- Problems[[Student version, January 17, 2003]] 349
-202468apparent change in excess turns,^05101520∆Mnumber of excess turns, -MFigure 9.13:(Experimental data.) Evidence for the B–Z transition in a 40 base pair tract inserted into a closed
circular loop of DNA (the plasmid pBR322). Each dot represents a particular topoisomer of DNA; the topoisomers
were separated in a procedure called two-dimensional gel electrophoresis. In the horizontal direction, each dot is
placed according to the topoisomer’s number of excess turns (the linking number), relative to the most relaxed form.
All dots shown correspond to negative excess linking number (tending to unwind the DNA duplex). Placement in
the vertical direction reflects the apparent change of excess linking number after a change in the environment has
allowed the B–Z transition to take place. [Data from Howell et al., 1996.]
Normally DNA is a right-handed helix, making one complete right-handed turn every 10.5
basepairs. This normal conformation is called B-DNA. Suppose we overtwist our DNA; that is, we
apply torsional stress tending to make the double helix tighter (one turn everyJbasepairs, where
J< 10 .5). Remarkably, it then turns out that the relation between torsional stress and excess
linking number really does have the simple linear form in Equation 9.46, even though the DNA
responds in a complicated way to the stress. (For example, the DNA can bend into a “supercoiled”
shape such as a figure-8.) The torsional spring constantktdepends on the length of the loop: A
typical value iskt=56kBTr/N,whereNis the number of basepairs in the loop.
When weundertwist DNA, however, something more spectacular can happen. Instead of re-
sponding to the stress by supercoiling, a tract of the DNA loop can pop into a totally different
conformation, aleft-handed helix! This new conformation is called Z-DNA. No atoms are added
or removed in this switch; no chemical bonds are broken. Z-DNA makes a left-handed turn every
Kbasepairs, whereKis a number you will find in a moment. Popping into the Z-form costs free
energy, but it also partially relaxes the torsional stress on the rest of the molecule. That is, totally
disrupting the duplex structure in a localized region allows a lot of the excess linking number to
go there, instead of being distributed throughout the rest of the molecule as torsional strain (small
deformations to the B-form helix).
Certain basepair sequences are especially susceptible to pop into the Z state. Figure 9.13 shows
some data taken for a loop of total lengthN=4300 basepairs. The sequence was chosen so that
atract of length 40 basepairs was able to pop into the Z state when the torsional stress exceeded
some threshold.
Each point of the graph represents a distinct topoisomer of the 4300 basepair loop, with the
absolute value ofMon the horizontal axis. Only negative values ofM(“negative supercoiling”)
are shown. Beyond a critical number of turns, suddenly the 40-basepair tract pops into the Z
conformation. As described above, this transition lets the rest of the molecule relax; it then behaves