DISSERTATION

______________________________________________________________________ Introduction
Accumulation of counterions occurs to a certain extent, until the charge density parameter
decreases to 1, that is, until b increases to lB. The remaining effective charge of DNA is reduced
by a factor r:
r = 1 − 1 zη
(1.6)
Thus, it is predicted that the charge of DNA in a solution with monovalent counterions is
reduced by 76 % 31 . An important condition of the MO theory is that condensation occurs only
if the relation κ -1 >> a is satisfied (where κ -1 is the Debye length and a is the polymer radius),
which means either for highly diluted solutions or an infinitely thin DNA strand. Furthermore,
the theory is valid only for vanishingly small DNA concentrations.
For finite DNA concentrations a more complicated model needs to be used that is based on
solving of the PB equation. The PB equation describes the Gouy-Chapman (GC) model, where
a charged solid comes into contact with an ionic solution creating a double layer. Due to the
thermal motion of ions the counterion layer is a diffuse layer. The remaining charge around the
DNA molecules (ions in the third zone) is described by a linearized form of the PB equation –
the Debye-Hückel equation 35 that explains the relationship between the electrostatic behavior
of DNA and the ionic strength. In the equation the screening of DNA is quantified by the Debye
length κ -1 :
κ 2 = 8πl B N A I (1.7)
κ 2 = 2e2 N A I
εε 0 kT
(1.8)
where NA is the Avogadro number (6.022 × 10 23 1/mol) and I is the ionic strength.
The first quantitative experimental studies about conformational properties of DNA as a
function of salt concentration were done by Harrington 36 , who measured the DNA radius of
gyration in dilute DNA solutions. The DNA radius of gyration (Rg) depends on the DNA
persistence length (lp):
R g = √ Ll p
3
(1.9)
1.2 DNA 10