide the much needed knowledge on the 20S proteasome degradation route. When completed, we anticipate that this work will be part of a new paradigm – no longer perceiving the 20S proteasome mediated degradation as a simple and passive event but rather a tightly regulated and coordinated process.
Summary
For many years, the ubiquitin-26S proteasome degradation pathway was considered the primary route for proteasomal degradation. However, it is now becoming clear that proteins can also be targeted for degradation by a ubiquitin-independent mechanism mediated by the core 20S proteasome itself. Although initially believed to be limited to rare exceptions, degradation by the 20S proteasome is now understood to have a wide range of substrates, many of which are key regulatory proteins. Despite its importance, little is known about the mechanisms that control 20S proteasomal degradation, unlike the extensive knowledge acquired over the years concerning degradation by the 26S proteasome. Our overall aim is to reveal the multiple regulatory levels that coordinate the 20S proteasome degradation route.
To achieve this goal we will carry out a comprehensive research program characterizing three distinct levels of 20S proteasome regulation:
Intra-molecular regulation- Revealing the intrinsic molecular switch that activates the latent 20S proteasome.
Inter-molecular regulation- Identifying novel proteins that bind the 20S proteasome to regulate its activity and characterizing their mechanism of function.
Cellular regulatory networks- Unraveling the cellular cues and multiple pathways that influence 20S proteasome activity using a novel systematic and unbiased screening approach.
Our experimental strategy involves the combination of biochemical approaches with native mass spectrometry, cross-linking and fluorescence measurements, complemented by cell biology analyses and high-throughput screening. Such a multidisciplinary approach, integrating in vitro and in vivo findings, will likely provide the much needed knowledge on the 20S proteasome degradation route. When completed, we anticipate that this work will be part of a new paradigm – no longer perceiving the 20S proteasome mediated degradation as a simple and passive event but rather a tightly regulated and coordinated process.
Max ERC Funding
1 500 000 €
Duration
Start date: 2015-04-01, End date: 2020-03-31
Project acronym 3DCellPhase-
Project In situ Structural Analysis of Molecular Crowding and Phase Separation
Researcher (PI) Julia MAHAMID
Host Institution (HI) EUROPEAN MOLECULAR BIOLOGY LABORATORY
Call Details Starting Grant (StG), LS1, ERC-2017-STG
Summary This proposal brings together two fields in biology, namely the emerging field of phase-separated assemblies in cell biology and state-of-the-art cellular cryo-electron tomography, to advance our understanding on a fundamental, yet illusive, question: the molecular organization of the cytoplasm.
Eukaryotes organize their biochemical reactions into functionally distinct compartments. Intriguingly, many, if not most, cellular compartments are not membrane enclosed. Rather, they assemble dynamically by phase separation, typically triggered upon a specific event. Despite significant progress on reconstituting such liquid-like assemblies in vitro, we lack information as to whether these compartments in vivo are indeed amorphous liquids, or whether they exhibit structural features such as gels or fibers. My recent work on sample preparation of cells for cryo-electron tomography, including cryo-focused ion beam thinning, guided by 3D correlative fluorescence microscopy, shows that we can now prepare site-specific ‘electron-transparent windows’ in suitable eukaryotic systems, which allow direct examination of structural features of cellular compartments in their cellular context. Here, we will use these techniques to elucidate the structural principles and cytoplasmic environment driving the dynamic assembly of two phase-separated compartments: Stress granules, which are RNA bodies that form rapidly in the cytoplasm upon cellular stress, and centrosomes, which are sites of microtubule nucleation. We will combine these studies with a quantitative description of the crowded nature of cytoplasm and of its local variations, to provide a direct readout of the impact of excluded volume on molecular assembly in living cells. Taken together, these studies will provide fundamental insights into the structural basis by which cells form biochemical compartments.
Summary
This proposal brings together two fields in biology, namely the emerging field of phase-separated assemblies in cell biology and state-of-the-art cellular cryo-electron tomography, to advance our understanding on a fundamental, yet illusive, question: the molecular organization of the cytoplasm.
Eukaryotes organize their biochemical reactions into functionally distinct compartments. Intriguingly, many, if not most, cellular compartments are not membrane enclosed. Rather, they assemble dynamically by phase separation, typically triggered upon a specific event. Despite significant progress on reconstituting such liquid-like assemblies in vitro, we lack information as to whether these compartments in vivo are indeed amorphous liquids, or whether they exhibit structural features such as gels or fibers. My recent work on sample preparation of cells for cryo-electron tomography, including cryo-focused ion beam thinning, guided by 3D correlative fluorescence microscopy, shows that we can now prepare site-specific ‘electron-transparent windows’ in suitable eukaryotic systems, which allow direct examination of structural features of cellular compartments in their cellular context. Here, we will use these techniques to elucidate the structural principles and cytoplasmic environment driving the dynamic assembly of two phase-separated compartments: Stress granules, which are RNA bodies that form rapidly in the cytoplasm upon cellular stress, and centrosomes, which are sites of microtubule nucleation. We will combine these studies with a quantitative description of the crowded nature of cytoplasm and of its local variations, to provide a direct readout of the impact of excluded volume on molecular assembly in living cells. Taken together, these studies will provide fundamental insights into the structural basis by which cells form biochemical compartments.
Max ERC Funding
1 228 125 €
Duration
Start date: 2018-02-01, End date: 2023-01-31
Project acronym ABDESIGN
Project Computational design of novel protein function in antibodies
Researcher (PI) Sarel-Jacob Fleishman
Host Institution (HI) WEIZMANN INSTITUTE OF SCIENCE
Call Details Starting Grant (StG), LS1, ERC-2013-StG
Summary We propose to elucidate the structural design principles of naturally occurring antibody complementarity-determining regions (CDRs) and to computationally design novel antibody functions. Antibodies represent the most versatile known system for molecular recognition. Research has yielded many insights into antibody design principles and promising biotechnological and pharmaceutical applications. Still, our understanding of how CDRs encode specific loop conformations lags far behind our understanding of structure-function relationships in non-immunological scaffolds. Thus, design of antibodies from first principles has not been demonstrated. We propose a computational-experimental strategy to address this challenge. We will: (a) characterize the design principles and sequence elements that rigidify antibody CDRs. Natural antibody loops will be subjected to computational modeling, crystallography, and a combined in vitro evolution and deep-sequencing approach to isolate sequence features that rigidify loop backbones; (b) develop a novel computational-design strategy, which uses the >1000 solved structures of antibodies deposited in structure databases to realistically model CDRs and design them to recognize proteins that have not been co-crystallized with antibodies. For example, we will design novel antibodies targeting insulin, for which clinically useful diagnostics are needed. By accessing much larger sequence/structure spaces than are available to natural immune-system repertoires and experimental methods, computational antibody design could produce higher-specificity and higher-affinity binders, even to challenging targets; and (c) develop new strategies to program conformational change in CDRs, generating, e.g., the first allosteric antibodies. These will allow targeting, in principle, of any molecule, potentially revolutionizing how antibodies are generated for research and medicine, providing new insights on the design principles of protein functional sites.
Summary
We propose to elucidate the structural design principles of naturally occurring antibody complementarity-determining regions (CDRs) and to computationally design novel antibody functions. Antibodies represent the most versatile known system for molecular recognition. Research has yielded many insights into antibody design principles and promising biotechnological and pharmaceutical applications. Still, our understanding of how CDRs encode specific loop conformations lags far behind our understanding of structure-function relationships in non-immunological scaffolds. Thus, design of antibodies from first principles has not been demonstrated. We propose a computational-experimental strategy to address this challenge. We will: (a) characterize the design principles and sequence elements that rigidify antibody CDRs. Natural antibody loops will be subjected to computational modeling, crystallography, and a combined in vitro evolution and deep-sequencing approach to isolate sequence features that rigidify loop backbones; (b) develop a novel computational-design strategy, which uses the >1000 solved structures of antibodies deposited in structure databases to realistically model CDRs and design them to recognize proteins that have not been co-crystallized with antibodies. For example, we will design novel antibodies targeting insulin, for which clinically useful diagnostics are needed. By accessing much larger sequence/structure spaces than are available to natural immune-system repertoires and experimental methods, computational antibody design could produce higher-specificity and higher-affinity binders, even to challenging targets; and (c) develop new strategies to program conformational change in CDRs, generating, e.g., the first allosteric antibodies. These will allow targeting, in principle, of any molecule, potentially revolutionizing how antibodies are generated for research and medicine, providing new insights on the design principles of protein functional sites.
Max ERC Funding
1 499 930 €
Duration
Start date: 2013-09-01, End date: 2018-08-31
Project acronym AGALT
Project Asymptotic Geometric Analysis and Learning Theory
Researcher (PI) Shahar Mendelson
Host Institution (HI) TECHNION - ISRAEL INSTITUTE OF TECHNOLOGY
Call Details Starting Grant (StG), PE1, ERC-2007-StG
Summary In a typical learning problem one tries to approximate an unknown function by a function from a given class using random data, sampled according to an unknown measure. In this project we will be interested in parameters that govern the complexity of a learning problem. It turns out that this complexity is determined by the geometry of certain sets in high dimension that are connected to the given class (random coordinate projections of the class). Thus, one has to understand the structure of these sets as a function of the dimension - which is given by the cardinality of the random sample. The resulting analysis leads to many theoretical questions in Asymptotic Geometric Analysis, Probability (most notably, Empirical Processes Theory) and Combinatorics, which are of independent interest beyond the application to Learning Theory. Our main goal is to describe the role of various complexity parameters involved in a learning problem, to analyze the connections between them and to investigate the way they determine the geometry of the relevant high dimensional sets. Some of the questions we intend to tackle are well known open problems and making progress towards their solution will have a significant theoretical impact. Moreover, this project should lead to a more complete theory of learning and is likely to have some practical impact, for example, in the design of more efficient learning algorithms.
Summary
In a typical learning problem one tries to approximate an unknown function by a function from a given class using random data, sampled according to an unknown measure. In this project we will be interested in parameters that govern the complexity of a learning problem. It turns out that this complexity is determined by the geometry of certain sets in high dimension that are connected to the given class (random coordinate projections of the class). Thus, one has to understand the structure of these sets as a function of the dimension - which is given by the cardinality of the random sample. The resulting analysis leads to many theoretical questions in Asymptotic Geometric Analysis, Probability (most notably, Empirical Processes Theory) and Combinatorics, which are of independent interest beyond the application to Learning Theory. Our main goal is to describe the role of various complexity parameters involved in a learning problem, to analyze the connections between them and to investigate the way they determine the geometry of the relevant high dimensional sets. Some of the questions we intend to tackle are well known open problems and making progress towards their solution will have a significant theoretical impact. Moreover, this project should lead to a more complete theory of learning and is likely to have some practical impact, for example, in the design of more efficient learning algorithms.
Max ERC Funding
750 000 €
Duration
Start date: 2009-03-01, End date: 2014-02-28
Project acronym ANOPTSETCON
Project Analysis of optimal sets and optimal constants: old questions and new results
Researcher (PI) Aldo Pratelli
Host Institution (HI) FRIEDRICH-ALEXANDER-UNIVERSITAET ERLANGEN NUERNBERG
Call Details Starting Grant (StG), PE1, ERC-2010-StG_20091028
Summary The analysis of geometric and functional inequalities naturally leads to consider the extremal cases, thus
looking for optimal sets, or optimal functions, or optimal constants. The most classical examples are the (different versions of the) isoperimetric inequality and the Sobolev-like inequalities. Much is known about equality cases and best constants, but there are still many questions which seem quite natural but yet have no answer. For instance, it is not known, even in the 2-dimensional space, the answer of a question by Brezis: which set,
among those with a given volume, has the biggest Sobolev-Poincaré constant for p=1? This is a very natural problem, and it appears reasonable that the optimal set should be the ball, but this has never been proved. The interest in problems like this relies not only in the extreme simplicity of the questions and in their classical flavour, but also in the new ideas and techniques which are needed to provide the answers.
The main techniques that we aim to use are fine arguments of symmetrization, geometric constructions and tools from mass transportation (which is well known to be deeply connected with functional inequalities). These are the basic tools that we already used to reach, in last years, many results in a specific direction, namely the search of sharp quantitative inequalities. Our first result, together with Fusco and Maggi, showed what follows. Everybody knows that the set which minimizes the perimeter with given volume is the ball.
But is it true that a set which almost minimizes the perimeter must be close to a ball? The question had been posed in the 1920's and many partial result appeared in the years. In our paper (Ann. of Math., 2007) we proved the sharp result. Many other results of this kind were obtained in last two years.
Summary
The analysis of geometric and functional inequalities naturally leads to consider the extremal cases, thus
looking for optimal sets, or optimal functions, or optimal constants. The most classical examples are the (different versions of the) isoperimetric inequality and the Sobolev-like inequalities. Much is known about equality cases and best constants, but there are still many questions which seem quite natural but yet have no answer. For instance, it is not known, even in the 2-dimensional space, the answer of a question by Brezis: which set,
among those with a given volume, has the biggest Sobolev-Poincaré constant for p=1? This is a very natural problem, and it appears reasonable that the optimal set should be the ball, but this has never been proved. The interest in problems like this relies not only in the extreme simplicity of the questions and in their classical flavour, but also in the new ideas and techniques which are needed to provide the answers.
The main techniques that we aim to use are fine arguments of symmetrization, geometric constructions and tools from mass transportation (which is well known to be deeply connected with functional inequalities). These are the basic tools that we already used to reach, in last years, many results in a specific direction, namely the search of sharp quantitative inequalities. Our first result, together with Fusco and Maggi, showed what follows. Everybody knows that the set which minimizes the perimeter with given volume is the ball.
But is it true that a set which almost minimizes the perimeter must be close to a ball? The question had been posed in the 1920's and many partial result appeared in the years. In our paper (Ann. of Math., 2007) we proved the sharp result. Many other results of this kind were obtained in last two years.
Max ERC Funding
540 000 €
Duration
Start date: 2010-08-01, End date: 2015-07-31
Project acronym ANTHOS
Project Analytic Number Theory: Higher Order Structures
Researcher (PI) Valentin Blomer
Host Institution (HI) GEORG-AUGUST-UNIVERSITAT GOTTINGENSTIFTUNG OFFENTLICHEN RECHTS
Call Details Starting Grant (StG), PE1, ERC-2010-StG_20091028
Summary This is a proposal for research at the interface of analytic number theory, automorphic forms and algebraic geometry. Motivated by fundamental conjectures in number theory, classical problems will be investigated in higher order situations: general number fields, automorphic forms on higher rank groups, the arithmetic of algebraic varieties of higher degree. In particular, I want to focus on
- computation of moments of L-function of degree 3 and higher with applications to subconvexity and/or non-vanishing, as well as subconvexity for multiple L-functions;
- bounds for sup-norms of cusp forms on various spaces and equidistribution of Hecke correspondences;
- automorphic forms on higher rank groups and general number fields, in particular new bounds towards the Ramanujan conjecture;
- a proof of Manin's conjecture for a certain class of singular algebraic varieties.
The underlying methods are closely related; for example, rational points on algebraic varieties
will be counted by a multiple L-series technique.
Summary
This is a proposal for research at the interface of analytic number theory, automorphic forms and algebraic geometry. Motivated by fundamental conjectures in number theory, classical problems will be investigated in higher order situations: general number fields, automorphic forms on higher rank groups, the arithmetic of algebraic varieties of higher degree. In particular, I want to focus on
- computation of moments of L-function of degree 3 and higher with applications to subconvexity and/or non-vanishing, as well as subconvexity for multiple L-functions;
- bounds for sup-norms of cusp forms on various spaces and equidistribution of Hecke correspondences;
- automorphic forms on higher rank groups and general number fields, in particular new bounds towards the Ramanujan conjecture;
- a proof of Manin's conjecture for a certain class of singular algebraic varieties.
The underlying methods are closely related; for example, rational points on algebraic varieties
will be counted by a multiple L-series technique.
Max ERC Funding
1 004 000 €
Duration
Start date: 2010-10-01, End date: 2015-09-30
Project acronym AQSER
Project Automorphic q-series and their application
Researcher (PI) Kathrin Bringmann
Host Institution (HI) UNIVERSITAET ZU KOELN
Call Details Starting Grant (StG), PE1, ERC-2013-StG
Summary This proposal aims to unravel mysteries at the frontier of number theory and other areas of mathematics and physics. The main focus will be to understand and exploit “modularity” of q-hypergeometric series. “Modular forms are functions on the complex plane that are inordinately symmetric.” (Mazur) The motivation comes from the wide-reaching applications of modularity in combinatorics, percolation, Lie theory, and physics (black holes).
The interplay between automorphic forms, q-series, and other areas of mathematics and physics is often two-sided. On the one hand, the other areas provide interesting examples of automorphic objects and predict their behavior. Sometimes these even motivate new classes of automorphic objects which have not been previously studied. On the other hand, knowing that certain generating functions are modular gives one access to deep theoretical tools to prove results in other areas. “Mathematics is a language, and we need that language to understand the physics of our universe.”(Ooguri) Understanding this interplay has attracted attention of researchers from a variety of areas. However, proofs of modularity of q-hypergeometric series currently fall far short of a comprehensive theory to describe the interplay between them and automorphic forms. A recent conjecture of W. Nahm relates the modularity of such series to K-theory. In this proposal I aim to fill this gap and provide a better understanding of this interplay by building a general structural framework enveloping these q-series. For this I will employ new kinds of automorphic objects and embed the functions of interest into bigger families
A successful outcome of the proposed research will open further horizons and also answer open questions, even those in other areas which were not addressed in this proposal; for example the new theory could be applied to better understand Donaldson invariants.
Summary
This proposal aims to unravel mysteries at the frontier of number theory and other areas of mathematics and physics. The main focus will be to understand and exploit “modularity” of q-hypergeometric series. “Modular forms are functions on the complex plane that are inordinately symmetric.” (Mazur) The motivation comes from the wide-reaching applications of modularity in combinatorics, percolation, Lie theory, and physics (black holes).
The interplay between automorphic forms, q-series, and other areas of mathematics and physics is often two-sided. On the one hand, the other areas provide interesting examples of automorphic objects and predict their behavior. Sometimes these even motivate new classes of automorphic objects which have not been previously studied. On the other hand, knowing that certain generating functions are modular gives one access to deep theoretical tools to prove results in other areas. “Mathematics is a language, and we need that language to understand the physics of our universe.”(Ooguri) Understanding this interplay has attracted attention of researchers from a variety of areas. However, proofs of modularity of q-hypergeometric series currently fall far short of a comprehensive theory to describe the interplay between them and automorphic forms. A recent conjecture of W. Nahm relates the modularity of such series to K-theory. In this proposal I aim to fill this gap and provide a better understanding of this interplay by building a general structural framework enveloping these q-series. For this I will employ new kinds of automorphic objects and embed the functions of interest into bigger families
A successful outcome of the proposed research will open further horizons and also answer open questions, even those in other areas which were not addressed in this proposal; for example the new theory could be applied to better understand Donaldson invariants.
Max ERC Funding
1 240 500 €
Duration
Start date: 2014-01-01, End date: 2019-04-30
Project acronym assemblyNMR
Project 3D structures of bacterial supramolecular assemblies by solid-state NMR
Researcher (PI) Adam Lange
Host Institution (HI) FORSCHUNGSVERBUND BERLIN EV
Call Details Starting Grant (StG), LS1, ERC-2013-StG
Summary Supramolecular assemblies – formed by the self-assembly of hundreds of protein subunits – are part of bacterial nanomachines involved in key cellular processes. Important examples in pathogenic bacteria are pili and type 3 secretion systems (T3SS) that mediate adhesion to host cells and injection of virulence proteins. Structure determination at atomic resolution of such assemblies by standard techniques such as X-ray crystallography or solution NMR is severely limited: Intact T3SSs or pili cannot be crystallized and are also inherently insoluble. Cryo-electron microscopy techniques have recently made it possible to obtain low- and medium-resolution models, but atomic details have not been accessible at the resolution obtained in these studies, leading sometimes to inaccurate models.
I propose to use solid-state NMR (ssNMR) to fill this knowledge-gap. I could recently show that ssNMR on in vitro preparations of Salmonella T3SS needles constitutes a powerful approach to study the structure of this virulence factor. Our integrated approach also included results from electron microscopy and modeling as well as in vivo assays (Loquet et al., Nature 2012). This is the foundation of this application. I propose to extend ssNMR methodology to tackle the structures of even larger or more complex homo-oligomeric assemblies with up to 200 residues per monomeric subunit. We will apply such techniques to address the currently unknown 3D structures of type I pili and cytoskeletal bactofilin filaments. Furthermore, I want to develop strategies to directly study assemblies in a native-like setting. As a first application, I will study the 3D structure of T3SS needles when they are complemented with intact T3SSs purified from Salmonella or Shigella. The ultimate goal of this proposal is to establish ssNMR as a generally applicable method that allows solving the currently unknown structures of bacterial supramolecular assemblies at atomic resolution.
Summary
Supramolecular assemblies – formed by the self-assembly of hundreds of protein subunits – are part of bacterial nanomachines involved in key cellular processes. Important examples in pathogenic bacteria are pili and type 3 secretion systems (T3SS) that mediate adhesion to host cells and injection of virulence proteins. Structure determination at atomic resolution of such assemblies by standard techniques such as X-ray crystallography or solution NMR is severely limited: Intact T3SSs or pili cannot be crystallized and are also inherently insoluble. Cryo-electron microscopy techniques have recently made it possible to obtain low- and medium-resolution models, but atomic details have not been accessible at the resolution obtained in these studies, leading sometimes to inaccurate models.
I propose to use solid-state NMR (ssNMR) to fill this knowledge-gap. I could recently show that ssNMR on in vitro preparations of Salmonella T3SS needles constitutes a powerful approach to study the structure of this virulence factor. Our integrated approach also included results from electron microscopy and modeling as well as in vivo assays (Loquet et al., Nature 2012). This is the foundation of this application. I propose to extend ssNMR methodology to tackle the structures of even larger or more complex homo-oligomeric assemblies with up to 200 residues per monomeric subunit. We will apply such techniques to address the currently unknown 3D structures of type I pili and cytoskeletal bactofilin filaments. Furthermore, I want to develop strategies to directly study assemblies in a native-like setting. As a first application, I will study the 3D structure of T3SS needles when they are complemented with intact T3SSs purified from Salmonella or Shigella. The ultimate goal of this proposal is to establish ssNMR as a generally applicable method that allows solving the currently unknown structures of bacterial supramolecular assemblies at atomic resolution.
Max ERC Funding
1 456 000 €
Duration
Start date: 2014-05-01, End date: 2019-04-30
Project acronym BeyondA1
Project Set theory beyond the first uncountable cardinal
Researcher (PI) Assaf Shmuel Rinot
Host Institution (HI) BAR ILAN UNIVERSITY
Call Details Starting Grant (StG), PE1, ERC-2018-STG
Summary We propose to establish a research group that will unveil the combinatorial nature of the second uncountable cardinal. This includes its Ramsey-theoretic, order-theoretic, graph-theoretic and topological features. Among others, we will be directly addressing fundamental problems due to Erdos, Rado, Galvin, and Shelah.
While some of these problems are old and well-known, an unexpected series of breakthroughs from the last three years suggest that now is a promising point in time to carry out such a project. Indeed, through a short period, four previously unattainable problems concerning the second uncountable cardinal were successfully tackled: Aspero on a club-guessing problem of Shelah, Krueger on the club-isomorphism problem for Aronszajn trees, Neeman on the isomorphism problem for dense sets of reals, and the PI on the Souslin problem. Each of these results was obtained through the development of a completely new technical framework, and these frameworks could now pave the way for the solution of some major open questions.
A goal of the highest risk in this project is the discovery of a consistent (possibly, parameterized) forcing axiom that will (preferably, simultaneously) provide structure theorems for stationary sets, linearly ordered sets, trees, graphs, and partition relations, as well as the refutation of various forms of club-guessing principles, all at the level of the second uncountable cardinal. In comparison, at the level of the first uncountable cardinal, a forcing axiom due to Foreman, Magidor and Shelah achieves exactly that.
To approach our goals, the proposed project is divided into four core areas: Uncountable trees, Ramsey theory on ordinals, Club-guessing principles, and Forcing Axioms. There is a rich bilateral interaction between any pair of the four different cores, but the proposed division will allow an efficient allocation of manpower, and will increase the chances of parallel success.
Summary
We propose to establish a research group that will unveil the combinatorial nature of the second uncountable cardinal. This includes its Ramsey-theoretic, order-theoretic, graph-theoretic and topological features. Among others, we will be directly addressing fundamental problems due to Erdos, Rado, Galvin, and Shelah.
While some of these problems are old and well-known, an unexpected series of breakthroughs from the last three years suggest that now is a promising point in time to carry out such a project. Indeed, through a short period, four previously unattainable problems concerning the second uncountable cardinal were successfully tackled: Aspero on a club-guessing problem of Shelah, Krueger on the club-isomorphism problem for Aronszajn trees, Neeman on the isomorphism problem for dense sets of reals, and the PI on the Souslin problem. Each of these results was obtained through the development of a completely new technical framework, and these frameworks could now pave the way for the solution of some major open questions.
A goal of the highest risk in this project is the discovery of a consistent (possibly, parameterized) forcing axiom that will (preferably, simultaneously) provide structure theorems for stationary sets, linearly ordered sets, trees, graphs, and partition relations, as well as the refutation of various forms of club-guessing principles, all at the level of the second uncountable cardinal. In comparison, at the level of the first uncountable cardinal, a forcing axiom due to Foreman, Magidor and Shelah achieves exactly that.
To approach our goals, the proposed project is divided into four core areas: Uncountable trees, Ramsey theory on ordinals, Club-guessing principles, and Forcing Axioms. There is a rich bilateral interaction between any pair of the four different cores, but the proposed division will allow an efficient allocation of manpower, and will increase the chances of parallel success.
Max ERC Funding
1 362 500 €
Duration
Start date: 2018-10-01, End date: 2023-09-30
Project acronym BIOSTRUCT
Project Multiscale mathematical modelling of dynamics of structure formation in cell systems
Researcher (PI) Anna Marciniak-Czochra
Host Institution (HI) RUPRECHT-KARLS-UNIVERSITAET HEIDELBERG
Call Details Starting Grant (StG), PE1, ERC-2007-StG
Summary The aim of this transdisciplinary project is to develop and analyse multiscale mathematical models of pattern formation in multicellular systems controlled by the dynamics of intracellular signalling pathways and cell-to-cell communication and to develop new mathematical methods for the modelling of such complex processes. This aim will be achieved through a close collaboration with experimental groups and comprehensive analytical investigations of the mathematical problems arising in the modelling of these biological processes. The mathematical methods and techniques to be employed will be the analysis of systems of partial differential equations, asymptotic analysis, as well as methods of dynamical systems. These techniques will be used to formulate the models and to study the spatio-temporal behaviour of solutions, especially stability and dependence on characteristic scales, geometry, initial data and key parameters. Advanced numerical methods will be applied to simulate the models. This comprehensive methodology goes beyond the state-of-the-art, since usually the analyses are limited to a single aspect of model behaviour. Groundbreaking impacts envisioned are threefold: (i) The project will contribute to the understanding of mechanisms of structure formation in the developmental process, in the context of recently discovered signalling pathways. In addition, some of the factors and mechanisms playing a role in developmental processes, such as Wnt signalling, are implicated in carcinogenesis, for instance colon and lung cancer. (ii) Accurate quantitative and predictive mathematical models of cell proliferation and differentiation are important for the control of tumour growth and tissue egeneration; (iii) Qualitative analysis of multiscale mathematical models of biological phenomena generates challenging mathematical problems and, therefore, the project will lead to the development of new mathematical theories and tools.
Summary
The aim of this transdisciplinary project is to develop and analyse multiscale mathematical models of pattern formation in multicellular systems controlled by the dynamics of intracellular signalling pathways and cell-to-cell communication and to develop new mathematical methods for the modelling of such complex processes. This aim will be achieved through a close collaboration with experimental groups and comprehensive analytical investigations of the mathematical problems arising in the modelling of these biological processes. The mathematical methods and techniques to be employed will be the analysis of systems of partial differential equations, asymptotic analysis, as well as methods of dynamical systems. These techniques will be used to formulate the models and to study the spatio-temporal behaviour of solutions, especially stability and dependence on characteristic scales, geometry, initial data and key parameters. Advanced numerical methods will be applied to simulate the models. This comprehensive methodology goes beyond the state-of-the-art, since usually the analyses are limited to a single aspect of model behaviour. Groundbreaking impacts envisioned are threefold: (i) The project will contribute to the understanding of mechanisms of structure formation in the developmental process, in the context of recently discovered signalling pathways. In addition, some of the factors and mechanisms playing a role in developmental processes, such as Wnt signalling, are implicated in carcinogenesis, for instance colon and lung cancer. (ii) Accurate quantitative and predictive mathematical models of cell proliferation and differentiation are important for the control of tumour growth and tissue egeneration; (iii) Qualitative analysis of multiscale mathematical models of biological phenomena generates challenging mathematical problems and, therefore, the project will lead to the development of new mathematical theories and tools.
Max ERC Funding
750 000 €
Duration
Start date: 2008-09-01, End date: 2013-08-31
