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From tiling theory to biological fibers (H/F)

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General information

Reference : UMR5127-LAUVUI-001
Workplace : LE BOURGET DU LAC
Date of publication : Wednesday, July 24, 2019
Scientific Responsible name : Laurent Vuillon
Type of Contract : PhD Student contract / Thesis offer
Contract Period : 36 months
Start date of the thesis : 1 October 2019
Proportion of work : Full time
Remuneration : 2 135,00 € gross monthly

Description of the thesis topic

The project investigates the relationships between the geometrical constraints and the dynamics of a system. The case study is the transition, induced by an amino acid mutation, of a protein oligomer to a protein fiber, transition, associated with many diseases (e.g. Alzheimer, type II diabetes, Parkinson, etc.). To model the fiber, the project is divided in three steps, each associated with a scale relevant to the problem. First, the amino acids and interactions affected by the mutation are identified using a network at the local scale of amino acids. These residues constitute the new interface required for the fiber. Second, the interactions between proteins within the interface domain in the fiber are modeled using a network at the scale of the interface. Finally, the last scale is the fiber whose construction is modeled using a tiling model. The combination of both network and tiling models allows reconciling all experimental data on fiber formation because tiling takes into account a scale uncovers by networks.

The PhD student will investigate the construction of biological fibers in general and validate the 3 scale procedure on many real biological fibers. Thus we are looking for a student trained in mathematics and in particular in network topology, statistical learning and tiling theory. The student will consider for example the p53 case whose oligomer has special symmetry, the ure2p, which combines disordered and structured domains and the synuclein, which is a disordered protein. In the two last cases, the network approach will be limited and the student will have to use information on the fiber properties gathered by the analysis of the fiber database combined with experimental data on the fiber to investigate the scale 3 as a first step. Thus the network approach will come after the global fiber scale, and it will be based more on experimental data of amino acid contacts and basic geometrical constraints from 2D and 3D interactions in proteins. The sequences of the proteins will be investigated in terms of first neighbors to try to design a network of interactions that respond to some mathematical invariant properties based on our database of amino acid neighborhoods. This will be a challenging task but will completely generalize the procedure to any case.

Work Context

The LAMA is a mathematics laboratory located in Bourget-du-Lac near Chambéry. It has about thirty permanent staff (researchers and teacher-researchers) in the fields of pure mathematics, applied mathematics and mathematics for computer science. The host team will be the LIMD team (Logic Informatics and Discrete Mathematics).
The doctoral student will also work at the IXXI of the ENS-Lyon and at the Ampère laboratory in Lyon with Claire Lesieur for the biological part.

Additional Information

The PhD thesis is supported by the CNRS project “80 Prime” and the MITI (Mission pour les initiatives transverses et interdisciplinaires) for the 80th year anniversary of the CNRS. The aim of the GeoFiber project is to make scientific researches at the interface between two CNRS institutes : the first one in mathematics and interactions (INSMI) and the second in engineering sciences and systems (INSIS). In particular, the main goal consists to understand the structures of biological fibers with protein building blocks. The PhD student, Laurent Vuillon professor at the LAMA (INSMI) and Claire Lesieur CNRS researcher at Ampère (IXXI, INSIS) will propose new mathematical models for biological fiber structures based on group theory, tiling theory, and network topological invariants. These models allow to study the impact of amino acid mutations on the geometrical transitions of polymers in order to tackle aging related diseases like Alzheimer, Parkinson and some cancers. The project will focus on three scales: the interface areas are deduced from the first scale analysis, and confirmed by the design of an interface network from the second scale analysis. According to the location of the interface in the oligomer and the structural properties (e.g. symmetry) of the oligomer, the third scale analysis yields a tiling model of the fiber. The final goal of the thesis will consist to apply the mathematical model of fiber construction to real biological fibers and to predict which conformations lead to oligomers and which conformations give birth to fibers and to pathological 3D structures.

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