DISSERTATION

______________________________________________________________________ Introduction
1.2.1 DNA in solution
DNA is a highly charged polymer with charge density equal to two elementary charges per base
pair. Therefore, in solution DNA interacts strongly with surrounding ions that counterbalance
its charge. These ions can be grouped into different zones 31 . In the region closest to the DNA
there are so called site-bound or inner-sphere ions that share water molecules with the DNA. In
the following zone are outer-sphere ions (territorial ions) that keep their inner hydration layer
and are free to move along the DNA molecule but are kept close to it due to the electrostatic
field. And in the last zone are free ions that form an ionic cloud around the DNA 3 .
The two most known approaches employed to investigate the extent of DNA-ion interaction are
the Manning-Oosawa (MO) counterion condensation theory 32 and the Poisson-Boltzmann (PB)
equation. MO theory addresses the DNA charge compensation by focusing on the counterions
that form a so-called condensed layer around the DNA (outer-sphere ions) in order to reduce
the charge density below a certain critical value 33 . According to the theory, counterion
accumulation at the DNA surface forming a condensed layer occurs under the condition that
the charge density parameter η is > 1:
η = zl B
b
(1.4)
where z is the valence of counterions, lB is the Bjerrum length and b is the charge separation.
The Bjerrum length represents the distance between charges at which their electrostatic
interaction energy equals the thermal energy and is defined as:
l B =
e 2
4πεε 0 kT
(1.5)
where e is the elementary charge, ε is the dielectric constant of the solvent, ε0 is the vacuum
permeability and kT is thermal energy scale. This means that the counterion condensation (for
monovalent ions) occurs when the charge separation b is smaller than the Bjerrum length, which
is true for both ss- and dsDNA. Namely, lB = 0.71 nm in aqueous solutions, while the charge
separation is 0.43 nm in ssDNA and 0.34 nm in dsDNA 31 . According to the theory, condensed
counterions are still assumed to be mobile 34 .
1.2 DNA 9