Theory of Ethidium Binding to DNA under Tension and Torque: Possible Role of Cruciforms at Inverted Repeat Sequences

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.