Small electrical field effects on biological polymers

Effects of small-magnitude, long-lasting external electric fields on the mechanical bending response of biological polymers such as microtubule are analyzed. We used coarse-grained Brownian dynamics simulations to model polymers as bead-spring with variable lengths and adjustable bending stiffness that are subject to external forces applied uniformly across the polymer or to the last monomer. Simulations show that, especially when applied over long periods of time, forces as low as 0.001 $k_{B}T/\sigma$ ( $\sigma$ is the length scale of a monomer) can cause detectable curvature variations in polymers. This small force, equivalent to $3V/\mathrm{cm}$ for microtubules and $6V/\mathrm{cm}$ for actin filaments, when applied to microtubules of lengths 400 and 1600 nm and to actin filaments of length 600 nm for the respective durations of 75, 4.8, and 34 μs, produces significant effects on the polymers. Furthermore a force of 0.01 $k_{B}T/\sigma$ $\simeq$ $6\mathrm{KV}/\mathrm{cm}$ for a 50-nm-long amyloid fibril requires a pulse duration of 600 μs to produce a significant change. Bending results are also influenced by the directionality of force application; perpendicular forces result in more angular deformation than parallel forces. A critical duration of force exposure required to induce structural changes was defined by the nonlinear dependence of polymer response on force magnitude and stiffness, as revealed by first passage time analysis. These results provide mechanistic insights into the effects of pulsed or variable electric fields on cytoskeletal deformation by quantifying the effective action time of PEFs in biophysical interventions like electroporation and tumor treating fields.