  Recently, Maassen et al. measured an appreciable pH difference between the
bulk solution and the solution in the lumen of virus-like particles,
self-assembled in an aqueous buffer solution containing the coat proteins of a
simple plant virus and polyanions. [Maassen, S. J.; et al. Small 2018, 14,
1802081] They attribute this to the Donnan effect, caused by an imbalance
between the number of negative charges on the encapsulated polyelectrolyte
molecules and the number of positive charges on the RNA binding domains of the
coat proteins that make up the virus shell or capsid. By applying
Poisson-Boltzmann theory, we confirm this conclusion and show that simple
Donnan theory is accurate even for the smallest of viruses and virus-like
particles. This, in part, is due to the additional screening caused by the
presence of a large number of immobile charges in the cavity of the shell. The
presence of a net charge on the outer surface of the capsid we find in practice
to not have a large effect on the pH shift. Hence, Donnan theory can indeed be
applied to connect the local pH and the amount of encapsulated material. The
large shifts up to a full pH unit that we predict must have consequences for
applications of virus capsids as nanocontainers in bionanotechnology and
artificial cell organelles.
