  The electrostatic potential profile of a spherical soft particle is derived
by solving the Poisson-Boltzmann equations on a spherical system both
numerically and analytically. The soft particle is assumed to consist of an
ion-permeable charged outer layer and a non-permeable charged core with
constant charged density. The contribution of the core to the potential profile
is calculated for different charges and dielectric constants. Our results show
that the charged core heavily influences the local potential within the soft
particle. In contrast, the potential distribution outside the particle in the
salt solution is found to be weakly dependent on the core features. These
findings are consistent with previous experiments showing the minor impact of
the core of the MS2 virus on its overall electrical properties. Our studies
also indicate that while a change in temperature from 290 K to 310 K only
slightly varies the potential, the ionic strength in the range of 1-600 mM has
a significant effect on the potential profile. Our studies would provide good
understanding for experimental research in the field of biophysics and
nanomedicine.
