DNA supercoiling occurs when the DNA double helix is over- or under-wound, known as positive and negative supercoiling respectively. The degree of supercoiling is numerically expressed using the linking number which accounts for twists and writhes in the DNA helix. Topoisomerases are enzymes that relieve torsional strain in supercoiled DNA by introducing nicks in one or both strands, allowing the strands to pass through one another and change the linking number.

1. Supercoiling of DNA
1. Topology
A. Right handed supercoiling = negative supercoiling
(underwinding)
B. Left handed supercoiling = positive supercoiling
C. Relaxed state is with no bends
D. DNA must be constrained: plasmid DNA or by
proteins
E. Unraveling the DNA at one position changes the
superhelicity -
F. Topology only defined for continuous deformation
- no strand breakage

3. Supercoiling of DNA
1. Topology
A. Right handed supercoiling = negative supercoiling
(underwinding)
B. Left handed supercoiling = positive supercoiling
C. Relaxed state is with no bends
D. DNA must be constrained: plasmid DNA or by
proteins
E. Unraveling the DNA at one position changes the
superhelicity -
F. Topology only defined for continuous deformation
- no strand breakage

5. Supercoiling of DNA
2. Numerical expression for degree of supercoiling
A. Equation Lk=Tw+Wr
B. L:linking number, # of times that one DNA
strand winds about the others strands, is always an
integer
C. T: twist,# of revolutions about the duplex helix
D. W: writhe, # of turns of the duplex axis about
the superhelical axis
by definition the measure of the degree of
supercoiling
E. specific linking difference or superhelical
density=∆Lk/Lk0

8. Supercoiling of DNA
2. Numerical expression for degree of supercoiling
A. Equation Lk=Tw+Wr
B. L:linking number, # of times that one DNA
strand winds about the others strands, is always an
integer
C. T: twist,# of revolutions about the duplex helix
D. W: writhe, # of turns of the duplex axis about
the superhelical axis
by definition the measure of the degree of
supercoiling
E. specific linking difference or superhelical
density=∆Lk/Lk0

11. Supercoiling of DNA
2. Numerical expression for degree of supercoiling
A. Equation Lk=Tw+Wr
B. L:linking number, # of times that one DNA
strand winds about the others strands, is always an
integer
C. T: twist,# of revolutions about the duplex helix
D. W: writhe, # of turns of the duplex axis about
the superhelical axis
by definition the measure of the degree of
supercoiling
E. specific linking difference or superhelical
density=∆Lk/Lk0

15. Supercoiling of DNA
1. Topology
A. Right handed supercoiling = negative supercoiling
(underwinding)
B. Left handed supercoiling = positive supercoiling
C. Relaxed state is with no bends
D. DNA must be constrained: plasmid DNA or by
proteins
E. Unraveling the DNA at one position changes the
superhelicity -
F. Topology only defined for continuous deformation
- no strand breakage

19. Supercoiling of DNA
3. DNA compaction requires special form
of supercoiling
A. Interwound: supercoiling of DNA
in solution
B. Toroidal- tight left handed turns,
packing of DNA
both forms are interconvertible

21. Supercoiling of DNA
4. Methods for measuring supercoiling -
based on how compact the DNA is
A. Gel electrophoresis
i. 1 dimensional
ii. 2 dimensional
B. Density sedimentation

24. Supercoiling of DNA
4. Topoisomerases are required to relieve
torsional strain
A. Topoisomerases I :
breaks only one strand
B. Topoisomerase II :
breaks both strands

27. Supercoiling of DNA
4. Topoisomerases are required to relieve torsional
strain
A. Topoisomerases I - breaks only one strand
i. monomeric protein
ii. after nicking DNA the 5'-PO4 is covalently linked to
enzyme (prokaryotes)
or the 3' end is linked to the enzyme (eukaryotes)
iii. evidence is the formation of catenates
iv. E. coli Topo I relaxes negatively supercoiled DNA
v. introduces a change of increments of 1 in writhe

28. Supercoiling of DNA
4. Topoisomerases are required to relieve torsional
strain
B. Topoisomerase II - breaks both strands
i. supercoils DNA at the expense of ATP
hydrolysis
ii. two subunits: (alpha)2 and (beta)2
iii. becomes covalently linked to the alpha subunit
iv. relaxes both negative and positively
supercoiled DNA
v. introduces a change in increments of 2 in
writhe.