Effect of Bending Anisotropy on the 3D Conformation of Short DNA Loops

The equilibrium three dimensional shape of relatively short loops of DNA is studied using an elastic model that takes into account anisotropy in bending rigidities. Using a reasonable estimate for the anisotropy, it is found that cyclized DNA with lengths that are not integer multiples of the pitch take on nontrivial shapes that involve bending out of planes and formation of kinks. The effect of sequence inhomogeneity on the shape of DNA is addressed, and shown to enhance the geometrical features. These findings could shed some light on the role of DNA conformation in protein–DNA interactions.

Figure 1

The ground-state conformation for a 94 bp DNA loop with bending anisotropy ($A_1=75\mathrm{nm}$ and $A_2=37\mathrm{nm}$). The center line of DNA is shown by a solid (blue or dark gray) line. In the right panel, the position of each base is shown by solid circles and the two strands of DNA are shown in different colors. The positions of kinks are shown by two arrows in the top left panel.

Figure 2

The local writhe $wr$, twist $tw$, and curvature $\kappa$ for half of the looped DNA for the two lengths of 87 bp and 94 bp. The solid red (medium gray) lines correspond to $A_1=75\mathrm{nm}$ and $A_2=37\mathrm{nm}$, the dashed blue (dark gray) lines correspond to a Gaussian random sequence centered around $A_1=75\mathrm{nm}$ and $A_2=37\mathrm{nm}$ with a width of 7 nm in the effective persistence length (the mean value of persistence length is 50 nm), and the light green (light gray) lines correspond to $A_1=A_2=50\mathrm{nm}$.

Figure 3

Energy of looped DNA as a function of its length for the isotropic ($A_1=A_2=50\mathrm{nm}$, solid curve) and the anisotropic ($A_1=75\mathrm{nm}$ and $A_2=37\mathrm{nm}$, filled circles) models. The inset shows the energy difference between two isotropic and anisotropic looped DNA as a function of its length for the lengths of 90–100 bp.