  We investigate the effects of the relative dielectric coefficient on ionic
flows in open ion channels, using mathematical analysis of reasonably general
Poisson-Nernst-Planck type models that can include the finite sizes of ions.
The value of the relative dielectric coefficient is of course a crucial
parameter for ionic behavior in general. Using the powerful theory of
singularly perturbed problems in applied mathematics, we show that some
properties of open channels are quite insensitive to variation in the relative
dielectric coefficient, thereby explaining such effects seen unexpectedly in
simulations. The ratio between the total number of one ion species and that of
another ion species, and the ratio between the flux of one ion species and that
of another ion species do not depend significantly on the relative dielectric
coefficient.
