= Solution
The bacterial <RNA polymerase> core associates with a <sigma factor> to form a holoenzyme. The <sigma factor> recognizes <promoter> features and helps position the <DNA> and stabilize its opening. Initial binding gives a closed <promoter> complex; local <DNA> unwinding creates an open <promoter> complex with the template accessible. Initial <RNA> synthesis can produce short abortive products while the <RNA polymerase> remains attached to the <promoter>, taking in downstream <DNA> by scrunching. Growth of the <RNA> eventually permits <promoter escape> and productive elongation. The <sigma factor> changes its interactions during this transition; immediate complete dissociation is not obligatory.
In <magnetic tweezers>, torsionally constrained <DNA> joins a surface to a magnetic bead. A field gradient applies upward <force>, rotation of the magnets controls the imposed <DNA supercoiling>, and optical tracking measures bead height. At suitable modest <force>, <DNA supercoiling> forms writhed loops, shortening the tether. Opening roughly one helical turn at fixed <linking number> makes the remaining <DNA> more positively twisted: $\Delta Tw_{\rm rest}+\Delta Wr=-\Delta Tw_{\rm bubble}$. Thus opening lengthens a negatively supercoiled tether by removing some negative writhe, but shortens a positively supercoiled tether by adding positive writhe. This opposite sign distinguishes unwinding from ordinary compaction, which shortens both tethers. Height-versus-turn calibration converts the two extension changes into an unwinding angle and a compaction contribution. Repeated height transitions give opening and closing dwell times.<Promoter unwinding and promoter clearance by RNA polymerase: Detection by single-molecule DNA nanomanipulation by Andrey Revyakin and others>[Figures 1–3: torsionally constrained tether, opposite-sign extension responses, and approximately one-turn unwinding]{ref}
\Image[/past-exam-of-the-biological-physics-course-of-the-university-of-oxford/2022-magnetic-promoter-opening.png]
{title=<Magnetic tweezers> and the opposite signs of the <promoter> opening signal}
The sketch is a schematic prediction, not a copy of an experimental trace. Opening must be distinguished from <promoter escape>: an unwound <DNA> region can remain associated with an elongating <RNA polymerase>.
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