We study a simple DNA helix model, consisting of two infinite chains of evenly spaced charges to represent the phosphate groups, wound in a helix which lies on an imaginary cylindrical surface. The change in the free energy per helix charge between coiled and uncoiled conformations of the helix in solution is studied as a function of the charge per unit length along the helix axis. This allows us to study the effects of the solution on the helix stability and coiling. The change in the free energy is calculated from Soumpasis's pair potential of mean force, applied to all pairs of helix charges [D. M. Soumpasis, Proc. Natl. Acad. Sci. U.S.A. 81, 5116 (1984)]. The local counterion concentration is calculated from the counterion radial distribution that results from solving the Poisson-Boltzmann equation for an infinite uniformly charged cylinder [R. M. Fuoss, A. Katchalsky, and S. Lifson, Proc. Natl. Acad. Sci. 37, 579 (1951)], whose linear charge density is equal to the charge per unit length along the helix axis. Our results show that the helix is less stable on decreasing bulk dielectric constant and more stable on increasing counterion radius. Experimental data are discussed on DNA in solutions with water, ethanol, and methanol as the solvent. \textcopyright{} 1996 The American Physical Society.
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