Emergence of unidirectionally propagating waves on bacterial biofilms.

(a-b) Optical imaging shows spiral, planar (a), and radially shrinking waves (b) propagating unidirectionally on biofilm surfaces. Left-right or radial symmetry is generally broken on growing biofilm surfaces. Scale bar 250 um. (c) Time response of optical scattering signal indicating the firing state of coupled pili dynamics. (d) Schematic representation of the coupling mechanism of pili on biofilm surfaces, modeled as an active solid. The oscillatory extension and retraction of pili act as active units. (e) Collective behavior of elastically coupled active biofilm surfaces characterized by local displacement (U) and pili polarization(P). Propagating waves remain localized on the surface and travel toward the direction of the sharp rising edge. f) Optical images of the leading edge of the growing biofilm with fingering instabilities. PN and PA14 show strong fingers compared to PAO1.

Numerical modeling of coupled pili dynamics as an active carpet.

(a-c) Numerical simulation results based on the nonreciprocal Kuramoto phase-field model. Nonreciprocal coupling term (α) among bacteria drives the emergence of spiral waves, while the excitability term (b) of the mechanical system induces pulsatile behavior. (d) Numerical simulations of local oscillation frequencies under varying conditions (α = 0, α = 0.2π, and b = 0.1π). (e) Experimental measurements of pulses on biofilm surfaces confirming pulsatile responses. (f-g) Numerical simulations of elastically coupled biofilm structures using the active solid model. Active solids exhibit large-scale spiral and planar wave formations. Displacement (U) and pili polarization (P) fields highlight the essential phase difference necessary for wave propagation and limit-cycle oscillations.

Controlling transitions between spiral, target, and planar waves.

(a-c) Numerical simulations illustrating transitions from spiral waves to target and planar waves. Pairs of spiral waves merge, forming topologically neutral target waves, which eventually give rise to planar waves dominating the biofilm surface. (d-f) Optical imaging of biofilm surfaces demonstrating similar transitions between spiral, target, and planar waves experimentally triggered by adding a water droplet. Red arrows indicate wave propagation direction. (g-i) Controlled recovery of spiral waves achieved by heating biofilm surfaces, removing excess moisture, and facilitating re-emergence of spiral waves.

Controlling dynamics of inward propagating waves.

(a) Optical imaging of inward propagating waves within a circular biofilm structure. (b) Period of pili oscillations decreases toward the colony center. (c) Application of a small droplet containing PEG creates a radially varying period profile, guiding inward wave propagation, capturing similar wave the dynamics on naturally growing radially symmetric biofilms. Error bar shows the S.D, N= 5 measurements.

Age-Dependent Dynamics of Oscillations.

a) Sample image showing multiple pairs of spiral waves on a uniform biofilm surface. Scale bar: 100 μm. b) Period of the oscillations increases as the biofilm ages. Error bar shows the S.D. N= 10 measurements.

Left-right symmetry breaking in naturally growing biofilms.

(a) Representative image of a bacterial biofilm at a late growth stage (3 days post-inoculation). Metachronal waves propagate towards the biofilm center, with the leading edge displaying chaotic dynamics. Following growth cessation, spiral waves gradually converge into planar waves propagating inward. (b) Oscillation period increases towards the biofilm center. Error bar indicates the S.D. N= 10 measurements (c-d) Numerical simulation demonstrating the formation of planar waves and the left-right symmetry-breaking process, driven by a spatially varying intrinsic oscillation frequency(d), capturing dynamics observed in naturally growing biofilms.

Temperature-Controlled Dynamics of Metachronal Waves and symmetry breaking.

a) Optical pulses from spiral waves on the biofilm surface as temperature increases from 21°C (TL) to 31°C (TH). b) An increase in temperature raises the oscillation frequency c, d) Controlling the propagation of the waves by creating a temperature gradient. Waves propagate from the warmer area (fast oscillating, TH) to the colder region (slow oscillating, TL). d) Reversing the temperature gradient changes the direction of propagations of the waves.

Asymmetric surface deformation drives directional propagation.

OCC imaging provides clear dark and bright optical contrasts, originating from oblique illumination and asymmetric scattering by surface waves. An oil droplet was used to investigate the shape-dependent propagation mechanism. Under oblique illumination, sharp rising edges generate dark contrasts, while falling edges create bright contrasts. Sharp edges correspond to rapid pili retraction, followed by gradual recovery.

GFP labeling and extracellular DNA staining were used to verify the origin of the optical scattering, specifically to distinguish between surface versus bulk oscillations in the biofilm.

Neither fluorescence imaging method revealed oscillatory signals. Simultaneously recorded gray signals, indicating the presence of original waves on the biofilm, were superimposed for comparison.

In PA14 strains, mutations in pilB and fliK were introduced to identify the processes responsible for driving the oscillations.

The pilB mutation abolished wave formation, whereas wave emergence persisted in the fliK mutant, which lacks functional flagella.

The PAO1 strain did not generate surface waves.

Additionally, the hyperpiliated pilH mutant also failed to exhibit oscillatory wave behavior.

Regular LB plates do not provide sufficient conditions for wave generation in PN.

However, eliminating yeast extract and replacing tryptone with a low concentration (0.2×) peptone restored wave formation.

Comparative analysis of the genomic region encoding pili subunit groups reveals that PA14 contains Group 3 pili, while PN exhibits a Group 4 and 5-like structure.

Both strains also encode accessory proteins associated with unknown pilus function.

Optical and thermal images of an NGM plate equipped with metallic pipes.

A closed-loop water pumping-heating system was used to control the local temperature and create a temperature gradient between the pipes. The spacing between the pipes was varied to identify the optimal gradient profile.

List of strains used in this study.