Du 17 au 19 septembre 2015
IRMA
La 96ème rencontre entre mathématiciens et physiciens théoriciens aura pour thème : Géométrie et biophysique
The 96th Encounter between Mathematicians and Theoretical Physicists will take place at Institut de Recherche Mathématique Avancée (University of Strasbourg and CNRS) on September 17-19, 2015. The theme will be : Geometry and biophysics
Organizers : Bob Penner (Caltech), Athanase Papadopoulos (Strasbourg) and Joanna Sulkowska (Chemistry Department, Warsaw University)
The invited speakers include :
- De Witt Sumners (Forida State Univ.)
- Ebbe Sloth Andersen (Aarhus)
- Joergen Andersen (Aarhus)
- Hiroyuki Fuji (Kagawa Univ.)
- Sigeo Ihara (Tokyo)
- Hervé Isambert (Paris)
- Masahide Manabe (Warsaw)
- Nadya Morozova (CNRS/IHES)
- Jose Onuchic (Rice Univ.)
- Renzo Ricca (Milan)
- Piotr Sulkowski (Warsaw and Caltech)
- Michael Waterman (USC)
The talks will be in english. Some of the talks will be survey talks intended for a general audience.
Graduate students and young mathematicians are welcome. Registration is required (and free of charge) at this link. Hotel booking can be asked for through the registration link.
For practical matters and other questions please contact the organizers:
- Bob Penner : rpenner@caltech.edu
- Joanna Sulkowska : jsulkowska@chem.uw.edu.pl
- Athanase Papadopoulos : athanase.papadopoulos@math.unistra.fr
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Jeudi 17 septembre 2015
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09:30
De Witt Sumners, Florida State U.
Reconnection in Biology and Physics
Reconnection is a fundamental event in many areas of science, including interaction of fluid vortices and flux tubes in fluid mechanics and magnetohydronamics, and site-specific recombination in DNA. This talk will discuss the similarities between reconnection events in biology and physics, and the relationship between iterated reconnection and curve topology. The helicity of a flux tube is a measure of knotting and linking of field lines in the tube, and the absolute value of the helicity is a lower bound for the energy. A theorem of Moffatt and Ricca computes the helicity (a lower bound for energy) of a flux tube in terms of the writhe of the tube centerline and the twist of a ribbon determined by the centerline and one of the other field lines in the tube. We discuss the computation of writhe, and show that the writhe is conserved in an antiparallel reconnection event. Hence, for a pair of interacting tubes of equal flux, if the twist of the reconnected tube is the sum of twists of the individual tubes, then helicity is conserved in a reconnection event. So, any deviation from helicity conservation is entirely due to twist inserted or deleted at the reconnection site.
This is joint work with Christian Laing and Renzo Ricca. -
10:30
Pause Café
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11:00
Ebbe Sloth Andersen, Aarhus
Principles of biomolecular design
A major goal of nanotechnology is to be able to rationally design and assemble advanced shapes and devices at the nanoscale. One approach to achieve this goal is to "learn from nature" and use biomolecules as a programmable and self-assembling building material. The rational design of biomolecular structure requires a detailed understanding of how the residue sequence of a biopolymer defines the self-assembly of its final three-dimensional structure. Despite the difficulty of this "folding problem" scientists have had initial successes in rationally designing and folding complicated molecular shapes using both DNA, RNA and protein [1,2,3]. In this talk I will review the current progress in biomolecular nanotechnology and describe the current design principles that allow for the successful creation of well-defined biomolecular shapes and devices. With examples from my own research on designing RNA nanostructures [2] I will focus on the considerations of geometry, topology and kinetics that are required for designing RNA structures that fold during synthesis. In this context I will introduce new graph theoretical approaches for biomolecular folding, a new geometry-topology analysis method that allows mapping of the folding process, and new sequence design methods that might allow larger RNA nanostructures to be realized. At last I will discuss how the employed theoretical-experimental design cycle will allow us to investigate and understand the folding process in more detail. -
14:00
Piotr Sulkowski, University of Warsaw & Caltech
Topology and entanglement in biomolecules
I will review some (quasi-)topological features of biomolecules discovered in recent years, such as identification of new motifs in proteins (knots, slipknots, and lassoes), and genus classification of RNA chains. The common feature of all these structures is some kind of entanglement, which can be characterized by means of certain tools from topology. However, these tools often turn out to be insufficient to characterize uniquely biological complexity (e.g. standard tools from knot theory are not quite adequate to characterize knots in proteins, which form open chains). I will present some ideas how to characterize entanglement in those structures, and illustrate them in various examples. -
15:00
Pause Café
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15:30
Masahide Manabe, Univ. Warsaw
Towards topological recursion for chord diagrams
In 2012, by Andersen, Chekhov, Penner, Reidys, and Sułkowski, a matrix model whose free energy enumerates the number of oriented chord diagrams and RNA secondary structures was introduced, and studied by the formalism of the topological recursion. In this talk, I will discuss the beta-deformation of the matrix model whose free energy enumerates not only oriented chord diagrams but also non-orientable chord diagrams. This is based on some joint works with Andersen, Fuji, Łach, and Sułkowski. -
16:30
Hiroyuki Fuji, Kagawa University
Enumerating chord diagrams via matrix models
In this talk, I will discuss about the enumerative problem of the chord diagrams by making use of matrix model techniques. In prior interdisciplinary works of biology and mathematics, the topological stratification of the secondary structure of the RNA is studied in terms of the chord diagrams. For this purpose, some efficient algorithms to enumerate the number of chord diagrams will be necessary to understand the statistical property of the RNA data in PDBs. As an approach to such problem, we will adopt some matrix model techniques that have been developed in the research of mathematical physics for the last decades. In this talk, I shall use a matrix model with an external field, and see the calculability of the number of chord diagrams with marked points. -
19:30
Dinner At The Restaurant "petit Bois Vert" Everybody Is Invited
(quartier petite France)
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Vendredi 18 septembre 2015
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09:30
Renzo Ricca, Univ. Milano-Bicocca
Geometric daemons in topological dynamics
Curious geometric features play sometimes an important rôle in aspects of filament dynamics, relevant for biological systems. By identifying the physical filament with a reference ribbon (given by a framed curve), we analyze the mechanism of multiple folding produced by continuous writhing and coiling of the ribbon in space. We show that only a small amount of twisting (hence of torsional energy) is sufficient to generate any arbitrarily large degree of folding, and this can produce by a continuous deformation through inflexional states, where torsion becomes singular, but torsional energy remains continuous and finite.
If the filament bounds some material surface, and the filament is continuously deformed from a planar loop to a folded coil, the surface undergoes a topological transition from two-sided to one-sided. This phenomenon has been investigated analytically and experimentally by studying the soap film transition that occurs, that can be described in terms of a local twisted fold of the material surface through a cusp catastrophe.
If the filament is knotted, the topology can be described by polynomial invariants that characterize knots and links. By referring to our recent derivation of the HOMFLYPT polynomial for classical filaments, we show how to interpret the associated skein relations in terms of physical writhe and twist. By considering topological transitions determined by anti-parallel filament strands recombination, we offer an interpretation of the unlinking process observed for DNA knots in terms of minimal pathway associated with the skein reduction process for the natural decay of topologically complex filament systems. -
10:30
Pause Café
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11:00
Michael Waterman, USC (Los Angeles)
Sequence Alignment: Algorithms and Statistics
The production of DNA and protein sequences has motivated mathematical methods for their analysis. This talk covers some simple dynamic programming techniques for sequence alignment. The large biological databases have motivated heuristics for more efficient search (alignment) methods. The statistical distribution of alignment scores is a rich subject with some outstanding unsolved problems. -
14:00
Nadya Morozova, CNRS and IHES
Geometry of Morphogenesis
The main goal of this work is to find an adequate mathematical formalism for the description of pattern formation in the course of development of living organisms (morphogenesis), which might enable to discover the main laws underlying the translation of molecular information in cells into the geometrical information in a developing and differentiating embryo.
I will discuss a set of theoretical concepts proposed for the enlightenment of key principals/laws of pattern formation and next the suggested approaches for their mathematical formalization. The constructed working models of Planaria regeneration based on the simplified versions of formalization of theoretical concepts will be presented. -
15:00
Pause Café
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Samedi 19 septembre 2015
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09:00
Joergen Ellegaard Andersen, Aarhus
H-bond rotations in proteins and H-bond networks
First we will review our joint work with Bob Penner, Ebbe Andersen, Jens Ledet Jensen and the rest of the Aarhus team concerning rotations for H-bonds in proteins. We will then discuss our latest results joint with Jens Ledet Jensen and Rasmus Villemoes regarding relations between H-bond rotations and the local networks the H-bonds form. -
10:00
Pause Café
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10:30
Sigeo Ihara, The University of Tokyo
Annulus diagram of SO(3) rotation of protein modules
A major challenge in working with structural biology is to elucidate the implications hidden in the three-dimensional atomic configurations of a given structure. Using data in Protein Data Bank, the SO(3) rotation of the peptide unit in protein backbone structure introduced by Penner et al. is mapped onto the annulus. With combining the distribution of water molecules and compounds, the annulus diagram provides a comprehensive picture of the three-dimensional structure. We found that it is useful in protein engineering. It is also useful in revealing a previously unrecognized role of the water molecules. (Collaboration with Y. Ohta, H. Kodama, A. Sugiyama, M. Matsuoka, H. Doi, T. Tsuboi, J.E. Andersen, R.C. Penner.) -
11:30
Hervé Isambert, CNRS
Robust Reconstruction of Causal Networks from Large Scale Genomic Data