Effects of dielectric inhomogeneity on electrostatic twist rigidity of a helical biomolecule in Debye-Hückel regime.

The electrostatic interactions play a crucial role in biological systems. Here we consider an impermeable dielectric molecule in the solvent with a different dielectric constant. The electrostatic free energy in the problem is studied in the Debye-Hückel regime using the analytical Green function that is calculated in the paper. Using this electrostatic free energy, we study the electrostatic contribution to the twist rigidity of a double stranded helical molecule such as a DNA and an actin filament. The dependence of the electrostatic twist rigidity of the molecule to the dielectric inhomogeneity, structural parameters, and the salt concentration is studied. It is shown that, depending on the parameters, the electrostatic twist rigidity could be positive or negative.