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病毒衣壳的弹性理论与形状转变

Elasticity theory and shape transitions of viral shells.

作者信息

Nguyen T T, Bruinsma Robijn F, Gelbart William M

机构信息

Department of Physics and Astronomy, University of California at Los Angeles, Los Angeles, California 90049, USA.

出版信息

Phys Rev E Stat Nonlin Soft Matter Phys. 2005 Nov;72(5 Pt 1):051923. doi: 10.1103/PhysRevE.72.051923. Epub 2005 Nov 21.

Abstract

Recently, continuum elasticity theory has been applied to explain the shape transition of icosahedral viral capsids--single-protein-thick crystalline shells--from spherical to "buckled" or faceted as their radius increases through a critical value determined by the competition between stretching and bending energies of a closed two-dimensional (2D) elastic network. In the present work we generalize this approach to capsids with nonicosahedral symmetries, e.g., spherocylindrical and conical shells. One key additional physical ingredient is the role played by nonzero spontaneous curvature. Another is associated with the special way in which the energy of the 12 topologically required fivefold sites depends on the "background" local curvature of the shell in which they are embedded. Systematic evaluation of these contributions leads to a shape "phase" diagram in which transitions are observed from icosahedral to spherocylindrical capsids as a function of the ratio of stretching to bending energies and of the spontaneous curvature of the 2D protein network. We find that the transition from icosahedral to spherocylindrical symmetry is continuous or weakly first order near the onset of buckling, leading to extensive shape degeneracy. These results are discussed in the context of experimentally observed variations in the shapes of a variety of viral capsids.

摘要

最近,连续介质弹性理论已被用于解释二十面体病毒衣壳(单蛋白厚度的晶体壳)的形状转变,即随着半径通过由封闭二维(2D)弹性网络的拉伸和弯曲能量之间的竞争所确定的临界值增加,其形状从球形转变为“弯曲”或多面体形。在本工作中,我们将这种方法推广到具有非二十面体对称性的衣壳,例如球柱形和圆锥形壳。一个关键的额外物理因素是非零自发曲率所起的作用。另一个因素与12个拓扑上必需的五重位点的能量依赖于它们所嵌入的壳的“背景”局部曲率的特殊方式有关。对这些贡献的系统评估导致了一个形状“相”图,其中观察到从二十面体衣壳到球柱形衣壳的转变是拉伸能量与弯曲能量之比以及二维蛋白质网络自发曲率的函数。我们发现,从二十面体到球柱形对称性的转变在屈曲开始附近是连续的或弱一级的,导致广泛的形状简并。这些结果在各种病毒衣壳形状的实验观察变化的背景下进行了讨论。

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