  An exact, analytic solution for a simple electrostatic model applicable to
biomolecular recognition is presented. In the model, a layer of high dielectric
constant material (representative of the solvent, water) whose thickness may
vary separates two regions of low dielectric constant material (representative
of proteins, DNA, RNA, or similar materials), in each of which is embedded a
point charge. For identical charges, the presence of the screening layer always
lowers the energy compared to the case of point charges in an infinite medium
of low dielectric constant. Somewhat surprisingly, the presence of a
sufficiently thick screening layer also lowers the energy compared to the case
of point charges in an infinite medium of high dielectric constant. For charges
of opposite sign, the screening layer always lowers the energy compared to the
case of point charges in an infinite medium of either high or low dielectric
constant. The behavior of the energy leads to a substantially increased
repulsive force between charges of the same sign. The repulsive force between
charges of opposite signs is weaker than in an infinite medium of low
dielectric constant material but stronger than in an infinite medium of high
dielectric constant material. The presence of this behavior, which we name
asymmetric screening, in the simple system presented here confirms the
generality of the behavior that was established in a more complicated system of
an arbitrary number of charged dielectric spheres in an infinite solvent.
