Nucleic Acids Research, 2006, Vol. 34, No. 10 3063 Table 2. Standard deviation sC of curvature distributions and standard deviation s<C>molecule and intrinsic curvature <C>0,molecule of mean curvature distributions sC,L¼5 nm(nm 1) sC, L¼25 nm (nm 1) s<C>molecule, L¼5 nm (nm 1) <C>0,molecule, L¼5 nm (nm 1) s<C>molecule, L¼25 nm (nm 1) <C>0,molecule, L¼25 nm (nm 1) Control 0.0547 ± 0.0007 0.0241 ± 0.0003 0.0077 ± 0.0003 0 0.007 ± 0.001 0 PPC 0.0618 ± 0.0005 0.0298 ± 0.0003 0.0072 ± 0.0008 ±0.010 ± 0.001 0.008 ± 0.001 ±0.013 ± 0.001 SQ100 0.0667 ± 0.0004 — 0.0163 ± 0.0005 0 — — SQ322 0.0737 ± 0.0004 — 0.024 ± 0.002 ±0.010 ± 0.002 — — Values correspond to Gaussian fits to distributions shown in Figures 4c, 4d, 5b and 5c. The segment length was 5 and 25 nm, where indicated. Distributions for the short DNAs were not calculated at L ¼ 25 nm. contours had smaller mean squared end-to-end distances than those of non-periodic SQ100 (Figure 4b). To stress the signiﬁcance of the result, we included in Figure 4b plots of Equation 1 with P ¼ 20, 30, 40, 50 and 60 nm to guide the eye. Whereas SQ100 data lay as expected between the curves of P ¼ 50 and 60 nm, SQ322 data overlaid the curve of P ¼ 25 nm. Summarizing the results from these different DNA samples (Figure 4a and b), we ﬁnd consistently that hyperperiodic 2 DNA results in a shorter hRs‚ sþLi than predicted by the WLC at the two length scales studied: hundreds of bp and tens of bp. This can be most easily explained by increased 2 bending of the DNWAL. CFuartthleorwmeorrep,ertshiestepnlcoet lfeonrgthhR.s‚ TsþhLisi deviates from the suggests that the increase in bending is not due to an increase in random bending/ﬂexibility, which would exhibit WLC behavior, but rather due to non-random bending. The presence of increased bending in hyperperiodic C.elegans DNA compared to non-periodic DNA was further supported by examining distributions of absolute curvatures jCj. We calculated curvatures from traces at a ﬁxed spacing L (see inset in Figure 3b as an example, for L ¼ 5 nm). To do this, we ﬁtted a circle to three points separated by L along the contour of the DNA. The curvature (C) at this spacing is deﬁned as the inverse of the radius of that circle and its value was assigned to the middle point of the three contour points. Hence to calculate Ci at a given position i, for a given L, we used DNA stretches of 2 · L nm. Then we moved to the next point i + ‘ along the contour, which is ‘ ¼ 2.5 nm (7 bp) apart from the previous, and we obtained a new value of Ci+‘. We arbitrarily assigned positive curva- ture if by progressing along the DNA the contour turned to the right, and we assigned negative curvature if it turned to the left. As expected, we found Gaussian distributions of C centered at zero for all type of molecules studied, proving no preferential curvature orientations due to adsorption (data not shown). Absolute curvatures j C j distributions were calculated at different values of L. Figure 4c shows absolute curvature distributions for the PPC and the control non-periodic DNA for L ¼ 5 nm. We analyzed 100 control DNA molecules, which yielded 12 000 curvature values, and 190 PPC molecules, which yielded 24 000 curvature values. Figure 4d shows similar absolute curvature distributions for the short DNA fragments studied, SQ100 (non-periodic) and SQ322 (highly-periodic). We analyzed 613 SQ100 and 567 SQ322 molecules, each yielding 12 000 curvature values. Distributions were normalized to have an area of one, and error bars denote normalized square root of number of points in the bin. All absolute curvature distributions were ﬁt with a Gaussian function centered at curvature zero. From these ﬁts we extracted the standard deviation sC. The values sC of the Control, PPC, SQ100 and SQ322 samples from curvature his- tograms calculated using a spacing of L ¼ 5 and 25 nm are quoted in Table 2 (the latter only for long DNAs). Systemat- ically, we found that DNA with hyperperiodic sequences had larger sC than non-periodic DNA. This was found to be inde- pendent of the spacing L used to calculate curvatures up to 50 nm. The inset in Figure 4c proves this by showing jCj dis- tributions for PPC and control samples calculated at a larger spacing of L ¼ 25 nm. Spacings larger than 50 nm, the per- sistence length of the DNA, did not generate statistically sig- niﬁcant curvature distributions. Intrinsic curvature in hyperperiodic C.elegans DNA In principle, a broad jCj distribution could result from either increased ﬂexibility or intrinsic curvature (Supplementary Data). In order to determine which of the two phenomena dominates in our hyperperiodic DNA, we performed two cal- culations: (i) we calculated the distance over which the hand- edness of the curvature persists, and (ii) we calculated an average curvature per single imaged AFM molecule and con- sidered its absolute value j<C>moleculej. One way to measure the persistence of handedness is to plot a correlation function CCL,D of the form: PL0 D CL;sCL;sþD ‚ s CCL‚ D ¼ PL0 D jCL;sjjCL;sþDj s 2 where CL,s is the curvature calculated at spacing L at position s and L0 is the total contour length of the molecule. CL,s can therefore be positive or negative as deﬁned above. The func- tion CCL,D involves addition over all the molecules con- sidered in this study, 100 for the control DNA and 190 for the PPC. To examine the persistence of handedness, renor- malization was included to compare the two datasets. For a given spacing L, CCL,D is a function that depends on the cor- relation spacing D. Figure 5a shows a plot of CCL,D for L ¼ 5, 15 and 25 nm for the PPC (dashed lines) and the control DNA (solid lines). Systematically, a signiﬁcantly larger correlation distance was found for the hyperperiodic DNA than for the non-periodic DNA. As expected, at large correlation spacing D, the correlation function approached zero for non-periodic DNA, showing that the ‘memory’ of handedness is lost very quickly. Interestingly, for hyperperiodic DNA the correla- tion function approaches a non-zero value, for large