Nucleic Acids in Chemistry and Biology

increase in binding affinity for cationic ligands as bulk salt concentration is decreased. Hence both the melt-
ing temperature (Tm, Section 2.5.1) and the observed equilibrium association constant (Kobs) are strongly
dependent on salt concentration. When values for these thermodynamic parameters are measured, it is import-
ant to take account of the solution conditions, especially salt concentration.
In Manning’s original formulation, condensation is described by a dimensionless structural parameter 

(9.1)

where e is the electronic charge magnitude, is the bulk solution dielectric constant, k Boltzmann’s con-
stant, T the temperature in K, and b the average phosphate group spacing. If B-DNA is modelled as a cylin-
der with two negatively charged phosphates spaced 3.4 Å apart, then b1.7 Å and 4.2. The Manning
theory states that the average fraction of monovalent cation associated with each DNA phosphate as a
result of condensation (c) is defined as

(9.2)

For B-DNA c 0.76. However, as noted by Thomas Record, cations not only associate viacondensa-
tion but can also bind through Debye–Hückel interactions. This fraction of associated counterions is defined
as s. Therefore, the overall fraction of monovalent cations associated with each phosphate can be defined
as where

(9.3)

For B-DNA the value of is 0.88, i.e.the double helix retains a net charge equal to 12% of the total
number of phosphates. Record has developed a particularly useful formulation that describes the effect of
salt concentration on nucleic acid equilibria.^4 He applied Wyman’s concept of linkage to quantify salt effects
on ligand binding. The magnitude of the apparent ligand binding constant Kobsfor the interaction of a charged
ligand with DNA is found to be strongly dependent on monovalent salt concentration [MX], as embodied
in the expression

(9.4)

where Zis the charge on the ligand and SK is the slope of a plot of lnKobsversus ln[MX]. The negative
sign of Zin Equation 9.4 indicates that Kobsdecreases with increasing concentrations of MX. The magnitude
of the decrease depends on Z, the charge on the ligand. In this analysis, any possible contribution from
changes in anion binding or hydration is omitted. For a cationic ligand Lbinding to a nucleic acid site Dto
form a ligand–nucleic acid complex Cin the presence of monovalent cation M
, the thermodynamic equi-
librium can be written as

(9.5)

This equilibrium describes the release of bound counter-ions concomitant with the binding of a cationic
ligand. The equilibrium constant for the above reaction is

(9.6)

Hence for the association of a positively charged ligand with DNA in the presence of excess monovalent
cation,

K

CM

DL

Z



[][ ]


[][]

⋅

⋅

DL CZM


 []







ln

ln[ ]

K

MX

obs    ZSK


 cs[()] 12   1

c    () 1    1



e

kTb

2

ε

344 Chapter 9

http://www.ebook3000.com