COMPARISON OF HARD-CYLINDER AND SCREENED COULOMB INTERACTIONS IN THE MODELING OF SUPERCOILED DNAS

A 1000 base pair (bp) model supercoiled DNA is simulated using spheric al screened Coulomb, interactions between subunits on one hand and equ ivalent hard-cylinder interactions on the other. The amplitudes, or ef fective charges, of the spherical screened Coulomb electrostatic poten tials are chosen so that the electrostatic potential surrounding the m iddle of a linear array of 2001 subunits (31.8 Angstrom diameter) clos ely matches the solution of the nonlinear Poisson-Boltzmann equation f or a cylinder with 12 Angstrom radius and the full linear charge densi ty of DNA at all distances beyond the 24 Angstrom hard-core diameter. This superposition of spherical screened Coulomb potentials is practic ally identical to the particular solution of the cylindrical linearize d Poisson-Boltzmann equation that matches the solution of the nonlinea r Poisson-Boltzmann equation at large distances. The interaction energ y between subunits is reckoned from the effective charges according to the standard DLVO expression. The equivalent hard-cylinder diameter i s chosen following Stigter's protocol for matching second virial coeff icients, but for the full linear charge density of DNA. The electrosta tic persistence length of the model with screened Coulomb interactions is extremely sensitive to the (arbitrarily) chosen subunit length at the higher salt concentrations. The persistence length of the hard-cyl inder model is adjusted to match that of the screened Coulomb model fo r each ionic condition. Simulations for a superhelix density sigma = 0 .05 using a spherical screened Coulomb interaction plus a 24 Angstrom hard-cylinder core (SCPHC) potential indicate that the radius of gyrat ion of this 1000 bp DNA actually undergoes a slight increase as the Na Cl concentration is raised from 0.01 to 1.0M. Thus, merely softening t he potential from hard-cylinder to screened Coulomb form does not prod uce a large decrease in radius of gyration with increasing NaCl concen tration for DNAs of this size. Radii of gyration, static structure fac tors, and diffusion coefficients obtained using the equivalent hard-cy linder (EHC) potential agree well with those obtained using the SCPHC potential in 1.0M NaCl, but in 0.1M NaCl the agreement is not as good, and in 0.01M NaCl the agreement is definitely unsatisfactory. These c onclusions differ in significant respects from those obtained in previ ous studies. (C) 1997 John Wiley & Sons, Inc.