Critical value of the torsional stress. The torque necessary to trigger the chiral transition of
a nucleosome into a R-octasome has been recently measured (Celedon et al., 2009). The
authors reported a value close to 10 pN.nm in very low salt conditions (10 mM phosphate
buffer). The torque exerted by E.coli RNAP has been estimated to be at least 6 pN.nm
(Harada et al., 2001). Hence, the torque created by an elongating polymerase is likely to be
sufficient to trigger the chiral transition of a nucleosome into a R-octasome under
physiological conditions.
Celedon A, Nodelman IM, Wildt B, Dewan R, Searson P, Wirtz D, Bowman GD, Sun SX.
(2009). Magnetic tweezers measurement of single molecule torque. NanoLetters 9, 1720-5.
Harada, Y., Ohara, O., Takatsuki, A., Itoh, H., Shimamoto, N., and Kinosita, K., Jr. (2001).
Direct observation of DNA rotation during transcription by Escherichia coli RNA polymerase.
Nature 409, 113–115.
Evaluation of the distance L.
According to the twin-supercoiled domain model, the
elongation over L bp involves the twisting of the downstream DNA by an amount of L/10 turns
(indeed, the progression of the Pol II over 10 bp, i.e. the pitch of the double helix, overtwists
the downstream DNA by 1 turn). According to the linking number conservation, this overtwist
is converted into the same amount of superhelical turns (writhe) by the transition of
nucleosomes into R-octasomes. As stated above, 2 turns of positive twist will allow the
transition of one ‘canonical’ L-octasome into an R-octasome. Hence, elongation over L bp
induces the transition of L/(2x10) nucleosomes into R-octasomes. The number N(t) of Roctasomes at time t is then equal to L/20 = Vt/20. As Pol II progresses at an average velocity
V~25 bp/s, we get N(t) = 25xt/20 = 1.25xt with t in seconds.
Therefore, N(t)=6 after 5
seconds. As there are N~20 nucleosomes in the downstream part of the locus (4000/200), all
the nucleosomes in the downstream part of the locus are turned into R-octasomes after only
16 s of ongoing transcription. Note that for the other gene, namely Hsp70Aa, the Pol II has to
translocate over a distance L’=20x(9000/200)=900 bp for destabilizing all the 45 nucleosomes
between -9000 and 0, which happens in only 36 s.
Wave velocity. The wave velocity is c=dN/dtx200 = V/20x200 = 10xV, i.e. c=10xV=200 bp/s.