Helical organization of DNA-like liquid crystal filaments in cylindrical viral capsids
Helical organization of DNA-like liquid crystal filaments in cylindrical viral capsids
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DOI：
10.1098/rspa.2022.0047
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发表时间：
2022-10
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影响因子：
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通讯作者：
Pei-Yuan Liu;J. Arsuaga;M. Calderer;D. Golovaty;M. Vázquez;Shawn Walker
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作者：
Pei-Yuan Liu;J. Arsuaga;M. Calderer;D. Golovaty;M. Vázquez;Shawn Walker
我们研究圆柱形病毒衣壳中双链 DNA 的平衡构型。衣壳化 DNA 的状态由一个无序的内核组成，该内核被紧邻衣壳壁的有序外部区域包围。 DNA 构型由单位螺旋矢量场描述，该矢量场与相关中心曲线相切，穿过适当选择的位置。我们基于柱状有色液晶的能量表达式假设了封装 DNA 的能量表达式。对欧拉-拉格朗日方程的彻底分析产生了多个解。我们证明存在一个平凡的非螺旋解，以及两个具有相反符号的非零螺旋度的解。通过分叉分析，我们推导出局部稳定性的条件，并确定何时首选卷绕状态为螺旋。分叉参数是 DNA 的扭曲与弯曲模量的比率以及有序区域和无序区域的大小之间的比率。
We study equilibrium configurations of double-stranded DNA in a cylindrical viral capsid. The state of the encapsidated DNA consists of a disordered inner core enclosed by an ordered outer region, next to the capsid wall. The DNA configuration is described by a unit helical vector field, tangent to an associated centre 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. We demonstrate that there is a trivial, non-helical solution, together with two solutions with non-zero helicity of opposite sign. Using bifurcation analysis, we derive the conditions for local stability and determine when the preferred coiling state is helical. The 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.