Appendix IV
123
APPENDIX IV
Record equation for the analysis of equilibrium constant dependence on salt concentration
The interaction between a positively charged dye and the polynucleotide backbone is a reaction that does occur between charged partners, being the polymer negatively charged due to the presence of the phosphate groups on the outer part of the helix. Therefore, upon dye interaction with the polynucleotide, some of the positive counter-ions situated in the vicinity of the polynucleotide are removed from its first coordination sphere.
At a first sight it might seem obvious that, for instance, a +1 positively charged dye intercalating into DNA will expulse one Na+ counter-ion. Nevertheless, the complexity of such macromolecular systems, make charge balance not so easy to quantify. Therefore, the equilibrium constant dependence on salt concentration can give interesting information on ion shielding and de-shielding effects.
If S(Na+)m indicates a DNA site with its counter-ions, D the dye, DS the DNA/dye complex and m the amount of charge borne by the mNa+ ions displaced, the complexation reaction might be written as
S(Na+)m + D ' DS + mNa+ (IV.1)
whose equilibrium constant K’ is
(IV.2) that is
K’= K[Na+]m (IV.3)
where K is the equilibrium constant obtained by the analysis described into Appendices II and III.
The logarithm form of (IV.3) is
logK’ = logK + m log[Na+] (IV.4)
that is
][D]
) [S(Na
] [DS][Na K'
m m +
+
=
Record equation
124
logK= logK’ – m log[Na+] (IV.5)
This equation was first derived by Record (1978) on the basis of a theory that assimilates polynucleotides in solution to negatively charged cylinders, surrounded by a positive counter-ions atmosphere.
The intercept of the plot yields logK’, defined as the binding constant in the absence of electrostatic effects. The slope, m, corresponds to m’ψ, where m’ is the number of counter ions displaced by one dye molecule and ψ is the extent of DNA charge shielded by counter-ions. The value of ψ is made by a shielding contribution (ψs) and by a contribution from ion condensation (ψc). Being for DNA ψ ≅ ψc, it turns out that m’ψ represents the number of condensed sodium ion displaced by one dye molecule. Moreover, the value of ψ for DNA being equal to 0.88 (Schelhorn, 1992), it follows that m’ ≅ m.
