Chirality and Equilibrium Biopolymer Bundles

We use continuum theory to show that chirality is a key thermodynamic control parameter for the aggregation of biopolymers: chirality produces a stable disperse phase of hexagonal bundles under moderately poor solvent conditions, as has been observed in in vitro studies of $F$ actin [O. Pelletier et al., Phys. Rev. Lett. 91, 148102 (2003)]. The large characteristic radius of these chiral bundles is not determined by a mysterious long-range molecular interaction but by in-plane shear elastic stresses generated by the interplay between a chiral torque and an unusual, but universal, nonlinear gauge term in the strain tensor of ordered chains that is imposed by rotational invariance.

Figure 1

Top view (left) and side view (right) of twisted bundle of hexagonally ordered filaments. For a torsional strain, $\Omega$, the outermost filaments make an angle $\theta =\Omega R$ with the central axis. Hence, elastic strain chain bending and lattice shear build up as twisted bundle grows.

Figure 2

The free-energy dependence of a chiral bundle on bundle radius, $R$, for columnar aggregates at the bulk condensation point ($\mu ={\mu }_c$). For surface tension greater than ${\Sigma }_c$ the free-energy minimum occurs for $R=0$ (single filaments). For $\Sigma \le {\Sigma }_c$ the minimum occurs at a finite radius, $R_0\ge {\lambda }_{3\perp }$. The inset shows the phase diagram for the columnar phase of aggregates for fixed chemical potential and surface tension.