Dielectric relaxation of DNA aqueous solutions

Abstract

We report on a detailed characterization of complex dielectric response of Na-DNA aqueous solutions by means of low-frequency dielectric spectroscopy $(40\phantom{\rule{0.3em}{0ex}}\mathrm{Hz}--110\phantom{\rule{0.3em}{0ex}}\mathrm{MHz})$. Results reveal two broad relaxation modes of strength $20<\ensuremath{\Delta}{\ensuremath{\epsilon}}_{\mathrm{LF}}<100$ and $5<\ensuremath{\Delta}{\ensuremath{\epsilon}}_{\mathrm{HF}}<20$, centered at $0.5\phantom{\rule{0.3em}{0ex}}\mathrm{kHz}<{\ensuremath{\nu}}_{\mathrm{LF}}<70\phantom{\rule{0.3em}{0ex}}\mathrm{kHz}$ and $0.1\phantom{\rule{0.3em}{0ex}}\mathrm{MHz}<{\ensuremath{\nu}}_{\mathrm{HF}}<15\phantom{\rule{0.3em}{0ex}}\mathrm{MHz}$. The characteristic length scale of the low-frequency (LF) process, $50<{L}_{\mathrm{LF}}<750\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$, scales with DNA concentration as ${c}_{\mathrm{DNA}}^{\ensuremath{-}0.29\ifmmode\pm\else\textpm\fi{}0.04}$ and is independent of the ionic strength in the low added salt regime. Conversely, the measured length scale of the LF process does not vary with DNA concentration but depends on the ionic strength of the added salt as ${I}_{s}^{\ensuremath{-}1}$ in the high added salt regime. On the other hand, the characteristic length scale of the high-frequency (HF) process, $3<{L}_{\mathrm{HF}}<50\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$, varies with DNA concentration as ${c}_{\mathrm{DNA}}^{\ensuremath{-}0.5}$ for intermediate and large DNA concentrations. At low DNA concentrations and in the low added salt limit the characteristic length scale of the HF process scales as ${c}_{\mathrm{DNA}}^{\ensuremath{-}0.33}$. We put these results in perspective regarding the integrity of the double stranded form of DNA at low salt conditions as well as regarding the role of different types of counterions in different regimes of dielectric dispersion. We argue that the free DNA counterions are primarily active in the HF relaxation, while the condensed counterions play a role only in the LF relaxation. We also suggest theoretical interpretations for all these length scales in the whole regime of DNA and salt concentrations and discuss their ramifications and limitations.