58 A. Gabibov et al.
form. Experiments with the native enzyme demonstrated that topoisomerase
I more actively forms covalent complexes with scDNA, and more frequency
produces camptothecin-induced nicks in scDNA as compared to the relaxed
one [27]. These facts are considered to be sufficient proof for the suggestion
that the dissociation constant of the topoisomerase I – scDNA complex is
significantly lower than of the topoisomerase I-relaxed DNA one, and that
catalytic activity of this enzyme is greater when DNA is highly supercoiled.
This conclusion was also supported by structural data. According to
X-ray diffraction data, the contact region between the human topoisomerase
I molecule and its DNA substrate is as long as one helix turn [29].
Precise calculations of the topoisomerase I – DNA contact region using
Voronoi polyhedra approach using TOPOS [30] program package reveal 20
dense contact sites between protein molecule and DNA. As seen from Fig. 4.9a,
b, these contact sites span more than 30 ̊Angstrom region on both strands of
DNA helix. Therefore, the hypothesis that the enzyme could be sensitive to
the tiny conformational changes affected by topological strain in DNA could
not be ruled out.
At first glance, our kinetic data contradict the facts listed above. To resolve
the contradiction, we made a series of calculations of the topoisomerase I
reaction under the condition when the values of the dissociation constants of
non-covalent enzyme substrate complex were dependent on the DNA topology
state. Since the dissociation rate is fast and, probably diffusion limited, in the
calculationskasswas assumed to be topologically independent and equal to
1 ,000 min−^1 .Thekndissdecreased gradually when|σ|increases, so forσ=0. 05
thekdissvalue was 10, 100, and 1,000 times lower than for the relaxed one.
Calculations made with above-mentioned sets of constants gave identical
results. No difference in kinetic curve shapes was observed. Actually, it means
that the process of dissociation of a topoisomerase I – highly scDNA complex
had no effect on the pattern observed. The possible explanation of this state-
ment may be presented. Topoisomerisation ofEsnintoEsn−^1 and ligation
(EsnESn) are processes in parallel. The driving force of topoisomerisation is a
tension energy of scDNA and the values of−knandknconstants obey (4.13)
and (4.14) in a broad range ofnvalues, but the ligation rate slightly depends
only on DNA topology. So, for scDNA,kn k 1 , but for the relaxed one–the
situation is quite opposite. Competition of topoisomerisation and ligation re-
sults in relaxing of the covalent enzyme–substrate complex till the degree of
DNA superhelicity drops to the level close to the equilibrium. During this, the
relaxing catalyst is covalently bound to DNA and is not able to dissociate. On
the contrary, topoisomerase I bound to relaxed DNA exists predominantly as
a non-covalent complex capable of dissociation.
In other words, there are two principally distinct mechanisms involved in
the conversion of the enzyme-substrate complex, which differed in the case of
scDNA and in the case of the relaxed one. For scDNA, the Briggs–Haldane
mechanism works and the enzyme–substrate dissociation constant value is