报告题目 (Title)：Mathematical Description of DNA Configuration in Bacteriophage Capsids （噬菌体衣壳的DNA构型的数学描述）
报告人 (Speaker)： Liu Pei（Florida Institute of Technology）
报告时间 (Time)：2022年10月12日(周三) 8:30
报告地点 (Place)：腾讯会议（ID：371-6810-3428 无密码）
邀请人(Inviter)：段成华
主办部门：理学院数学系
报告摘要：
Bacteriophages densely pack their long dsDNA genome inside a protein capsid. The conformation of the viral genome inside the capsid is consistent with a hexagonal liquid crystalline structure. Experiments have confirmed that the details of the hexagonal packing depend on the electrochemistry of the capsid and its environment.
In this talk, I will introduce how we develop a mathematical model and analyze the model to study the equilibrium configurations of ds-DNA in a viral capsid. In our approach, the DNA is described by a unit helical vector field, tangent to an associated center curve, passing through properly selected locations. We postulate an expression for the energy of the encapsulated DNA based on that of columnar chromonic liquid crystals. A thorough analysis of the Euler-Lagrange equations yields multiple solutions to the corresponding boundary value problems. We demonstrate that there is a trivial, non-helical solution, together with two other solutions with nonzero helicity of the opposite sign. Using bifurcation analysis, we derive the conditions for local stability of such solutions and determine when the preferred coiling state is helical. The relevant bifurcation parameters are the ratio of the twist versus the bend moduli of DNA and the ratio between the sizes of the ordered and the disordered regions.
I will also introduce a computational approach that quantifies the relationship between DNA configurations inside bacteriophage capsids and the types and concentrations of ions present in a biological system. The numerical results show good agreement with existing experiments and molecular dynamics simulations.
