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