Effects of long-range interactions on curvature energies of viral shells

We formulate a theory of the effects of long-range interactions on the surface tension and spontaneous curvature of proteinaceous shells based on the general Deryaguin-Landau-Verwey-Overbeek mesoscale approach to colloid stability. We derive the full renormalization formulas for the elastic properties of the shell and consider in detail the renormalization of the spontaneous curvature as a function of the corresponding Hamaker coefficient, inner and outer capsid charges, and bathing solution properties. The renormalized spontaneous curvature is found to be a nonmonotonic function of several parameters describing the system.

Figure 1

Dependence of the dimensional scaling functions $\tilde{\sigma }$, Eq. (34), the surface charge ratio, $r={\sigma }_1/{\sigma }_2$, and different values of the inverse screening length, $\kappa$. The renormalized surface tension is always positive and tends to 0 for large screening but shows nonmonotonic dependence on the charge asymmetry ratio.

Figure 2

Dependence of the dimensional scaling function, $1/{\tilde{R}}_0$, Eq. (35), on the surface charge ratio, $r={\sigma }_1/{\sigma }_2$, and different values of the inverse screening length, $\kappa$. The renormalized curvature is in general a nonmonotonic function of $r$ and $\kappa$ and can be of either sign, depending on the charge asymmetry parameter and the amount of screening in the system.