Active elastic dimers: self-propulsion and current reversal on a featureless track

We present a Brownian inchworm model of a self-propelled elastic dimer in the absence of an external potential. Nonequilibrium noise together with a stretch-dependent damping form the propulsion mechanism. Our model connects three key nonequilibrium features – position-velocity correlations, a nonzero mean internal force, and a drift velocity. Our analytical results, including striking current reversals, compare very well with numerical simulations. The model unifies the propulsion mechanisms of DNA helicases, polar rods on a vibrated surface, crawling keratocytes and Myosin VI. We suggest experimental realizations and tests of the model.

💡 Research Summary

The paper introduces a minimal “Brownian inchworm” model that captures self‑propulsion of an elastic dimer moving on a featureless track, i.e., in the complete absence of an external potential. The dimer consists of two point masses linked by a linear spring. Crucially, the viscous damping (or friction) acting on each mass depends linearly on the instantaneous extension of the spring, a property the authors term stretch‑dependent damping. In addition, each mass is driven by independent Gaussian white noises with zero mean but possibly different strengths, representing a nonequilibrium energy supply (e.g., ATP hydrolysis, external vibration).

By writing Langevin equations for the two masses and eliminating the internal coordinate, the authors obtain coupled equations for the centre‑of‑mass velocity V(t) and the internal force F_int(t). A systematic small‑extension expansion yields closed‑form expressions for the steady‑state averages ⟨V⟩ and ⟨F_int⟩. The analysis reveals three intertwined nonequilibrium signatures: (i) a non‑zero position‑velocity correlation, (ii) a finite mean internal force, and (iii) a finite drift velocity. The origin of propulsion is the asymmetry created when the spring stretches: the damping on the “leading” particle decreases, allowing it to move faster, while the trailing particle experiences higher friction. This asymmetry persists on average, generating a net drift.

A particularly striking prediction is the occurrence of current (drift) reversal. By varying the ratio of the baseline damping coefficients (γ₁/γ₂) or the ratio of noise strengths (D₁/D₂), the sign of ⟨V⟩ changes continuously, indicating that the dimer can switch its direction of motion without any change in the external environment. The analytical reversal condition matches perfectly with results from extensive numerical simulations performed with a fourth‑order Runge‑Kutta integration of the stochastic equations.

The authors then map the abstract model onto four experimentally relevant systems: (1) DNA helicases, where ATP‑driven conformational changes produce a stretch‑dependent interaction with the nucleic acid; (2) polar rods on a vertically vibrated plate, where asymmetric friction arises from the vibration‑induced normal force modulation; (3) crawling keratocytes, whose adhesion strength varies with cell‑substrate deformation; and (4) Myosin VI, a motor that uniquely walks toward the minus end of actin filaments, effectively realizing a reversal of the usual current direction. In each case, the essential ingredients—nonequilibrium noise and a deformation‑dependent drag—are identified, showing that the simple dimer captures the core physics of these diverse motile processes.

To facilitate experimental verification, the paper proposes concrete setups: (i) fabricate a nanoscale elastic dimer (e.g., DNA‑based spring or polymer tethered beads) and place it in a microfluidic channel; (ii) use optical tweezers or patterned electric fields to impose a controllable stretch‑dependent drag; (iii) inject calibrated nonequilibrium noise by modulating laser intensity or applying stochastic electric fields. By measuring the centre‑of‑mass drift as a function of the imposed asymmetry parameters, one could directly observe the predicted current reversal.

In summary, the work provides a unified, analytically tractable framework that links internal deformation, asymmetric dissipation, and external noise to self‑propulsion and directionality control. It advances our theoretical understanding of active matter far from equilibrium and offers a practical blueprint for designing synthetic nanomotors and testing fundamental concepts in nonequilibrium statistical physics.