Screwlike order, macroscopic chirality, and elastic distortions in high-density DNA mesophases

We investigate a new screwlike liquid-crystalline ordering in solutions of helical biopolymers and its influence on the state of individual molecules. In the resulting mesophase translational and rotational motions of molecules are coupled in screw fluctuations. We show that in contrast to the case of conventional chiral liquid crystals the elastic distortion does not twist the screw order but leads to overwinding of individual helical molecules. This explains the peculiarities of high-density DNA mesophases.

Figure 1

(Color online) Fluctuational motion of helical molecules: (a) translational motion; (b) rotational motion; (c) coupled screwlike motion. See the text.

Figure 2

(Color online) Screwlike order in the mesophase with correlated helical molecules. Though $i$th and $j$th molecules carry out screwlike fluctuational motion their total helical phases ${\psi }^i$ and ${\psi }^j$ are correlated in any plane $z=\mathrm{const}$. (a) Instantaneous positions and orientations of the $i$th and $j$th molecules, $z_0^i-z_0^j$ being the difference of initial translational phases. Correlation in two different sections $z=z_1$ and $z=z_2$ is shown. (b) ${\mathbf{R}}^i$ and ${\mathbf{R}}^j$ vectors remain parallel in the planes $z=z_1$ and $z=z_2$ though their common direction varies during a screwlike motion.