Scaling Equations for a Biopolymer in Salt Solution

The effect of the simultaneous presence of monovalent and divalent cations on the thermodynamics of polyelectrolyte solutions is an incompletely solved problem. In physiological conditions, combinations of these ions affect structure formation in biopolymer systems. Dynamic light scattering measurements of the collective diffusion coefficient $D$ and the osmotic compressibility of semidilute hyaluronan solutions containing different ratios of sodium and calcium ions are compared with simple polyelectrolyte models. Scaling relationships are proposed in terms of polymer concentration and ionic strength $J$ of the added salt. Differences in the effects of sodium and calcium ions are found to be expressed only through $J$.

Figure 1

Dependence of $D$ (fast mode) upon $1/J$ in HA solutions at $25°\mathrm{C}$ for four different polymer concentrations $c_p$. Dotted line separates results from samples with and without ${\mathrm{CaCl}}_2$. Inset: Enlarged view of intensity correlation function $g^{(2)}(t)-1$ ($c_p=26.7\mathrm{m}M$, $c_s=100\mathrm{m}M$ NaCl, $\theta =120°$) showing fast (continuous curve) and slow (dashed curve) components.

Figure 2

Dependence of $D$ on $c_p/J$. Slope of straight line $3/4$. (Open circles) $50\mathrm{m}M$ NaCl; (open squares) $100\mathrm{m}M$ NaCl; (+) $100\mathrm{m}M$ NaCl and $20\mathrm{m}M$ ${\mathrm{CaCl}}_2$; (×) $100\mathrm{m}M$ NaCl and $50\mathrm{m}M$ ${\mathrm{CaCl}}_2$; (filled triangles) $100\mathrm{m}M$ NaCl and $100\mathrm{m}M$ ${\mathrm{CaCl}}_2$; (filled circles) $100\mathrm{m}M$ NaCl and $200\mathrm{m}M$ ${\mathrm{CaCl}}_2$.

Figure 3

Variation of DLS intensity $R_{\theta }$ of the collective (fast) mode with $J^{3/4}/c_p^{1/4}$. Dashed line is least squares straight line fit through data. Symbols as in Fig. 2.

Figure 4

The product $D{R}_{\theta }/c_p=K{k}_{B}T/f$. In this plot, the least squares fit of Fig. 3 is linearized to $R_{\theta }=1.20\times {10}^{-5}{J}^{3/4}/c_p^{1/4}{\mathrm{cm}}^{-1}$. Lines are guides for the eye. Inset: Same data as a function of $c_p/J^{1/4}$. Symbols as in Fig. 2.