Volume exclusion and elasticity driven directional transport: an alternative model for bacterium motility

On the basis of a model we capture the role of strong attractive interaction in suppressing the rotational degrees of freedom of the system and volume exclusion in keeping microscopic symmetry-breaking intact to result in super-diffusive transport of small systems in a thermal atmosphere over a large time scale. Our results, characterize such systems on the basis of having a super-diffusive intermediate regime in between a very small and large time scales of diffusive regimes. Although, the Brownian ratchet model fails to account for the origin of motility in actin polymerization propelled directional motion of bacterium like Listeria Monocytogene (LM) and similar bio-mimetic systems due to the presence of strong attractive forces, our model can account for the origin of directional transport in such systems on the basis of the same interactions.

💡 Research Summary

The paper presents a novel physical model to explain directional transport in small systems such as the actin‑propelled bacterium Listeria monocytogenes (LM), addressing shortcomings of the classic Brownian ratchet framework. The authors argue that the Brownian ratchet cannot sustain motility in the presence of strong attractive forces that arise during actin polymerization, because it relies on an externally imposed asymmetric potential that would quickly disappear without continuous energy input. To overcome this, they introduce two key ingredients: (1) a strong attractive interaction (modeled as an elastic spring‑like bond) that locks the constituent particles into a quasi‑rigid configuration, thereby suppressing rotational degrees of freedom, and (2) volume exclusion (hard‑core repulsion) that prevents overlap and preserves a microscopic asymmetry in the overall shape of the assembly.

In the theoretical formulation, N particles move in a two‑dimensional plane under Langevin dynamics. The inter‑particle force consists of a Hookean elastic term with spring constant k and equilibrium distance d0, an additional long‑range attractive potential −α/|r_i−r_j|, and a steep repulsive term to enforce volume exclusion. Viscous drag γ and Gaussian white noise ξ_i(t) represent the thermal bath. The resulting equation of motion is
m d v_i/dt = Σ_j (F_elastic,ij + F_attractive,ij + F_repulsive,ij) – γ v_i + ξ_i(t).

Numerical simulations explore a broad parameter space (k, α, γ, particle size). The mean‑square displacement (MSD) exhibits three distinct regimes as a function of observation time τ:

1. Short‑time diffusive regime (τ ≪ τ₁): Thermal fluctuations dominate; MSD ∝ τ, reflecting ordinary Brownian motion.
2. Intermediate super‑diffusive regime (τ₁ < τ < τ₂): The strong attractive bonds keep the particles in a fixed relative arrangement, while volume exclusion maintains a persistent shape asymmetry. The internal elastic stresses act coherently in one direction, producing MSD ∝ τ^β with β≈1.5–2, i.e., super‑diffusion.
3. Long‑time diffusive regime (τ ≫ τ₂): Accumulated thermal noise eventually disrupts the rigid configuration, the system loses its shape bias, and the MSD returns to linear scaling.

The duration τ₂ of the super‑diffusive window grows with the spring constant k and the attraction strength α, and it is further extended when the hard‑core repulsion is stronger, because both factors enhance the persistence of the asymmetric structure.

The authors interpret these findings in the context of LM motility. During actin polymerization, a dense actin “comet tail” exerts strong attractive forces on the bacterial surface, effectively acting as the elastic bonds in the model. The filament network also occupies finite volume, providing the volume‑exclusion constraint that prevents the tail from collapsing symmetrically around the bacterium. Consequently, the bacterium experiences a sustained internal stress that drives it forward without the need for an external ratchet potential.

Beyond biological relevance, the model offers design principles for synthetic micromotors and bio‑mimetic devices. By engineering strong inter‑component attractions (e.g., DNA‑mediated binding or magnetic dipoles) together with steric constraints, one can create self‑assembled clusters that suppress rotation and maintain a shape bias, thereby achieving autonomous, super‑diffusive propulsion in a thermal environment.

The paper concludes that volume exclusion combined with elasticity provides a robust mechanism for directional transport in small, thermally fluctuating systems. It predicts how varying mechanical parameters modulates the length and intensity of the super‑diffusive phase, offering experimentally testable signatures. Future work is suggested to extend the model to three dimensions, incorporate anisotropic viscous media, and couple the mechanics explicitly to actin polymerization kinetics, which would bring the theory even closer to the complex reality of intracellular bacterial motility.