Motion of a Cylindrical Dielectric Boundary
Mr. Michael White
Department of Mathematics and Center for Theoretical Biological Physics
UC San Diego
The interplay between geometry and electrostatics contributes significantly
to hydrophobic interactions of biomolecules in an aqueous solution.
With an implicit solvent, such a system can be described macroscopically by
the dielectric boundary that separates the high-dielectric solvent
from low-dielectric solutes. This work concerns the motion of a model cylindrical
dielectric boundary as the steepest descent of a free-energy functional that consists
of both the surface and electrostatic energies.
The effective dielectric boundary force is defined and an explicit formula of the force
is obtained. It is found that such a force always points from the solvent region
to solute region. In the case that the interior of a cylinder is of a lower dielectric,
the motion of the dielectric boundary is driven initially by the surface force
but is then driven inward quickly to the cylindrical axis by both the surface and
electrostatic forces. In the case that the interior of a cylinder is of a higher dielectric,
the competition between the geometrical and electrostatic contributions
leads to the existence of equilibrium boundaries that are circular cylinders.
Linear stability analysis is presented to show that such an equilibrium is only
stable for a perturbation with a wavenumber larger than a critical value.
Numerical simulations are reported for both of the cases, confirming
the analysis on the role of each component of the driving force.
Implications of the mathematical findings to the understanding of charged
molecular systems are discussed.
This is joint work with Li-Tien Cheng, Bo Li, and Shenggao Zhou.