Persistence length of short homopolymeric single-stranded DNA sequences in polyvalent cations

Abstract

We used simulations of short single stranded DNA (ssDNA) homopolymers, based on the sequence dependent Three Interaction Site (TIS) model, to calculate the persistence length ($l_p$) in polyvalent cations. The TIS model accounts for stacking interactions and electrostatic interactions are treated using the Coulomb potential. We find that $l_p$ for $\mathrm{dT_{30}}$ (T is thymine) and $\mathrm{dA_{30}}$ (A is adenine) is quantitatively fit using $l_p = l_p^0 + \lambda \kappa^{-1}$ ($l_p^0$ is the bare persistence length, $\lambda$ is a dimensionless constant, and $\kappa$ is the inverse Debye length) in the divalent cations $\mathrm{Mg^{2+}}$ and $\mathrm{Ca^{2+}}$. The dependence of $l_p$ on $\kappa$ is surprising because it was derived for long flexible polyelectrolytes in which the charges interact via the Debye-H\"{u}ckel potential. The $l_p^0$ values are 0.4 nm and 1.1 nm for polyT and polyA, respectively. Strikingly, $l_p$ is almost independent of the tetravalent spermine concentration. There is no clear theoretical explanation although simulations suggest that the number of spermine molecules that bind to the ssDNA saturates at a small value. A qualitative picture, based on the restrictions of access to the phosphate groups due to volume exclusion of the anisotropic structure of $\mathrm{Spm^{4+}}$, rationalizes the simulation results. The predicted dependence of $l_p$ in spermine awaits experimental test.