Manning free counterion fraction for a rodlike polyion: Aqueous solutions of short DNA fragments in presence of very low added salt

We quantified the Manning free (uncondensed) counterions fraction $\theta$ for dilute aqueous solutions of rodlike polyions: 150 bp DNA fragments, in the presence of a very low concentration of monovalent salt $c_{\mathrm{salt}}<0.05$ mM. Conductivity measurements of these solutions for DNA base pair concentration range $0.015⩽c⩽8$ mM were complemented by fluorescence correlation spectroscopy (FCS) measurements of the DNA polyion diffusion coefficient $D_p(c)$. We observed a crossover in the normalized conductivity $\sigma (c)/c$ that nearly halved across the $c=0.05$–1 mM range, while $D_p(c)$ remained rather constant, as we established by FCS. Analyzing these data we extracted $\theta (c)=0.30$–0.45, and taking the Manning asymmetry field effect on polyelectrolyte conductivity into account we got $\theta (c)=0.40$–0.60. We relate the $\theta (c)$ variation to gradual DNA denaturation occurring, in the very low salt environment, with the decrease in DNA concentration itself. The extremes of the experimental $\theta (c)$ range occur toward the highest, above 1 mM, and the lowest, below 0.05 mM, DNA concentrations and correspond to the theoretical $\theta$ values for dsDNA and ssDNA, respectively. Therefore, we confirmed Manning condensation and conductivity models to be valuable in description of dilute solutions of rodlike polyions.

Figure 1

Conductometry data for DNA146 solutions before (black circles) and after denaturation at 97 ${}^{°}$C (open circles). (a) DNA146 solution conductivity versus DNA base pair (monomer) concentration. (b) Conductivity normalized by concentration versus DNA base pair (monomer) concentration. The dotted line shows the average value for denatured samples, 180 $\mu$S cm${}^{-1}/$mM. The values for untreated samples at the lowest concentrations also approach this value. Shaded rectangle denotes the crossover concentration region. Measurements were performed at 25 ${}^{°}$C.

Figure 2

Diffusion coefficient $D_{146}^{\text{exp}}(c)$ for DNA146 polyion, obtained by fluorescence correlation spectroscopy (FCS) is shown versus DNA base pair (monomer) concentration $c$. Shaded rectangle denotes the crossover concentration region identified from conductivity measurements. Black triangle denotes diffusion coefficient $D^{\mathrm{ss}}$ derived for 146 bp ssDNA.

Figure 3

Free counterion fraction $\theta$ for 146 bp nucleosomal DNA (DNA146) in pure water versus the DNA base pair (monomer) concentration $c$. Squares denote $\theta (c)$ calculated according to Eq. (19). Diamonds denote ${\theta }^{\text{'}}(c)$, the results of a calculation where the assymetry field effect was taken into account, Eq. (23). Dashed lines denote the theoretical value of $\theta =0.24$ for dsDNA and $\theta =0.59$ for ssDNA, as labeled. Shaded rectangle denotes the crossover concentration region identified from conductivity measurements.