강연자: Maria Carme Calderer (University of Minnesota, USA)
제목: Free boundary problems in viral research
일시 : 2021년 10월 14일 19:00~20:00
Zoom ID: 815 1485 9393
연락처: 박진해 교수
초록(abstract):
Problems of packaging, organization and condensation of DNA, RNA, semiflexible polymers and actin-type biological networks, either in confined domains, capsids, or in free solution, present many challenges in analysis, numerical simulation and data science.
With a toolbox consisting of continuum mechanics, partial differential equations, dynamical systems and their numerical methods, what new tools do we need to acquire to study problems in biology? Molecular Dynamics (MD) and Monte Carlo (MC) methods have been ubiquitous tools in many aspects of biological modeling: what can we add to it with our tools? Can we solve any open problems? In this talk, we will present mathematical models and their analysis to study the structure of confined viral DNA. We will first focus on mechanically based problems that fall into the context of calculus of variations, and relevant free boundary settings. From biological point of view, this problems are connected with the ability of a virus to infect (bacteria, in our analysis), otherwise becoming non-viable. A key ingredient in our approach relies on the earlier discovery that confined DNA arranges itself as an hexagonal chromonic liquid crystal. The analysis relies on the study of the vector (or tensor) field associated with the confined DNA and its integrability into a line, the center curve of the DNA, with a possibly complex topological structure.
We will also explore the clustering of DNA and that of chromonic liquid crystals into toroidal structures. This occurs in DNA in free solution but in the presence of condensing agents (osmolites). We show how the anisotropy of the surface tension yields energy minimizers with edges and corners, in full agreement with experimental observations.
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