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Manning free counterions fraction for a rod-like polyion - short DNA fragments in very low salt

We quantified the Manning free (uncondensed) counterions fraction $θ$ for dilute solutions of rod-like polyions - 150bp DNA fragments, in very low salt $<0.05$mM. Conductivity measurements of aqueous DNA solutions in the concentration range $0.015\leq c \leq 8$~mM (bp) 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 $σ(c)/c$ which nearly halved across $c=0.05-1$ mM range, while $D_p(c)$ remained rather constant, as we established by FCS. Analyzing these data we extracted $θ(c)=0.30 - 0.45$, and taking the Manning asymmetry field effect on polyelectrolyte conductivity into account we got $θ(c)=0.40-0.60$. We relate the $θ(c)$ variation to gradual DNA denaturation occuring, in the very low salt environment, with the decrease in DNA concentration itself. The extremes of the experimental $θ(c)$ range occur towards the highest, above 1 mM and the lowest, below 0.05 mM, DNA concentrations, and correspond to the theoretical $θ$ values for dsDNA and ssDNA, respectively. Therefore, we confirmed Manning condensation and conductivity models to be valuable in description of dilute solutions of rod-like polyions.