4 Dynamics of DNA Supercoiling 51However a full set of the constants regarding human topoisomerases is not
available. In this connection, as regarding the values of kinetic constant
derived from (4.1) the following assumption have been made:
- Since in the given reaction the driving force of the topoisomerisation
depends on the tension of DNA that is proportional to the square of
DNA density of superhelix [6], the dependence of the constants of topoi-
somerisation∼knandknover the density of the superturns looks as:
kn=krexp((Bn+0.5)/RT), (4.14)
∼k
n=krexp((−Bn+0.5)/RT). (4.15)- It is clear thatkr=∼k(0)=k(0), i.e. thatkris the topoisomerisation
rate constant of the covalent complex of the fully relaxed DNA with a
topoisomerase. In accordance with the preceding evaluations,krvalue is
rather high, so when calculated some of thekrvalues ranging between 3
and 60 s−^1 were applied. - The cleavage and ligation rate constants were taken as equal to 0.1 and
1 min−^1 , respectively. These values were estimated for the vaccine virus
topoisomerase using shot oligonucleotide substrates. Taking into account
the low rigidity of DNA, it seems to be plausible that those constants
reveal independence of the DNA topology [26]. - The value of the association rate constantkass,wasequalto1,000 s−^1 ,
which had to be higher thankdiss,k 1 ,kc 1. - The value of the dissociation rate constant was taken either as independent
of the topological state of DNA or it grew along with the increase of|σ|.
For modelling a reaction of topoisomerase II running in accordance with a
“cleavage-changing linking number by 2-ligation” the following kinetic scheme
was proposed:
Scheme 4.2