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 DissectIFT
Project In vitro reconstitution and mechanistic dissection of Intraflagellar Transport in C.elegans sensory cilia
Researcher (PI) Zeynep Ökten
Host Institution (HI) TECHNISCHE UNIVERSITAET MUENCHEN
Call Details Starting Grant (StG), LS1, ERC-2013-StG
Summary Cilia are microtubule-based protrusions of the plasma membrane found on many eukaryotic cells, including most cell types of the human body. Whereas the functions of motile cilia were immediately obvious, the role of the immotile or so-called primary cilia remained largely unrecognized for many decades. Once referred to as aberrant solitary cilia with no obvious function, these ancient structures now hold the promise of revealing no less than the secrets of multicellularity and development. Even though the importance of primary cilia is now evident, molecular mechanisms underlying their assembly and function are far from being understood. The construction and maintenance of cilia relies on an ancient, universally conserved machinery termed IntraFlagellar Transport (IFT). IFT requires a multi-subunit, non-membranous protein complex assembled from more than 20 distinct subunits. At the heart of IFT are the microtubule-associated motors, -kinesin and dynein-, that continuously ferry cargo in a bi-directional fashion needed for ciliary assembly and function. To pave the way towards a molecular understanding of this fascinating organelle, we propose to employ a bottom-up approach in which we stepwise reconstitute the IFT complex from recombinantly expressed subunits of the so far best understood primary cilium from C.elegans. The structural integrity and stability of the IFT complex will be characterized using multifaceted approaches such as chemical crosslinking or thermophoresis. To mechanistically dissect the kinesin-dependent transport in vitro, we will make use of enzymatic bulk and single-molecule assays. Collectively, these results will provide a quantitative understanding of the assembly and kinesin-dependent motility of the IFT machinery. Given that cells mobilize ~600 components to build their cilia, this experimental platform will significantly streamline future efforts to identify novel cargoes and the effects of putative regulators of the IFT machinery.
Summary
Cilia are microtubule-based protrusions of the plasma membrane found on many eukaryotic cells, including most cell types of the human body. Whereas the functions of motile cilia were immediately obvious, the role of the immotile or so-called primary cilia remained largely unrecognized for many decades. Once referred to as aberrant solitary cilia with no obvious function, these ancient structures now hold the promise of revealing no less than the secrets of multicellularity and development. Even though the importance of primary cilia is now evident, molecular mechanisms underlying their assembly and function are far from being understood. The construction and maintenance of cilia relies on an ancient, universally conserved machinery termed IntraFlagellar Transport (IFT). IFT requires a multi-subunit, non-membranous protein complex assembled from more than 20 distinct subunits. At the heart of IFT are the microtubule-associated motors, -kinesin and dynein-, that continuously ferry cargo in a bi-directional fashion needed for ciliary assembly and function. To pave the way towards a molecular understanding of this fascinating organelle, we propose to employ a bottom-up approach in which we stepwise reconstitute the IFT complex from recombinantly expressed subunits of the so far best understood primary cilium from C.elegans. The structural integrity and stability of the IFT complex will be characterized using multifaceted approaches such as chemical crosslinking or thermophoresis. To mechanistically dissect the kinesin-dependent transport in vitro, we will make use of enzymatic bulk and single-molecule assays. Collectively, these results will provide a quantitative understanding of the assembly and kinesin-dependent motility of the IFT machinery. Given that cells mobilize ~600 components to build their cilia, this experimental platform will significantly streamline future efforts to identify novel cargoes and the effects of putative regulators of the IFT machinery.
Max ERC Funding
1 497 740 €
Duration
Start date: 2014-03-01, End date: 2019-02-28
Project acronym EVOLMAPPING
Project An integrated assessment of recent evolutionary change
through genome wide mapping of regulatory changes and signatures of selection in natural sculpin (Cottus) hybrids
Researcher (PI) Arne W. Nolte
Host Institution (HI) CARL VON OSSIETZKY UNIVERSITAET OLDENBURG
Call Details Starting Grant (StG), LS8, ERC-2013-StG
Summary It is the unprecedented access to genome wide data that highlights the potential of current evolutionary studies and this proposal aims at exploiting this progress to analyze evolutionary processes in a well-established fish system of hybrid speciation. We study natural populations of freshwater fish referred to as sculpins (Cottus). In these we have identified species that have recently (<200 years) hybridized as a result of secondary contact through man-made canals between river systems. This gave rise to a new lineage with new adaptations that have allowed it to invade habitats that were not used by the parental species before. We are thus also dealing with evolutionary change that is associated with man-made ecological perturbations, the analysis of which is particularly timely. It is now possible to perform a near exhaustive search to identify genes and to study gene expression as a measure of evolutionary change in Cottus. A combination of genetic mapping experiments and screens for genotypic selection can reveal loci and functions as targets of selection in the adaptive evolution of invasive Cottus. This proposal specifically aims at identifying genomic traits such as copy number changes of coding sequences or changes in the gene regulatory architecture that have evolved as a direct consequence of hybridization and to explore their implication in adaptive evolution. The results will contribute to our understanding of the genetics of adaptation and the invasion of a new environment. With respect to hybrid zones and the evolution of new species, we will identify candidate genes and functions that can explain barriers to reproduction in the wild. Finally, we will be able to make significant progress with respect to the genetics associated with hybrid speciation.
Summary
It is the unprecedented access to genome wide data that highlights the potential of current evolutionary studies and this proposal aims at exploiting this progress to analyze evolutionary processes in a well-established fish system of hybrid speciation. We study natural populations of freshwater fish referred to as sculpins (Cottus). In these we have identified species that have recently (<200 years) hybridized as a result of secondary contact through man-made canals between river systems. This gave rise to a new lineage with new adaptations that have allowed it to invade habitats that were not used by the parental species before. We are thus also dealing with evolutionary change that is associated with man-made ecological perturbations, the analysis of which is particularly timely. It is now possible to perform a near exhaustive search to identify genes and to study gene expression as a measure of evolutionary change in Cottus. A combination of genetic mapping experiments and screens for genotypic selection can reveal loci and functions as targets of selection in the adaptive evolution of invasive Cottus. This proposal specifically aims at identifying genomic traits such as copy number changes of coding sequences or changes in the gene regulatory architecture that have evolved as a direct consequence of hybridization and to explore their implication in adaptive evolution. The results will contribute to our understanding of the genetics of adaptation and the invasion of a new environment. With respect to hybrid zones and the evolution of new species, we will identify candidate genes and functions that can explain barriers to reproduction in the wild. Finally, we will be able to make significant progress with respect to the genetics associated with hybrid speciation.
Max ERC Funding
1 377 162 €
Duration
Start date: 2014-02-01, End date: 2019-01-31
Project acronym FUNCSPECGEN
Project What is the engine of biodiversity? Comparative and Functional Speciation Genetics in the Post-genomic Era
Researcher (PI) Jochen Brock Wacain Wolf
Host Institution (HI) LUDWIG-MAXIMILIANS-UNIVERSITAET MUENCHEN
Call Details Starting Grant (StG), LS8, ERC-2013-StG
Summary More than 150 years after the seminal works of Charles Darwin on speciation, we are beginning to unravel the genetic underpinnings of the splitting process (Ellegren H [..] JBW Wolf, Nature, in press). The genomic revolution is progressing at full speed, and for the first time in history we are equipped with the necessary tools to investigate the genomic architecture of speciation at base-pair resolution in any organisms of our choice. When integrated to the mature theoretical framework of the evolutionary sciences, this wealth of genome-scale data will produce fundamental insights into the processes governing adaptation and speciation.
Here, I identify a novel evolutionary model system - crows and ravens of the genus Corvus - and demonstrate its potential for speciation genetic and functional genomic research. Central to this system is the phylogenetically independent recurrence of a pied colour-pattern in several species that stands in contrasts to the predominant all-black plumage in the clade. Building on the idea that colour polymorphism can promote speciation through sexual selection, I choose a number of black and pied species pairs that can be positioned along a time line representing different stages of the speciation process. This comparative framework is unrivalled in its setup and is uniquely suited to study the genetics of speciation across different stages of species divergence. It also provides a promising entry point to the fascinating theme of parallel evolution.
This research program is among the first to harness the possibilities of the post-genomic era in a wild organism. Using a combination of population- and phylo-genomic approaches, single sperm sequencing, experimental work in a breeding population, systems biology approaches and in situ mRNA quantification at cellular resolution, this interdisciplinary program covers novel ground in the nascent field of functional avian genomics and pushes the boundaries of speciation genetic research.
Summary
More than 150 years after the seminal works of Charles Darwin on speciation, we are beginning to unravel the genetic underpinnings of the splitting process (Ellegren H [..] JBW Wolf, Nature, in press). The genomic revolution is progressing at full speed, and for the first time in history we are equipped with the necessary tools to investigate the genomic architecture of speciation at base-pair resolution in any organisms of our choice. When integrated to the mature theoretical framework of the evolutionary sciences, this wealth of genome-scale data will produce fundamental insights into the processes governing adaptation and speciation.
Here, I identify a novel evolutionary model system - crows and ravens of the genus Corvus - and demonstrate its potential for speciation genetic and functional genomic research. Central to this system is the phylogenetically independent recurrence of a pied colour-pattern in several species that stands in contrasts to the predominant all-black plumage in the clade. Building on the idea that colour polymorphism can promote speciation through sexual selection, I choose a number of black and pied species pairs that can be positioned along a time line representing different stages of the speciation process. This comparative framework is unrivalled in its setup and is uniquely suited to study the genetics of speciation across different stages of species divergence. It also provides a promising entry point to the fascinating theme of parallel evolution.
This research program is among the first to harness the possibilities of the post-genomic era in a wild organism. Using a combination of population- and phylo-genomic approaches, single sperm sequencing, experimental work in a breeding population, systems biology approaches and in situ mRNA quantification at cellular resolution, this interdisciplinary program covers novel ground in the nascent field of functional avian genomics and pushes the boundaries of speciation genetic research.
Max ERC Funding
1 494 300 €
Duration
Start date: 2014-04-01, End date: 2019-03-31
