Breakage of double-stranded DNA due to single-stranded nicking

Enzymes such as pancreatic deoxyribonuclease (DNase I) nick the single strands of double-stranded DNA. Two nicks sufficiently close on opposite strands will lead to breakage of the DNA molecule. This paper gives a mathematical model for the breakage of circular, supercoiled DNA under the action of an enzyme which nicks at random sites (or at preferred sites, these being in abundance and randomly positioned around the circle). After the first nick the DNA loses its supercoiled structure; after many nicks it breaks to become topologically linear; further nicks lead to fragmentation of this linear form. Formulae are given for the proportions of DNA molecules in each of the four classes: supercoiled; nicked but still circular; linear; fragmented. Formulae are also presented for the case when there is, in addition to nicking, simultaneous action of an endonuclease which produces direct double-stranded breaks in the DNA. Finally, a general theory is given for the case where a third type of enzyme, topoisomerase I, is operative, with all three DNA modifications taking place simultaneously.