Fig. 7. Coarse graining analysis of curvature reveals the true rigidity of WLCs.

The calculations use WLCs with l_p = 500 pixels (n = 40 filaments). A: Schematic of coarse graining. The black dots represent the sampling points of the active contour that are separated by Δs_snake. Without coarse-graining, the coordinates of i − 1,i, and i + 1 are used to calculate the tangent vectors and curvature. With coarse-graining, Δs_c = 2 in this example, sites k − 1,k, and k + 1 are used instead. B: The tangent correlations are weakly dependent on coarse graining length Δs_c and follow single exponential decay (solid line). Error bars indicate standard deviation of individual measurements. C: Plot of curvature distributions for different coarse-graining lengths Δs_c. The widths depend on Δs_c, as expected from Equation (21). In addition to this change, the value of the extracted persistence lengths (shown in the panel) change with Δs_c as well. D: Measured persistence lengths as a function of Δs_c calculated from the tangent correlation (circles) and curvature distribution (squares) as compared to the intrinsic persistence length of WLCs (triangles). The accuracy of estimates of persistence length using the curvature distribution increases with increasing Δs_c.