Celedon et al. reported an unexpectedly low slope of applied torque vs turns (or apparent torsional rigidity) for
a long DNA subject to 0.8 pN tension and modest negative torques
(up to approximately −5 pN nm) in 3.4 × 10–9 M ethidium (J. Phys. Chem. B
2010, 114, 16929–16935). Extrusion of inverted repeat sequences
to create cruciforms with anomalously large association constants
for binding 4 ethidiums to the cruciform arms is investigated as a
possible explanation for this observation and also for its compatibility
with other observations of Celedon et al. The equilibrium between
the linear main chain and cruciform states of an inverted repeat sequence
under the prevailing tension, torque, and ethidium concentration is
treated by first computing the free energy per bp of the linear main
chain. This is done for a complex model, wherein every bp in the linear
main chain participates in both the recently reviewed cooperative
two-state a ⇔ b equilibrium
(Quarterly Reviews of Biophysics
2021, 54, e5, 1–25) and in ethidium binding with
a modest relative preference for either the a- or b-state. Plausible assumptions are made concerning the relative
populations of the cruciform and linear main chain states of an inverted
repeat, and also the relative populations of cruciform states with
and without 4 bound ethidiums in the presence of tension, torque,
and 3.4 × 10–9 M ethidium. Besides a large
drop in slope (or apparent torsional rigidity) from
10–9 to 10–8 M ethidium, this
theory also predicts maxima between 6.4 × 10–8 and 2.0 × 10–7 M ethidium, a region where
no measurements were made. Overall agreement between theoretical and
experimental values of the slope (or apparent torsional
rigidity), and also the number of negative turns due to bound ethidium
at zero torque, is fairly good for all of the ethidium concentrations
studied by Celedon et al., provided that there is a modest preference
for binding to the b-state. When there is a modest
preference for binding to the a-state, the theory
significantly underestimates experimental values at the higher ethidium
concentrations, likely ruling out that possibility.