Observed pattern of probe–probe distance variation and the predictions of different mechanical models. (*A*) The experimentally obtained distance-distribution variances (circles) are plotted together with predicted values based on the linear elastic rod model (blue line, χ^{2} = 8.4) and the knowledge-based model (brown line, χ^{2} = 6.0). (*B*) Variance predictions of a reparameterized linear elastic rod model (black line, χ^{2} = 5.4). The bending and twisting rigidity were optimized together with the five probe and helical parameters (*SI Appendix*, Table S3*B*) so as to minimize the χ^{2} of a fit against both the mean and variance data. The optimized bending persistence length is 55 ± 10 nm, and the optimized twisting persistence length is 20 nm (16–34 nm give χ^{2} values that differ by less than 10%). (*C*) Variance predictions of the reparameterized linear elastic rod model (black) with no twisting fluctuations (yellow; χ^{2} = 14). (*D*) Variance predictions of the reparameterized linear elastic rod model (black) with no bending fluctuations (yellow; χ^{2} = 29). (*E*) Variance predictions of the reparameterized linear elastic rod model without (black) and with a 0.29 Å per base pair cooperative stretching transition (red line, χ^{2} = 4.9). (*F*) End-to-end distance variance of DNA duplexes measured previously () (circles) and variance predictions of the reparameterized linear elastic rod model with (red line, χ^{2} = 3.8) and without (black line, χ^{2} = 20) a cooperative stretching transition. The *y*-intercept values fit to the data are 4.2, 0.5, 0.4, 0.0, and 3.7 Å^{2}, respectively, for the linear elastic rod model (blue line in *A*), the knowledge-based model (brown line in *A*), the reparameterized linear elastic rod model (*B*), and the reparameterized linear elastic rod model with a cooperative stretch (*E* and *F*). These small intercepts, which approximate the contribution to the variance from flexibility of the Au nanocrystal attachment to the DNA, suggest that there is little residual motion of the probe. The experimental data are from sequences 1a–1d (red and magenta), sequence 2 (green), and sequence 3 (cyan), which are shown in and *SI Appendix*, Table S1.

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