Fig. 3
Residence time measurements and threshold electric field reduction. a Mean residence times measured at various nanochannel electric field strengths, E, in three different nanofunnels (defined by α = 0.78, α = 0.45, and α = 0; see Eq. 2) and in the absence of a nanofunnel. Each dataset is associated with the nanofunnel indicated directly above it in the figure and is color coded accordingly. Data were collected using stained λ-phage (48.5 kbp, open circles) and T4-phage (165.6 kbp, filled squares) DNA molecules. The error bars indicate the standard deviations of at least 20 independent measurements per experimental data point. The curves represent the best-fit of the theoretical model to these experimental data. b Extrapolating the experimental electric field data in (a) to τ 0 = 6 ms results in the characteristic threshold electric field strength, E 0 (normalized to the threshold electric field strength measured in the absence of a nanofunnel E 0 (no funnel)) for each of the three nanofunnels (red, green, and blue symbols obtained from the data in (a) of the same colors). τ 0 = 6 ms corresponds to the Zimm relaxation time of the leading portion (~3000 bp) of the nanofunnel-confined molecule23, 24. This 3000-bp segment is the length of DNA that must enter the nanochannel to initiate threading, as determined from the theoretical monomer concentration profiles shown in Supplementary Fig. 7b. The experimental values in (b) for the α = 1.46 and α = 1.89 nanofunnels were determined as described in the Supplementary Methods. The solid and dashed black lines are interpolations of theoretical values calculated for T4-phage and λ-phage DNA, respectively, over a wider range of α values. The error bars indicate the 1σ confidence level of the threshold electric field strengths determined from the experimental data and are smaller than the symbols for the results from nanofunnels where α > 0.45
