Geometry-driven collective ordering of bacterial vortices (1705.02136v3)

Abstract: Controlling the phases of matter is a challenge that spans from condensed materials to biological systems. Here, by imposing a geometric boundary condition, we study controlled collective motion of Escherichia coli bacteria. A circular microwell isolates a rectified vortex from disordered vortices masked in bulk. For a doublet of microwells, two vortices emerge but their spinning directions show transition from parallel to anti-parallel. A Vicsek-like model for confined self-propelled particles gives the point where two spinning patterns occur in equal probability and one geometric quantity governs the transition as seen in experiments. This mechanism shapes rich patterns including chiral configurations in a quadruplet of microwells, thus revealing a design principle of active vortices.

• The paper demonstrates that geometric confinement drives singular vortex formation in E. coli colonies, with a transition at a critical microwell radius of 37 µm.
• Experimental observations in doublet microwells reveal a switch from ferromagnetic to antiferromagnetic vortex pairing as the inter-circle distance surpasses 1.4 times the radius.
• A Vicsek-like theoretical model incorporating boundary-induced nematic interactions successfully predicts the phase transitions, highlighting implications for active matter design.

Geometry-driven Collective Ordering of Bacterial Vortices

The paper "Geometry-driven collective ordering of bacterial vortices" investigates the structured dynamic behavior of bacterial swarms under geometric confinement. Through a series of experiments and theoretical modeling, it demonstrates how geometric constraints can influence and control the ordering of vortical structures within bacterial colonies, specifically using Escherichia coli as the model organism. This research provides a fundamental understanding of the interaction between boundary conditions and collective motion in active matter systems, broadening our perception of phase transitions in biological contexts.

Experimental Observations

The paper employs a system of isolated microwells to confine E. coli bacteria in quasi-two-dimensional spaces. In these experiments, circular microwells facilitate the formation of singular vortical structures, proving that geometric constraints effectively isolate and define vortex formations that are otherwise hidden in turbulent bacterial suspensions. The authors identify a critical microwell radius ($R = 37 \, \mu m$) beyond which the motion transitions from a single oriented vortex to disordered turbulence. This critical size correlates with the bacterium-dependent characteristic diameter derived from energy spectra analyses.

The presence of elongated bacteria, treated with cephalexin (CEP), shifts the system's characteristic length scale, indicating how morphological changes in the bacteria influence vortex configurations. By varying microwell size, the researchers determine that the formation of a single vortex in bacterial colonies is contingent upon the microwell radius being less than the bacterial correlation length scale $l^*$.

Geometric Influence on Vortex Pairing

In exploring more complex geometrical constraints, the authors examine doublet microwells consisting of two overlapping circles. They identify two distinct collective states or phases: ferromagnetic vortices (FMV) and antiferromagnetic vortices (AFMV), dependent on the inter-circle distance $\Delta$ relative to the radius $R$. The FMV state—characterized by uniformly rotating vortices—transitions into the heterogeneous AFMV state as $\Delta$ surpasses a critical threshold, identified experimentally as $\Delta/R \approx 1.4$.

Theoretical Modeling

The paper elaborates on a Vicsek-like model for confined self-propelled particles to theoretically predict these empirical observations. Applying a mean-field approximation, the model incorporates boundary-induced nematic interactions to elucidate the mechanism driving these vortex pair transitions. The model successfully predicts the experimental transition point at $\phi_c = \pi/4$, aligning the experimental $\Delta_c/R$ to the theoretically obtained $\sqrt{2}$.

Implications and Future Directions

These findings have both practical and theoretical implications. Practically, understanding how geometry governs collective dynamic states in bacteria suggests avenues for designing bacterial transport systems or autonomous biochemical reactors. Theoretically, it reinforces the applicability of lattice models, similar to those used in magnetism and superconductivity, to biological systems—a step towards a generalized understanding of phase transitions in active matter.

Future research could leverage these results to explore vortex configurations in triplet or higher-order microwell systems, potentially uncovering new collective states under more complex boundary configurations. Additionally, studies might consider the hydrodynamic interplay in microbial environments to fine-tune the model or extend similar investigations to other active matter systems like cytoskeletons or colloidal suspensions.

In conclusion, this research delineates a clear connection between geometry, boundary conditions, and the collective dynamics of active matter, paving the way for improved control and utilization of biological systems and extending our understanding of phase transitions in active materials.