On the influence of bending energy on the assembly of spherical viral capsids

The protective shell, or capsid, of many spherical viruses is formed via a self-assembly process whose underlying physical principles have not yet been fully elucidated. In this article, we analyze the role of elastic bending energy in the in vitro self-assembly of a spherical capsid in the limit where such energetic contribution dominates over compression stress. The model predicts that the capsid closes prematurely, and its final size is completely determined by a dimensionless constant fr, which is the ratio of the bending modulus to the line tension of the edge. In addition, we compute the critical size, the nucleation barrier, and the assembly rate of capsids and compare our results with those previously obtained by the original classical nucleation theory of viral capsids, where the elastic energy was neglected. Our model suggests that the competition between line tension and bending energy accelerates the rate of capsid nuclei production and causes capsids to close at suboptimal sizes, suggesting that capsomers have optimal bending angles that differ from the values measured in native viruses.