Project acronym ACTMECH
Project Emergent Active Mechanical Behaviour of the Actomyosin Cell Cortex
Researcher (PI) Stephan Wolfgang Grill
Host Institution (HI) TECHNISCHE UNIVERSITAET DRESDEN
Call Details Starting Grant (StG), LS3, ERC-2011-StG_20101109
Summary The cell cortex is a highly dynamic layer of crosslinked actin filaments and myosin molecular motors beneath the cell membrane. It plays a central role in large scale rearrangements that occur inside cells. Many molecular mechanisms contribute to cortex structure and dynamics. However, cell scale physical properties of the cortex are difficult to grasp. This is problematic because for large scale rearrangements inside a cell, such as coherent flow of the cell cortex, it is the cell scale emergent properties that are important for the realization of such events. I will investigate how the actomyosin cytoskeleton behaves at a coarse grained and cellular scale, and will study how this emergent active behaviour is influenced by molecular mechanisms. We will study the cell cortex in the one cell stage C. elegans embryo, which undergoes large scale cortical flow during polarization and cytokinesis. We will combine theory and experiment. We will characterize cortex structure and dynamics with biophysical techniques such as cortical laser ablation and quantitative photobleaching experiments. We will develop and employ novel theoretical approaches to describe the cell scale mechanical behaviour in terms of an active complex fluid. We will utilize genetic approaches to understand how these emergent mechanical properties are influenced by molecular activities. A central goal is to arrive at a coarse grained description of the cortex that can predict future dynamic behaviour from the past structure, which is conceptually similar to how weather forecasting is accomplished. To date, systematic approaches to link molecular scale physical mechanisms to those on cellular scales are missing. This work will open new opportunities for cell biological and cell biophysical research, by providing a methodological approach for bridging scales, for studying emergent and large-scale active mechanical behaviours and linking them to molecular mechanisms.
Summary
The cell cortex is a highly dynamic layer of crosslinked actin filaments and myosin molecular motors beneath the cell membrane. It plays a central role in large scale rearrangements that occur inside cells. Many molecular mechanisms contribute to cortex structure and dynamics. However, cell scale physical properties of the cortex are difficult to grasp. This is problematic because for large scale rearrangements inside a cell, such as coherent flow of the cell cortex, it is the cell scale emergent properties that are important for the realization of such events. I will investigate how the actomyosin cytoskeleton behaves at a coarse grained and cellular scale, and will study how this emergent active behaviour is influenced by molecular mechanisms. We will study the cell cortex in the one cell stage C. elegans embryo, which undergoes large scale cortical flow during polarization and cytokinesis. We will combine theory and experiment. We will characterize cortex structure and dynamics with biophysical techniques such as cortical laser ablation and quantitative photobleaching experiments. We will develop and employ novel theoretical approaches to describe the cell scale mechanical behaviour in terms of an active complex fluid. We will utilize genetic approaches to understand how these emergent mechanical properties are influenced by molecular activities. A central goal is to arrive at a coarse grained description of the cortex that can predict future dynamic behaviour from the past structure, which is conceptually similar to how weather forecasting is accomplished. To date, systematic approaches to link molecular scale physical mechanisms to those on cellular scales are missing. This work will open new opportunities for cell biological and cell biophysical research, by providing a methodological approach for bridging scales, for studying emergent and large-scale active mechanical behaviours and linking them to molecular mechanisms.
Max ERC Funding
1 500 000 €
Duration
Start date: 2011-12-01, End date: 2017-08-31
Project acronym AMAREC
Project Amenability, Approximation and Reconstruction
Researcher (PI) Wilhelm WINTER
Host Institution (HI) WESTFAELISCHE WILHELMS-UNIVERSITAET MUENSTER
Call Details Advanced Grant (AdG), PE1, ERC-2018-ADG
Summary Algebras of operators on Hilbert spaces were originally introduced as the right framework for the mathematical description of quantum mechanics. In modern mathematics the scope has much broadened due to the highly versatile nature of operator algebras. They are particularly useful in the analysis of groups and their actions. Amenability is a finiteness property which occurs in many different contexts and which can be characterised in many different ways. We will analyse amenability in terms of approximation properties, in the frameworks of abstract C*-algebras, of topological dynamical systems, and of discrete groups. Such approximation properties will serve as bridging devices between these setups, and they will be used to systematically recover geometric information about the underlying structures. When passing from groups, and more generally from dynamical systems, to operator algebras, one loses information, but one gains new tools to isolate and analyse pertinent properties of the underlying structure. We will mostly be interested in the topological setting, and in the associated C*-algebras. Amenability of groups or of dynamical systems then translates into the completely positive approximation property. Systems of completely positive approximations store all the essential data about a C*-algebra, and sometimes one can arrange the systems so that one can directly read of such information. For transformation group C*-algebras, one can achieve this by using approximation properties of the underlying dynamics. To some extent one can even go back, and extract dynamical approximation properties from completely positive approximations of the C*-algebra. This interplay between approximation properties in topological dynamics and in noncommutative topology carries a surprisingly rich structure. It connects directly to the heart of the classification problem for nuclear C*-algebras on the one hand, and to central open questions on amenable dynamics on the other.
Summary
Algebras of operators on Hilbert spaces were originally introduced as the right framework for the mathematical description of quantum mechanics. In modern mathematics the scope has much broadened due to the highly versatile nature of operator algebras. They are particularly useful in the analysis of groups and their actions. Amenability is a finiteness property which occurs in many different contexts and which can be characterised in many different ways. We will analyse amenability in terms of approximation properties, in the frameworks of abstract C*-algebras, of topological dynamical systems, and of discrete groups. Such approximation properties will serve as bridging devices between these setups, and they will be used to systematically recover geometric information about the underlying structures. When passing from groups, and more generally from dynamical systems, to operator algebras, one loses information, but one gains new tools to isolate and analyse pertinent properties of the underlying structure. We will mostly be interested in the topological setting, and in the associated C*-algebras. Amenability of groups or of dynamical systems then translates into the completely positive approximation property. Systems of completely positive approximations store all the essential data about a C*-algebra, and sometimes one can arrange the systems so that one can directly read of such information. For transformation group C*-algebras, one can achieve this by using approximation properties of the underlying dynamics. To some extent one can even go back, and extract dynamical approximation properties from completely positive approximations of the C*-algebra. This interplay between approximation properties in topological dynamics and in noncommutative topology carries a surprisingly rich structure. It connects directly to the heart of the classification problem for nuclear C*-algebras on the one hand, and to central open questions on amenable dynamics on the other.
Max ERC Funding
1 596 017 €
Duration
Start date: 2019-10-01, End date: 2024-09-30
Project acronym ANAMULTISCALE
Project Analysis of Multiscale Systems Driven by Functionals
Researcher (PI) Alexander Mielke
Host Institution (HI) FORSCHUNGSVERBUND BERLIN EV
Call Details Advanced Grant (AdG), PE1, ERC-2010-AdG_20100224
Summary Many complex phenomena in the sciences are described by nonlinear partial differential equations, the solutions of which exhibit oscillations and concentration effects on multiple temporal or spatial scales. Our aim is to use methods from applied analysis to contribute to the understanding of the interplay of effects on different scales. The central question is to determine those quantities on the microscale which are needed to for the correct description of the macroscopic evolution.
We aim to develop a mathematical framework for analyzing and modeling coupled systems with multiple scales. This will include Hamiltonian dynamics as well as different types of dissipation like gradient flows or rate-independent dynamics. The choice of models will be guided by specific applications in material modeling (e.g., thermoplasticity, pattern formation, porous media) and optoelectronics (pulse interaction, Maxwell-Bloch systems, semiconductors, quantum mechanics). The research will address mathematically fundamental issues like existence and stability of solutions but will mainly be devoted to the modeling of multiscale phenomena in evolution systems. We will focus on systems with geometric structures, where the dynamics is driven by functionals. Thus, we can go much beyond the classical theory of homogenization and singular perturbations. The novel features of our approach are
- the combination of different dynamical effects in one framework,
- the use of geometric and metric structures for coupled partial differential equations,
- the exploitation of Gamma-convergence for evolution systems driven by functionals.
Summary
Many complex phenomena in the sciences are described by nonlinear partial differential equations, the solutions of which exhibit oscillations and concentration effects on multiple temporal or spatial scales. Our aim is to use methods from applied analysis to contribute to the understanding of the interplay of effects on different scales. The central question is to determine those quantities on the microscale which are needed to for the correct description of the macroscopic evolution.
We aim to develop a mathematical framework for analyzing and modeling coupled systems with multiple scales. This will include Hamiltonian dynamics as well as different types of dissipation like gradient flows or rate-independent dynamics. The choice of models will be guided by specific applications in material modeling (e.g., thermoplasticity, pattern formation, porous media) and optoelectronics (pulse interaction, Maxwell-Bloch systems, semiconductors, quantum mechanics). The research will address mathematically fundamental issues like existence and stability of solutions but will mainly be devoted to the modeling of multiscale phenomena in evolution systems. We will focus on systems with geometric structures, where the dynamics is driven by functionals. Thus, we can go much beyond the classical theory of homogenization and singular perturbations. The novel features of our approach are
- the combination of different dynamical effects in one framework,
- the use of geometric and metric structures for coupled partial differential equations,
- the exploitation of Gamma-convergence for evolution systems driven by functionals.
Max ERC Funding
1 390 000 €
Duration
Start date: 2011-04-01, End date: 2017-03-31
Project acronym AngioBone
Project Angiogenic growth, specialization, ageing and regeneration
of bone vessels
Researcher (PI) Ralf Heinrich Adams
Host Institution (HI) WESTFAELISCHE WILHELMS-UNIVERSITAET MUENSTER
Call Details Advanced Grant (AdG), LS3, ERC-2013-ADG
Summary The skeleton and the sinusoidal vasculature form a functional unit with great relevance in health, regeneration, and disease. Currently, fundamental aspects of sinusoidal vessel growth, specialization, arteriovenous organization and the consequences for tissue perfusion, or the changes occurring during ageing remain unknown. Our preliminary data indicate that key principles of bone vascularization and the role of molecular regulators are highly distinct from other organs. I therefore propose to use powerful combination of mouse genetics, fate mapping, transcriptional profiling, computational biology, confocal and two-photon microscopy, micro-CT and PET imaging, biochemistry and cell biology to characterize the growth, differentiation, dynamics, and ageing of the bone vasculature. In addition to established angiogenic pathways, the role of highly promising novel candidate regulators will be investigated in endothelial cells and perivascular osteoprogenitors with sophisticated inducible and cell type-specific genetic methods in the mouse. Complementing these powerful in vivo approaches, 3D co-cultures generated by cell printing technologies will provide insight into the communication between different cell types. The dynamics of sinusoidal vessel growth and regeneration will be monitored by two-photon imaging in the skull. Finally, I will explore the architectural, cellular and molecular changes and the role of capillary endothelial subpopulations in the sinusoidal vasculature of ageing and osteoporotic mice.
Technological advancements, such as new transgenic strains, mutant models or cell printing approaches, are important aspects of this proposal. AngioBone will provide a first conceptual framework for normal and deregulated function of the bone sinusoidal vasculature. It will also break new ground by analyzing the role of blood vessels in ageing and identifying novel strategies for tissue engineering and, potentially, the prevention/treatment of osteoporosis.
Summary
The skeleton and the sinusoidal vasculature form a functional unit with great relevance in health, regeneration, and disease. Currently, fundamental aspects of sinusoidal vessel growth, specialization, arteriovenous organization and the consequences for tissue perfusion, or the changes occurring during ageing remain unknown. Our preliminary data indicate that key principles of bone vascularization and the role of molecular regulators are highly distinct from other organs. I therefore propose to use powerful combination of mouse genetics, fate mapping, transcriptional profiling, computational biology, confocal and two-photon microscopy, micro-CT and PET imaging, biochemistry and cell biology to characterize the growth, differentiation, dynamics, and ageing of the bone vasculature. In addition to established angiogenic pathways, the role of highly promising novel candidate regulators will be investigated in endothelial cells and perivascular osteoprogenitors with sophisticated inducible and cell type-specific genetic methods in the mouse. Complementing these powerful in vivo approaches, 3D co-cultures generated by cell printing technologies will provide insight into the communication between different cell types. The dynamics of sinusoidal vessel growth and regeneration will be monitored by two-photon imaging in the skull. Finally, I will explore the architectural, cellular and molecular changes and the role of capillary endothelial subpopulations in the sinusoidal vasculature of ageing and osteoporotic mice.
Technological advancements, such as new transgenic strains, mutant models or cell printing approaches, are important aspects of this proposal. AngioBone will provide a first conceptual framework for normal and deregulated function of the bone sinusoidal vasculature. It will also break new ground by analyzing the role of blood vessels in ageing and identifying novel strategies for tissue engineering and, potentially, the prevention/treatment of osteoporosis.
Max ERC Funding
2 478 750 €
Duration
Start date: 2014-02-01, End date: 2019-01-31
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 APOQUANT
Project The quantitative Bcl-2 interactome in apoptosis: decoding how cancer cells escape death
Researcher (PI) Ana Jesús García Sáez
Host Institution (HI) EBERHARD KARLS UNIVERSITAET TUEBINGEN
Call Details Starting Grant (StG), LS3, ERC-2012-StG_20111109
Summary The proteins of the Bcl-2 family function as key regulators of apoptosis by controlling the permeabilization of the mitochondrial outer membrane. They form an intricate, fine-tuned interaction network which is altered in cancer cells to avoid cell death. Currently, we do not understand how signaling within this network, which combines events in cytosol and membranes, is orchestrated to decide the cell fate. The main goal of this proposal is to unravel how apoptosis signaling is integrated by the Bcl-2 network by determining the quantitative Bcl-2 interactome and building with it a mathematical model that identifies which interactions determine the overall outcome. To this aim, we have established a reconstituted system for the quantification of the interactions between Bcl-2 proteins not only in solution but also in membranes at the single molecule level by fluorescence correlation spectroscopy (FCS).
(1) This project aims to quantify the relative affinities between an reconstituted Bcl-2 network by FCS.
(2) This will be combined with quantitative studies in living cells, which include the signaling pathway in its entirety. To this aim, we will develop new FCS methods for mitochondria.
(3) The structural and dynamic aspects of the Bcl-2 network will be studied by super resolution and live cell microscopy.
(4) The acquired knowledge will be used to build a mathematical model that uncovers how the multiple interactions within the Bcl-2 network are integrated and identifies critical steps in apoptosis regulation.
These studies are expected to broaden the general knowledge about the design principles of cellular signaling as well as how cancer cells alter the Bcl-2 network to escape cell death. This systems analysis will allow us to predict which perturbations in the Bcl-2 network of cancer cells can switch signaling towards cell death. Ultimately it could be translated into clinical applications for anticancer therapy.
Summary
The proteins of the Bcl-2 family function as key regulators of apoptosis by controlling the permeabilization of the mitochondrial outer membrane. They form an intricate, fine-tuned interaction network which is altered in cancer cells to avoid cell death. Currently, we do not understand how signaling within this network, which combines events in cytosol and membranes, is orchestrated to decide the cell fate. The main goal of this proposal is to unravel how apoptosis signaling is integrated by the Bcl-2 network by determining the quantitative Bcl-2 interactome and building with it a mathematical model that identifies which interactions determine the overall outcome. To this aim, we have established a reconstituted system for the quantification of the interactions between Bcl-2 proteins not only in solution but also in membranes at the single molecule level by fluorescence correlation spectroscopy (FCS).
(1) This project aims to quantify the relative affinities between an reconstituted Bcl-2 network by FCS.
(2) This will be combined with quantitative studies in living cells, which include the signaling pathway in its entirety. To this aim, we will develop new FCS methods for mitochondria.
(3) The structural and dynamic aspects of the Bcl-2 network will be studied by super resolution and live cell microscopy.
(4) The acquired knowledge will be used to build a mathematical model that uncovers how the multiple interactions within the Bcl-2 network are integrated and identifies critical steps in apoptosis regulation.
These studies are expected to broaden the general knowledge about the design principles of cellular signaling as well as how cancer cells alter the Bcl-2 network to escape cell death. This systems analysis will allow us to predict which perturbations in the Bcl-2 network of cancer cells can switch signaling towards cell death. Ultimately it could be translated into clinical applications for anticancer therapy.
Max ERC Funding
1 462 900 €
Duration
Start date: 2013-04-01, End date: 2019-03-31
Project acronym APOSITE
Project Apoptotic foci: composition, structure and dynamics
Researcher (PI) Ana GARCIA SAEZ
Host Institution (HI) EBERHARD KARLS UNIVERSITAET TUEBINGEN
Call Details Consolidator Grant (CoG), LS3, ERC-2018-COG
Summary Apoptotic cell death is essential for development, immune function or tissue homeostasis, and it is often deregulated in disease. Mitochondrial outer membrane permeabilization (MOMP) is central for apoptosis execution and plays a key role in its inflammatory outcome. Knowing the architecture of the macromolecular machineries mediating MOMP is crucial for understanding their function and for the clinical use of apoptosis.
Our recent work reveals that Bax and Bak dimers form distinct line, arc and ring assemblies at specific apoptotic foci to mediate MOMP. However, the molecular structure and mechanisms controlling the spatiotemporal formation and range of action of the apoptotic foci are missing. To address this fundamental gap in our knowledge, we aim to unravel the composition, dynamics and structure of apoptotic foci and to understand how they are integrated to orchestrate function. We will reach this goal by building on our expertise in cell death and cutting-edge imaging and by developing a new analytical pipeline to:
1) Identify the composition of apoptotic foci using in situ proximity-dependent labeling and extraction of near-native Bax/Bak membrane complexes coupled to mass spectrometry.
2) Define their contribution to apoptosis and its immunogenicity and establish their assembly dynamics to correlate it with apoptosis progression by live cell imaging.
3) Determine the stoichiometry and structural organization of the apoptotic foci by combining single molecule fluorescence and advanced electron microscopies.
This multidisciplinary approach offers high chances to solve the long-standing question of how Bax and Bak mediate MOMP. APOSITE will provide textbook knowledge of the mitochondrial contribution to cell death and inflammation. The implementation of this new analytical framework will open novel research avenues in membrane and organelle biology. Ultimately, understanding of Bax and Bak structure/function will help develop apoptosis modulators for medicine.
Summary
Apoptotic cell death is essential for development, immune function or tissue homeostasis, and it is often deregulated in disease. Mitochondrial outer membrane permeabilization (MOMP) is central for apoptosis execution and plays a key role in its inflammatory outcome. Knowing the architecture of the macromolecular machineries mediating MOMP is crucial for understanding their function and for the clinical use of apoptosis.
Our recent work reveals that Bax and Bak dimers form distinct line, arc and ring assemblies at specific apoptotic foci to mediate MOMP. However, the molecular structure and mechanisms controlling the spatiotemporal formation and range of action of the apoptotic foci are missing. To address this fundamental gap in our knowledge, we aim to unravel the composition, dynamics and structure of apoptotic foci and to understand how they are integrated to orchestrate function. We will reach this goal by building on our expertise in cell death and cutting-edge imaging and by developing a new analytical pipeline to:
1) Identify the composition of apoptotic foci using in situ proximity-dependent labeling and extraction of near-native Bax/Bak membrane complexes coupled to mass spectrometry.
2) Define their contribution to apoptosis and its immunogenicity and establish their assembly dynamics to correlate it with apoptosis progression by live cell imaging.
3) Determine the stoichiometry and structural organization of the apoptotic foci by combining single molecule fluorescence and advanced electron microscopies.
This multidisciplinary approach offers high chances to solve the long-standing question of how Bax and Bak mediate MOMP. APOSITE will provide textbook knowledge of the mitochondrial contribution to cell death and inflammation. The implementation of this new analytical framework will open novel research avenues in membrane and organelle biology. Ultimately, understanding of Bax and Bak structure/function will help develop apoptosis modulators for medicine.
Max ERC Funding
2 000 000 €
Duration
Start date: 2019-04-01, End date: 2024-03-31
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 ASYMMEM
Project Lipid asymmetry: a cellular battery?
Researcher (PI) André NADLER
Host Institution (HI) MAX-PLANCK-GESELLSCHAFT ZUR FORDERUNG DER WISSENSCHAFTEN EV
Call Details Starting Grant (StG), LS3, ERC-2017-STG
Summary It is a basic textbook notion that the plasma membranes of virtually all organisms display an asymmetric lipid distribution between inner and outer leaflets far removed from thermodynamic equilibrium. As a fundamental biological principle, lipid asymmetry has been linked to numerous cellular processes. However, a clear mechanistic justification for the continued existence of lipid asymmetry throughout evolution has yet to be established. We propose here that lipid asymmetry serves as a store of potential energy that is used to fuel energy-intense membrane remodelling and signalling events for instance during membrane fusion and fission. This implies that rapid, local changes of trans-membrane lipid distribution rather than a continuously maintained out-of-equilibrium situation are crucial for cellular function. Consequently, new methods for quantifying the kinetics of lipid trans-bilayer movement are required, as traditional approaches are mostly suited for analysing quasi-steady-state conditions. Addressing this need, we will develop and employ novel photochemical lipid probes and lipid biosensors to quantify localized trans-bilayer lipid movement. We will use these tools for identifying yet unknown protein components of the lipid asymmetry regulating machinery and analyse their function with regard to membrane dynamics and signalling in cell motility. Focussing on cell motility enables targeted chemical and genetic perturbations while monitoring lipid dynamics on timescales and in membrane structures that are well suited for light microscopy. Ultimately, we aim to reconstitute lipid asymmetry as a driving force for membrane remodelling in vitro. We expect that our work will break new ground in explaining one of the least understood features of the plasma membrane and pave the way for a new, dynamic membrane model. Since the plasma membrane serves as the major signalling hub, this will have impact in almost every area of the life sciences.
Summary
It is a basic textbook notion that the plasma membranes of virtually all organisms display an asymmetric lipid distribution between inner and outer leaflets far removed from thermodynamic equilibrium. As a fundamental biological principle, lipid asymmetry has been linked to numerous cellular processes. However, a clear mechanistic justification for the continued existence of lipid asymmetry throughout evolution has yet to be established. We propose here that lipid asymmetry serves as a store of potential energy that is used to fuel energy-intense membrane remodelling and signalling events for instance during membrane fusion and fission. This implies that rapid, local changes of trans-membrane lipid distribution rather than a continuously maintained out-of-equilibrium situation are crucial for cellular function. Consequently, new methods for quantifying the kinetics of lipid trans-bilayer movement are required, as traditional approaches are mostly suited for analysing quasi-steady-state conditions. Addressing this need, we will develop and employ novel photochemical lipid probes and lipid biosensors to quantify localized trans-bilayer lipid movement. We will use these tools for identifying yet unknown protein components of the lipid asymmetry regulating machinery and analyse their function with regard to membrane dynamics and signalling in cell motility. Focussing on cell motility enables targeted chemical and genetic perturbations while monitoring lipid dynamics on timescales and in membrane structures that are well suited for light microscopy. Ultimately, we aim to reconstitute lipid asymmetry as a driving force for membrane remodelling in vitro. We expect that our work will break new ground in explaining one of the least understood features of the plasma membrane and pave the way for a new, dynamic membrane model. Since the plasma membrane serves as the major signalling hub, this will have impact in almost every area of the life sciences.
Max ERC Funding
1 500 000 €
Duration
Start date: 2018-01-01, End date: 2022-12-31
