END EFFECTS IN ELECTROSTATIC POTENTIALS OF CYLINDERS - MODELS FOR DNA FRAGMENTS

Gauss-Seidel and conjugate gradient methods are used to solve the Poisson-Boltzmann equation around finite rod models for DNA in the (monovalent) salt concentration range 0.001-0.1 mol/L. Cylindrical and a combination of cylindrical and spherical coordinate systems are used in discretizing the space around the model polyions, Electrostatic potentials at the center of long chains extrapolate to the correct infinite chain values to within about 0.1%. The effects of the chain ends on the electrostatic potential are examined. At the surface of the rod (used to model DNA) ''end effects'' in the electrostatic potential persist about 5 base pairs into the interior of the chain. At greater distances from the surface, however, the ''end effects'' are longer ranged. How these end effects depend on the modeling of the chain ends and the difference in dielectric constant inside and outside the rod is also examined.