Spontaneous curvature as a regulator of the size of virus capsids

We investigate the physical reasons underlying the high monodispersity of empty virus capsids assembled in thermodynamical equilibrium in conditions of favorable pH and ionic strength. We propose that the high fidelity of the assembly results from the effective spontaneous curvature of the viral protein assemblies and the corresponding bending rigidity that penalizes curvatures which are larger and smaller from the spontaneous one. On the example of hepatitis B virus, which has been thoroughly studied experimentally in the context of interest to us, we estimate the magnitude of bending rigidity that is needed to suppress the appearance of aberrant capsid structures (approximately 60k(B)T). Our approach also demonstrates that the aberrant capsids that can be classified within the Caspar-Klug framework are in most circumstances likely to be smaller from the regular ones, in agreement with the experimental findings.