Dual high-stroke and high-work capacity artificial muscles inspired by DNA supercoiling

Powering miniature robots using actuating materials that mimic skeletal muscle is attractive because conventional mechanical drive systems cannot be readily downsized. However, muscle is not the only mechanically active system in nature, and the thousandfold contraction of eukaryotic DNA into the cell nucleus suggests an alternative mechanism for high-stroke artificial muscles. Our analysis reveals that the compaction of DNA generates a mass-normalized mechanical work output exceeding that of skeletal muscle, and this result inspired the development of composite double-helix fibers that reversibly convert twist to DNA-like plectonemic or solenoidal supercoils by simple swelling and deswelling. Our modeling-optimized twisted fibers give contraction strokes as high as 90% with a maximum gravimetric work 36 times higher than skeletal muscle. We found that our supercoiling coiled fibers simultaneously provide high stroke and high work capacity, which is rare in other artificial muscles.

When Is a Helix Stable?

We determine which helical equilibria of an isotropic Kirchhoff elastic rod with clamped ends are stable and which are unstable. Although the set of all helical equilibria is parametrized by four variables, with an additional fifth parameter determined by the rod's material, we show that only three of these five parameters are needed to distinguish between stable and unstable equilibria. We also show that the closure of the set of stable equilibria is star convex. With these results, we are able to compute and visualize the boundary between stable and unstable helices for the first time.

Kinetic Pathway of Torsional DNA Buckling

In magnetic tweezers experiments, we observe that torsional DNA buckling rates and transition state distances are insensitive to base-pairing defects. This is surprising because defects are expected to kink DNA and lower the energy of a localized loop. Nonetheless, base-pairing defects lead to pinning of buckled structures at the defects, which may be important for DNA repair in vivo. We find that the decrease in entropy from pinning roughly balances the decrease in bending energy, explaining why defects have little effect on buckling rates. Our data are generally consistent with elastic rod theory, which predicts that the transition state structure for torsional buckling is a localized wave with a specific shape ("soliton"). The transition state soliton decays to a metastable looped intermediate ("curl") that is separated from the final, fully buckled state by a second, low energy barrier. DNAs with base mismatch defects buckle at lower torque, where elastic rod theory predicts the loop structure is more stable, and manifest an intermediate buckling structure consistent with such a loop. We estimate that, under our high force, high salt experimental conditions, the soliton barrier is approximately 10 k_B T and, to reach this transition state from the unbuckled state, the system torque instantaneously decreases by approximately 1 pN·nm for DNA with or without a small defect.

Genetic defects in β-spectrin and tau sensitize C. elegans axons to movement-induced damage via torque-tension coupling

Our bodies are in constant motion and so are the neurons that invade each tissue. Motion-induced neuron deformation and damage are associated with several neurodegenerative conditions. Here, we investigated the question of how the neuronal cytoskeleton protects axons and dendrites from mechanical stress, exploiting mutations in UNC-70 β-spectrin, PTL-1 tau/MAP2-like and MEC-7 β-tubulin proteins in Caenorhabditis elegans. We found that mechanical stress induces supercoils and plectonemes in the sensory axons of spectrin and tau double mutants. Biophysical measurements, super-resolution, and electron microscopy, as well as numerical simulations of neurons as discrete, elastic rods provide evidence that a balance of torque, tension, and elasticity stabilizes neurons against mechanical deformation. We conclude that the spectrin and microtubule cytoskeletons work in combination to protect axons and dendrites from mechanical stress and propose that defects in β-spectrin and tau may sensitize neurons to damage.

DOI:http://dx.doi.org/10.7554/eLife.20172.001

Twisted vortex filaments in the three-dimensional complex Ginzburg-Landau equation

The structure and dynamics of vortex filaments that form the cores of scroll waves in three-dimensional oscillatory media described by the complex Ginzburg-Landau equation are investigated. The study focuses on the role that twist plays in determining the bifurcation structure in various regions of the (alpha,beta) parameter space of this equation. As the degree of twist increases, initially straight filaments first undergo a Hopf bifurcation to helical filaments; further increase in the twist leads to a secondary Hopf bifurcation that results in supercoiled helices. In addition, localized states composed of superhelical segments interspersed with helical segments are found. If the twist is zero, zigzag filaments are found in certain regions of the parameter space. In very large systems disordered states comprising zigzag and helical segments with positive and negative senses exist. The behavior of vortex filaments in different regions of the parameter space is explored in some detail. In particular, an instability for nonzero twist near the alpha=beta line suggests the existence of a nonsaturating state that reduces the stability domain of straight filaments. The results are obtained through extensive simulations of the complex Ginzburg-Landau equation on large domains for long times, in conjunction with simulations on equivalent two-dimensional reductions of this equation and analytical considerations based on topological concepts.

Dynamics of helical strips

The dynamics of inertial elastic helical thin rods with noncircular cross sections and arbitrary intrinsic curvature, torsion, and twist is studied. The classical Kirchhoff equations are used together with a perturbation scheme at the level of the director basis, and the dispersion relation for helical strips is derived and analyzed. It is shown that all naturally straight helical strips are unstable whereas free-standing helices are always stable. There exists a one-parameter family of stationary helical solutions depending on the ratio of curvature to torsion. A bifurcation analysis with respect to this parameter is performed, and bifurcation curves in the space of elastic parameters are identified. The different modes of instabilities are analyzed.

Twirling and whirling: viscous dynamics of rotating elastic filaments

Motivated by diverse phenomena in cellular biophysics, including bacterial flagellar motion and DNA transcription and replication, we study the overdamped nonlinear dynamics of a rotationally forced filament with twist and bend elasticity. Competition between twist injection, twist diffusion, and writhing instabilities is described by coupled PDEs for twist and bend evolution. Analytical and numerical methods elucidate the twist/bend coupling and reveal two regimes separated by a Hopf bifurcation: (i) diffusion-dominated axial rotation, or twirling, and (ii) steady-state crankshafting motion, or whirling. The consequences of these phenomena for self-propulsion are investigated, and experimental tests proposed.