= Solution
At initiation, <RNA polymerase> recognizes a <promoter> and forms a closed bound complex; bacterial <promoter> recognition involves its specificity factor. Local strand opening exposes the template in an <Open promoter complex>[open complex], after which initial <RNA> synthesis can precede <promoter escape> into elongation. Binding, opening and productive escape are distinct transitions.
For <DNA unwinding measured by magnetic tweezers>, <magnetic tweezers> report the mechanics of a torsionally constrained <DNA>[DNA tether] through the position of an attached magnetic bead. Axial magnetic <force> extends the tether, while imposed rotation controls its linking constraint. Video localization measures extension changes. The important physical relation is
$$
\boxed{Lk=Tw+Wr,\qquad \Delta Tw+\Delta Wr=0\quad\text{at fixed linking number}.}
$$
Opening a small helical region decreases twist, so the rest of the tether acquires compensating positive <writhe>. On a negatively <DNA supercoiling>[supercoiled] tether this removes some <writhe> magnitude and raises its extension; on a positively <DNA supercoiling>[supercoiled] tether it increases <writhe> magnitude and lowers extension. A change with opposite signs under the two torsional conditions therefore distinguishes unwinding from simple compaction, which would shorten both tethers. Calibrating extension against imposed turns converts a mechanical step into a change in helical winding. This is a conceptual readout of local opening, rather than a direct optical image of separated bases.<Promoter unwinding and promoter clearance by RNA polymerase: Detection by single-molecule DNA nanomanipulation by Andrey Revyakin and others>[2004 study, linking-number argument and opposite extension responses for positive and negative supercoiling]{ref}
\Image[/past-exam-of-the-biological-physics-course-of-the-university-of-oxford/2017-dna-torsion-tweezers.png]
{title=Torsional constraint converts local DNA opening into a bead-extension signal}
{description=An original conceptual magnetic-tweezers schematic is paired with illustrative extension-versus-turns curves. Local unwinding shifts the curve and produces opposite extension changes on its negatively and positively supercoiled branches. The diagram does not reproduce the source experiment or specify a laboratory protocol.}
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