Definition of the persistence length in the coarse-grained models of DNA elasticity

By considering the detailed structure of DNA in the base pair level, two possible definitions of the persistence length are compared. One definition is related to the orientation of the terminal base pairs, and the other is based on the vectors which connect two adjacent base pairs at each end of the molecule. It is shown that although these definitions approach each other for long DNA molecules, they are dramatically different on short length scales. We show analytically that the difference mostly comes from the shear flexibility of the molecule and can be used to measure the shear modulus of DNA.

Figure 1

(a) Schematic representation of the two choices for defining the unit vectors. Rectangles represent the base pairs, dashed vectors (red [gray]) are normal to the base pairs, and solid vectors (blue [gray]) are along the lines that connect two adjacent base pairs. (b) Simulation data for $l_p^n$ (squares, red [gray]) and $l_p^c$ (circles, blue [gray]) as a function of DNA length, along with the theoretical results (solid and dashed curves). Filled symbols and solid curves show the simulation data and theoretical results in three dimensions (3D), while empty symbols and dashed curves correspond to two-dimensional (2D) DNA. The inset shows $-\ln \langle \cos \theta \left(L\right)\rangle$ vs $L$ for the same data and with the same markers.

Figure 2

Schematic representation of the local coordinates and midframe. Cuboids represent two adjacent base pairs. The local coordinates corresponding to each base pair and the midframe are shown with solid and dashed arrows respectively.

Figure 3

Plot of ${\alpha }^{3\mathrm{D}}$ (squares, red [gray]) and ${\alpha }^{2\mathrm{D}}$ (circles, blue [gray]) for different values of coarse-graining length. Solid curve (red [gray]) and dashed curve (blue [gray]) correspond to 3D and 2D theoretical results respectively.

Figure 4

Plots of $l_p^c$ vs DNA length for different values of the coarse-graining length: $l=1bp$ (circles, blue [dark gray]), $l=2bp$ (squares, red [light gray]), $l=4bp$ (triangles, green [drak gray]), and $l=8bp$ (diamonds, purple [light gray]). Empty and filled symbols correspond to 2D and 3D simulations respectively, and solid curves show the theoretical results. The dashed line indicates the value of $l_p^n$.