Project acronym MATHFOR
Project Formalization of Constructive Mathematics
Researcher (PI) Thierry Coquand
Host Institution (HI) GOETEBORGS UNIVERSITET
Call Details Advanced Grant (AdG), PE6, ERC-2009-AdG
Summary The general theme is to explore the connections between reasoning and computations in mathematics. There are two main research directions. The first research direction is a refomulation of Hilbert's program, using ideas from formal, or pointfree topology. We have shown, with multiple examples, that this allows a partial realization of this program in commutative algebra, and a new way to formulate constructive mathematics. The second research direction explores the computational content using type theory and the Curry-Howard correspondence between proofs and programs. Type theory allows us to represent constructive mathematics in a formal way, and provides key insight for the design of proof systems helping in the analysis of the logical structure of mathematical proofs. The interest of this program is well illustrated by the recent work of G. Gonthier on the formalization of the 4 color theorem.
Summary
The general theme is to explore the connections between reasoning and computations in mathematics. There are two main research directions. The first research direction is a refomulation of Hilbert's program, using ideas from formal, or pointfree topology. We have shown, with multiple examples, that this allows a partial realization of this program in commutative algebra, and a new way to formulate constructive mathematics. The second research direction explores the computational content using type theory and the Curry-Howard correspondence between proofs and programs. Type theory allows us to represent constructive mathematics in a formal way, and provides key insight for the design of proof systems helping in the analysis of the logical structure of mathematical proofs. The interest of this program is well illustrated by the recent work of G. Gonthier on the formalization of the 4 color theorem.
Max ERC Funding
1 912 288 €
Duration
Start date: 2010-04-01, End date: 2015-03-31
Project acronym UBIQUITIN BALANCE
Project The balance of ubiquitin conjugation and deconjugation
Researcher (PI) Titia Karen Sixma
Host Institution (HI) STICHTING HET NEDERLANDS KANKER INSTITUUT-ANTONI VAN LEEUWENHOEK ZIEKENHUIS
Call Details Advanced Grant (AdG), LS1, ERC-2009-AdG
Summary Ubiquitin conjugation is one of the most important signaling systems in the eukaryotic cell. Different types of mono- and polyubiquitin chains determine the fate of target proteins by redirecting them for degradation, relocalization or interaction with new partners. The type of ubiquitin modification on any target is determined by the interplay between the conjugating E2/E3 complexes on the one hand and deubiquitinating enzymes on the other. In practice, it is the balance between conjugating and deconjugating systems that determines the result of the various ubiquitination signals. For three different regulatory systems that are critical for correct genome maintenance, we are now in a position to study not just the individual process of conjugation or deconjugation in isolation, but rather, reconstitute the entire reaction on a defined physiological target. These three target systems, histone H2A, PCNA and P53, can be mono-ubiquitinated by a defined E3-ligase, poly-ubiquitinated by a second ligase and deconjugated by defined deubiquitinating enzymes in a reaction that is affected by known allosteric modulators. Our unique collection of tools to study these systems in vitro allows reconstitution of the full reaction, to trap intermediates, and to study their interaction from atomic detail to kinetic reactivity. Using X-ray crystallography of critical intermediates and kinetic analysis of individual reactions by FRET and surface plasmon resonance, we can address how the mono-, poly and deubiquitinating reactions affect each other. By answering mechanistic questions on the relative effect of the forward and backward reaction components and their modulators we will provide a solid basis for drug design studies that target these pathways against cancer development.
Summary
Ubiquitin conjugation is one of the most important signaling systems in the eukaryotic cell. Different types of mono- and polyubiquitin chains determine the fate of target proteins by redirecting them for degradation, relocalization or interaction with new partners. The type of ubiquitin modification on any target is determined by the interplay between the conjugating E2/E3 complexes on the one hand and deubiquitinating enzymes on the other. In practice, it is the balance between conjugating and deconjugating systems that determines the result of the various ubiquitination signals. For three different regulatory systems that are critical for correct genome maintenance, we are now in a position to study not just the individual process of conjugation or deconjugation in isolation, but rather, reconstitute the entire reaction on a defined physiological target. These three target systems, histone H2A, PCNA and P53, can be mono-ubiquitinated by a defined E3-ligase, poly-ubiquitinated by a second ligase and deconjugated by defined deubiquitinating enzymes in a reaction that is affected by known allosteric modulators. Our unique collection of tools to study these systems in vitro allows reconstitution of the full reaction, to trap intermediates, and to study their interaction from atomic detail to kinetic reactivity. Using X-ray crystallography of critical intermediates and kinetic analysis of individual reactions by FRET and surface plasmon resonance, we can address how the mono-, poly and deubiquitinating reactions affect each other. By answering mechanistic questions on the relative effect of the forward and backward reaction components and their modulators we will provide a solid basis for drug design studies that target these pathways against cancer development.
Max ERC Funding
2 299 720 €
Duration
Start date: 2010-02-01, End date: 2015-01-31
