62 A. Gabibov et al.
Summarising these statements one can conclude that all aspects of
topoisomerase I kinetics could be described within the frame of “dumb” topoi-
somerase acting as a reversible DNA swivel with constant friction. Our calcu-
lations reproduce all experimental kinetics curves correctly even in the case
when all the kinetics constants of the equation (excludingknbandkfn)donot
depend on DNA topology.
We succeeded in a direct manner, using a non-disturbing technique to
show the absence of the intermediate topoisomers in a reaction mixture dur-
ing DNA topoisomerisation, catalysed by human topoisomerase I. Utilising an
advanced mathematical model, we demonstrated that such topoisomers could
not be detected in the mixture in the case when the reaction mechanism
corresponds to Scheme 4.1. In turn, for topoisomerase II-induced relaxation
of scDNA, significant amounts of intermediate topoisomers were registered
(Fig. 4.12). A good coincidence takes place between experimentally observed
kinetic curves and those calculated using rather simple kinetic Schemes 4.1
and 4.2. In our calculations, all kinetic constants (except two per one topoi-
somerisation step) were assumed to be independent of the DNA topology, so
only a DNA steric strain (which obeys Hook’s law) was a driving force in de-
termining a topoisomerisation direction. So no special hypothesis describing
a possible mechanism of recognition of DNA topology by topoisomerases I
and II is necessary in the case of highly supercoiled DNA in contrast to those
having near-to-equilibrium topology [32].
Fig. 4.12.The full-length kinetic curve of scDNA relaxation catalysed by topoiso-
merase II. Experimental conditions: FLD monitoring of kinetics of topoisomerisation
pTM (8μg) plasmid DNA catalysed by human topoisomerase II (4 u.) in reaction
buffer (0.05 M Tris–HCl pH 8.0, 120 mM KCl, 10 mM MgCl 2 , 0.5 mM ATP, 0.5
mM DTT, 30μgml−^1 BSA). Inset: the results of electrophoretic analysis of pTM
DNA in the probes of reaction mixtures corresponding to the kinetic curves taken
at specified moments