Writhe distribution of stiff biopolymers

Motivated by the interest in the role of stiff polymers like actin in cellular processes and as components of biopolymer networks like the cytoskeleton, we present a statistical mechanical study of the twist elasticity of stiff polymers. We obtain simple, approximate analytical forms for the writhe distribution at zero applied force. We also derive simple analytical expressions for the torque-twist relation and discuss buckling of stiff polymers due to the applied torques. The theoretical predictions presented here can be tested against single-molecule experiments on neurofilaments and cytoskeletal filaments like actin and microtubules.

Figure 1

Normalized writhe distribution for the boundary condition in which the tangent vectors at both the ends of the polymer are held fixed for $f=0$ and $\beta =0.5,1$. Larger values of the average link (or writhe) are suppressed for the smaller value of $\beta$.

Figure 2

Mean extension vs torque $\tau$ for $\beta =0.5$ and $f=30,40$ for a setup with both ends clamped.

Figure 3

Mean extension as a function of the torque $\tau$ for a pulling force $f=30$ for a stiff polymer with both the ends clamped for $\beta =0.5$ and 1.

Figure 4

Buckling of the stiff polymer for $f=0$ and $\beta =0.7,0.8$ with the tangent vectors at both ends of the polymer held fixed.

Figure 5

Torque-link relation for $f=30$ and $\beta =0.5,1$. For the same applied torque, larger values of the average link (or writhe) are suppressed for the stiffer polymer.