Extended Data Fig. 4: Comparison between ranges of bending angles compatible with a given measured energy transfer efficiency for GET and FRET.

a) Sketch showing a simple model for kinked dsDNA, consisting of two rigid cylinders which can rotate around their respective axes (with torsion angles φ and ψ, respectively). They move with respect to each other (\({{\boldsymbol{x}}}_{{\boldsymbol{0}}}{,\,{\boldsymbol{y}}}_{{\boldsymbol{0}}}\) and \({{\boldsymbol{z}}}_{{\boldsymbol{0}}}\) represent the displacements in three dimensions of the bottom of the upper cylinder with respect to the top of the lower one), and bend by an angle \({\boldsymbol{\theta }}\). b) Plot showing the minimum and maximum bending angle \({\boldsymbol{\theta }}\) compatible with a given energy transfer efficiency between 40% and 60%, for GET and FRET. The model shown in a) was considered for the calculations, with 0.34 nm base pair (bp) length, 1 nm dsDNA radius, and 10.5 bp per double helix full turn as physical parameters. Two different labeling strategies were chosen for the two methods: for GET, the kink was positioned at 36 bp distance from graphene, and the dye at 30 bp distance from the kink, in the upper segment; for FRET, the two dyes were both positioned at 8 bp distance from the kink. \({{\boldsymbol{d}}}_{{\boldsymbol{0}}}\) for GET and \({{\boldsymbol{r}}}_{{\boldsymbol{0}}}\) for FRET were set at 17.7 nm and 5 nm respectively. For each value of the energy transfer efficiency \({{\boldsymbol{x}}}_{{\boldsymbol{0}}}{,\,{\boldsymbol{y}}}_{{\boldsymbol{0}}}\) were varied from −1 nm to 1 nm in steps of 0.5 nm, \({{\boldsymbol{z}}}_{{\boldsymbol{0}}}\) was varied between 0 nm and 1 nm (with no steps in between), φ and ψ were varied from −90° to 90° in steps of 1°. For each combination of these parameters, the value of \({\boldsymbol{\theta }}\) leading to the chosen energy transfer efficiency was computed. The plotted minimum and maximum values of \({\boldsymbol{\theta }}\) refer to all the possible combinations of parameters.