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.