Chemistry Reference
In-Depth Information
one form to another (10
− 7
- 10
− 5
s).
34
Thus for modelling of DNA structural changes
stimulated by interactions with various transition metal ions it is necessary to esti-
mate the correlation between the energy of interaction and the lifetime of the
complexes formed.
2.2 Interactions of Metal Ions with DNA
2.2.1 Thermodynamic Adsorption Model of Complex Formation
The catalytic characteristics of DNA are closely related to structural changes caused
by interactions with different species, particularly with metal ions. Evidently, transi-
tion metal ions can locally infl uence the structure of DNA only when the lifetimes
of the complexes are commensurable with the specifi c times of inner mobility in
DNA (oscillation of small groups of atoms, untwisting of the double helix, opening
of the individual base pairs, untwisting of helix binding of proteins and cell division).
The movements last from 10
− 10
s to hundreds of seconds and longer. We have
managed to fi nd a correlation between dynamics and stability
28
by applying
Frenkel's phenomenological thermodynamic approach,
35- 37
which was used as early
as 1924 for the study of gas adsorption on the surface of solids. Frenkel introduced
a new term ' lifetime ' ( t) for the adsorption state and connected it to the energy
of interaction |
∆
E| between adsorbate and adsorbent surface by the following
expression:
(
)
τ=⋅
as
−
exp
∆
EkT
(2.1)
0
B
where
τ
0
a−
is the time of a single oscillation of the adsorbate on the surface, assumed
to be 10
− 13
- 10
− 12
s and
k
B
is the Boltzmann constant.
36
The above model can, with good approximation, be applied to the study of
interactions between small molecular species and biomacromolecules in solution.
Using the relationship D
G
=
−
RT
ln
K
, a simplifi ed expression of (2.1) can be
derived:
τ=
0
K
(2.2)
where t is the lifetime of a metal ion-macromolecule complex. Now we must clarify
the value t
0
for solutions. Frenkel' s
τ
0
a−
is the duration of the fl uctuation excitation
of adsorbing atoms or molecules interacting with a solid surface. It is supposed to
be equal to the period of oscillation of the adsorbate relative to the adsorbent
surface. In solutions, t
0
describes the duration of relaxation of rotary and translation
movements of the solvent molecules, ions, solvated ions or low-molecular-weight
substances and lies between 10
− 11
and 10
− 10
s. Thus, if we assume a p
K
in the range
4-6 for binding of DNA with two-fold positively charged metal ions of the fi rst
transition series, and t
0
= 10
− 11
s, then the life span of these complexes is in the range
10
− 7
- 10
− 5
s .
