Nucleic Acids Research, 2006, Vol. 34, No. 10 3061 Figure 3. High-resolution AFM images of DNA samples. (a) Two representative DNA molecules of the PPC adsorbed on a mica surface. (b) Illustration of the data analysis and tracing of the DNA molecules. A segmented line made of points separated by ‘ ¼ 2.5 nm follows the contour of the molecule. The important parameters we employ are the contour length spacing L, the end-to-end distance R and the curvature C defined as the inverse of the curvature radius r that embraces three contour points, C ¼ 1/r. In the inset in (b), these parameters are shown together with an example of three values of R for the same contour length spacing L, in this case L ¼ 3 · ‘ ¼ 7.5 nm. We also show an example for the calculation of r for three points separated by L ¼ 2 · ‘ ¼ 5 nm (red arc). (c) AFM image of sample SQ100 and histogram of contour lengths L0 [inset in (c)]. (d) AFM image of sample SQ322 and histogram of contour lengths L0 [inset in (d)]. DNA structures in previous studies (3). Similar migration anomalies were observed in other two different hyperperiodic fragments from C.elegans (data not shown). Single-molecule AFM imaging After the electrophoresis experiments indicated the presence of unusual DNA structures, we analyzed our samples with quantitative AFM analysis. The different DNA samples were imaged at high resolution and traced using a custom-written tracing routine. Typically, measured DNA proﬁles displayed a width of 4–7 nm at half height. We imaged the PPC (2885 bp), the control DNA (2743 bp) and the short C.elegans fragments (182 and 185 bp). Figure 3a shows an image of the PPC, where two DNA molecules are visible. The average measured contour length L0 was 1032 ± 27 nm, yielding a rise per bp of 0.36 ± 0.01 nm. To illustrate the analysis, we plotted in Figure 3b an example of a single trace. The tracing routine accurately generates XY pairs sep- arated by ‘ ¼ 2.5 nm that follow the contour of the molecule. We found this length to be the lowest meaningful length that faithfully followed the contour given the pixel size of the images, 1.95 nm, and the high resolution obtained by using ultra-sharp tips. A magniﬁcation of the trace illustrates the three quantities deduced that are important for the analysis that follows (Figure 3b, inset). These are the contour length spacing L (in the example, L equals 3 · 2.5 ¼ 7.5 nm), and the end-to-end distance R. Clearly, a given contour length spacing L can be associated with several values of R (three of them are plotted in the inset). The inset also shows the def- inition of curvature, C. The curvature of a 10 nm long seg- ment is deﬁned as the inverse of the radius r of the circle that encompasses three points separated by 5 nm (showing in red in the inset in Figure 3b). High-resolution AFM images of the short DNA samples, SQ100 and SQ322, are shown in Figure 3c and d. Figure 3c corresponds to the non-periodic sequence and Figure 3d to the hyperperiodic one. By eye, one can already notice that Figure 3d displays more bent molecules. This was conﬁrmed in the subsequent numerical and analytical analysis (see below). Insets represent histograms of contour lengths for each sample. They show that our tracing routine precisely deduces the contour length with a standard deviation of 3 nm. For samples SQ100 and SQ322, 692 and 653 molecules were analyzed, respectively. Single molecule AFM-based quantitative analysis of hyperperiodic C.elegans DNA A quantitative analysis of the traces of hyperperiodic DNA showed systematic deviations from the worm-like-chain (WLC) model consistent with extra bending induced by