Figure 4.

Dependence of the assembly rate on the force applied to the DNA molecule in stopped-flow experiments. Forces were determined as described in the text. Because at forces >3 pN, the extension l is within ≈10% of the contour B-form length of λ-DNA (16.4 μm; ref. 36), we used 16 μm as an initial estimate of l. Once a first-approximation force was calculated by using this value of l and the measured 〈Δx²〉, the extension at this force was estimated by interpolation from the force vs. extension curve (figure 8 of ref. 36), and a second-approximation force was calculated by using this interpolated value of l. After one round of iteration, the accuracy in the determination of force at each distance was within ≈10% for forces >3 pN and within ≈20% in the range of 0.5–3 pN. Assembly curve of the same DNA molecule was subjected to different forces in the course of a single assembly experiment. The distances (and forces) were adjusted during the course of the assembly, as indicated. The lines drawn through the straight portions of the experimental traces at each force indicate that the assembly rates change as a function of force, with ever-increasing rates at ever-decreasing forces. (A) Travel in the x–y plane. (B) Tether length (calculated by using the angle φ, as depicted in Fig. 1A). (C) Initial assembly rate as a function of the applied force (data from 18 individual assembly experiments). Assembly rates were calculated from the slope of lines drawn through the data points in length vs. time plots (see example lines drawn in B). A possible exponential fit to the data points is indicated by the dashed curve. However, we do not intend to imply any theoretical significance to this specific fit. Exhibiting the same data on a semilog scale (see graph, Inset) shows the same fit as a dashed straight line.