a, Cartoon of the dumbbell geometry with schematic force versus position curves (dark red) shown for both trap beams (not drawn to scale). A single, transcriptionally active molecule of RNAP (green) is attached to a bead (blue) held in trap T_weak (pink, right) and tethered via the upstream DNA (dark blue) to a larger bead held in trap T_strong (pink, left). The right bead is maintained at a position near the peak of the force-extension curve of T_weak, where trap stiffness vanishes (white arrow), creating a force clamp (trap stiffness k = dF/dx). During elongation, the DNA tether lengthens and the beads move apart. Owing to the force clamp arrangement, only the right bead moves: displacement is measured for this bead. b, Power spectrum acquired for a stiffly trapped bead with external optics under air (red) or helium (blue). Inset: integrated noise spectra for air (red) and helium (blue) showing a tenfold reduction in power. c, Steps resolved for a stiffly trapped bead moved in 1-Å increments at 1 Hz. Data were median filtered with a 5-ms (pink) and 500-ms (black) window. d, Steps resolved for a bead–DNA–bead dumbbell held at 27 pN of tension, produced by moving T_strong in 3.4-Å increments at 1 Hz and measuring the corresponding displacements in T_weak.

a, A power stroke model where translocation (δ, red) is driven by irreversible PP_i release. b, A brownian ratchet model where reversible oscillation between pre- and post-translocated enzyme states can occur before NTP binding (blue). c, A brownian ratchet model where translocation and NTP binding can occur in either order. This model postulates the existence of a secondary NTP site to accommodate the possibility of nucleotide binding when the enzyme is in its pre-translocated state.

a, b, Measured force–velocity relationships for RNAP at [NTP]_eq, 10[NTP]_eq, 100[NTP]_eq and 250[NTP]_eq, with off-pathway events removed (see text) (a), and single-molecule velocity as a function of [NTP] measured at 27 pN assisting load (open circles) with associated errors (see Methods) (b). Negative forces correspond to hindering loads; positive forces to assisting loads. Global fits to the power stroke model of Fig. 3a (green dashed line), the brownian ratchet model of Fig. 3b (blue dotted line) and the brownian ratchet model of Fig. 3c (solid red line) are shown. c, The F_½ value as a function of [NTP] derived from free fits of the data in a to equation (1) (Supplementary Fig. S4), shown together with predictions from the three models (coloured lines) (Supplementary Fig. S5).

a, Representative records for single molecules of RNAP transcribing at [NTP]_eq under 18 pN of assisting load, median-filtered at 50 ms (pink) and 750 ms (black). Horizontal lines (dotted) are spaced at 3.4-Å intervals. b, The average autocorrelation function derived from position histograms (N = 37) exhibits periodicity at multiples of the step size. c, The power spectrum of b shows a peak at the dominant spatial frequency, corresponding to the inverse of the fundamental step size, 3.7 ± 0.6 Å.

a, Backstepping observed under assisting loads of 18 pN at [NTP]_eq. Molecules were occasionally found to move backward by one base pair (left and middle panels) or by two base pairs (right panel) before resuming elongation. b, Backtracking (>3 bp) under a hindering load of 9 pN. Molecules dwelled at specific preferred locations on the template before irreversibly backtracking (top) or recovering (bottom). Horizontal gridlines (dotted) are spaced at 3.4-Å intervals. (See Supplementary Information for a discussion.)