Controlling the synchronization and symmetry breaking of coupled bacterial pili on active biofilm carpets
- Department of Physics, Koç University, Turkiye
- Department of Physics, Undergraduate Program, Boğaziçi University, Turkiye
- Department of Materials, University of Manchester, United Kingdom
- Department of Electrical and Computer Engineering, Saint Louis University, United States
- Koç University Surface Science and Technology Center, Koç University, Turkiye
Figures
Figure 1 with 13 supplements
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 μm. (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. Red cylinders represent the bacteria in the biofilm. The oscillatory extension and retraction of pili act as active units. (e) Schematic representation of the collective behavior of elastically coupled active biofilm surfaces, characterized by local displacement (U) and pili polarization (P) undergoing limit-cycle oscillations. 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. Pseudomonas nitroreducens (PN) and PA14 show strong fingers compared to PAO1.
Figure 1—figure supplement 1
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.
Figure 1—figure supplement 2
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.
Figure 1—figure supplement 3
Image showing the elastic properties of the biofilm (Pseudomonas nitroreducens, PN) at the center of the colony.
The biofilm was elastically stretched using a sharp needle. Unlike the finger-forming colony edge, this elastic central region generates spiral waves.
Figure 1—figure supplement 4
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.
Figure 1—figure supplement 5
The PAO1 strain did not generate surface waves.
Additionally, the hyperpiliated pilH mutant also failed to exhibit oscillatory wave behavior.
Figure 1—figure supplement 6
Regular LB plates do not provide sufficient conditions for wave generation in Pseudomonas nitroreducens (PN).
However, eliminating yeast extract and replacing tryptone with a low concentration (0.2×) peptone restored wave formation.
Figure 1—figure supplement 7
Comparative analysis of the genomic region encoding pili subunit groups reveals that PA14 contains Group 3 pili, while Pseudomonas nitroreducens (PN) exhibits a Group 4 and 5-like structure.
Both strains also encode accessory proteins associated with an unknown pilus function.
Figure 1—video 1
Time-lapse imaging of active Pseudomonas nitroreducens biofilm surfaces generating metachronal waves.
Global left-right symmetry is broken, and merging spiral waves at the edge drive unidirectional planar waves toward the biofilm center. The wave wavelength is approximately 100 µm. Associated with Figure 1a.
Figure 1—video 2
Time-lapse imaging of circularly symmetric active biofilm surfaces generating inward-propagating metachronal waves.
Associated with Figure 1b.
Figure 1—video 3
High magnification (100×) time-lapse imaging of biofilm surfaces illustrating bacterial displacement and optical contrast changes.
Image size is 200 μm × 200 μm.
Figure 1—video 4
Time-lapse imaging of biofilm growth initiated from a single bacterium.
After growth cessation, dense regions begin firing first, and waves dominate the biofilm surface. Image size is .0.5mm × 0.5 mm.
Figure 1—video 5
Time-lapse imaging of fingering formation at the biofilm edge.
Bacteria remain motile and exhibit collective flow. Image size is 400 μm × 400 μm.
Figure 1—video 6
Time-lapse imaging of the biofilm center generating propagating waves.
Bacteria are attached to the surface; however, they periodically lift up and deform the surface, resembling Mexican-wave dynamics. Image size is 50 μm × 50 μm.
Figure 2 with 7 supplements
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.
Figure 2—figure supplement 1
Global order parameter as a function of time for reciprocally and nonreciprocally coupled oscillators.
Figure 2—figure supplement 2
Vector configuration around a topological defect, where the displacement vector changes direction.
Figure 2—figure supplement 3
Defect dynamics as a function of the control parameter.
(a) In the nonreciprocally coupled oscillator model, a large number of defects persist at high nonreciprocity, whereas at low nonreciprocity, oppositely charged (+/−) defect pairs annihilate. (b) In the active gel model, similarly, +/− defect pairs remain stable at high nonreciprocity, demonstrating consistent defect stabilization across both systems.
Figure 2—figure supplement 4
Separation between the defect pairs.
The annihilation of +/− defect pairs, defect separation strongly depends on the nonreciprocity coefficient of the system. At high nonreciprocity, the system can sustain closely separated defect pairs. This regime corresponds to the dry condition of the biofilm.
Figure 2—figure supplement 5
Simulation results of defect generation by introducing nonuniformities.
Figure 2—video 1
Numerical simulation using the nonreciprocal Kuramoto model.
Colors indicate oscillation phases. Spiral waves merge to form target waves, eventually converging into planar waves. Associated with Figure 2c.
Figure 2—video 2
Numerical simulation based on the active solid model.
Emergence of spiral and planar waves within the lattice. Associated with Figure 2e.
Figure 3 with 1 supplement
Controlling transitions between spiral, target, and planar waves.
(a) Experimentally observed transitions from spiral waves to target and planar waves spontaneously emerge across the plate. Pairs of spiral waves merge, forming topologically neutral target waves, which eventually give rise to planar waves dominating the biofilm surface. (b, c) Optical imaging of biofilm surfaces demonstrating similar controlled transitions between spiral, target, and planar waves experimentally triggered by adding a water droplet. Red arrows indicate wave propagation direction. (e–g) Controlled recovery of spiral waves achieved by heating biofilm surfaces, removing excess moisture, and facilitating re-emergence of spiral waves around specific inhomogeneities. Image size is 1 mm × 1 mm.
Figure 3—video 1
Time-lapse imaging of controlling the transition between waves to target and spiral by manipulating the moisture of biofilm surface.
Associated with Figure 3d–g.
Figure 4
Controlling dynamics of inward propagating waves.
(a) Optical imaging of inward propagating waves within a circular biofilm structure. Scale bar: 100 μm (b) Period of pili oscillations decreases toward the colony center. (c) Application of a small droplet containing polymer polyethylene glycol (PEG) creates a radially varying period profile, guiding inward wave propagation, capturing similar wave dynamics on naturally growing radially symmetric biofilms. Error bar shows the SD, N=5 measurements.
Figure 5
Age-dependent dynamics of oscillations.
(a) Sample image showing multiple pairs of spiral waves on a uniform biofilm surface. (b) Period of the oscillations increases as the biofilm ages. Error bar shows the SD, N=10 measurements. Image size is 1 mm × 1 mm.
Figure 6 with 2 supplements
Left-right asymmetry 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. Image size is 1 mm × 1 mm (b) Oscillation period increases towards the biofilm center. Error bar indicates the SD, 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.
Figure 6—video 1
Time-lapse imaging of a bacterial biofilm with broken left-right symmetry.
Associated with Figure 6.
Figure 6—video 2
Numerical simulation of propagating planar waves influenced by a frequency gradient.
Figure 7 with 4 supplements
Temperature-controlled dynamics of metachronal waves generating left-right asymmetry.
(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 propagation of the waves. Image size is 1 mm × 1 mm.
Figure 7—figure supplement 1
Optical and thermal images of a nematode growth media (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.
Figure 7—video 1
Numerical simulation of defect dynamics triggered by nonuniformities at low nonreciprocal conditions (α=0.1π).
Figure 7—video 2
Numerical simulation of defect generation triggered by nonuniformities at high (α=0.2π) nonreciprocal conditions.
Figure 7—video 3
Time-lapse imaging of controlling propagating planar waves under a varying temperature gradient.
Associated with Figure 7.
Author response image 1
Comparison between the elastic biofilm core and the motile colony edge.
Highresolution video recordings revealing individual bacterial motion highlight the key physical differences driving wave-generating. Time-lapse snapshots show that bacteria at the colony edge move freely and form fingering structures, whereas bacteria in the elastic central biofilm periodically lift vertically, producing a Mexican-wave–like collective motion across the surface. See new Video
Author response image 2
Critical order parameters of the coupled biofilm system.
(a) The Kuramoto global order parameter increases continuously as the system becomes globally synchronized. In contrast, in the nonreciprocally coupled system the order parameter saturates at a critical level. (b) In the experimentally observed biofilm, however the flux generated by the coupled oscillations provides a more appropriate measure of synchronization. Blue curves indicate directionally propagating planar waves, red curves correspond to spiral wave formation, and green curves represent the globally synchronized reciprocal system.
Author response image 3
Comparison of flux profiles of the simulations with experimental measurements.
Directional optical illumination enhances the flux term on the surface of the biofilm.
Author response image 4
Experimental observation showing that small surface nonuniformities on the biofilm surface trigger the formation of closely separated defect pairs.
Arrows indicate the position of the nonuniformities
Tables
Table 1
List of strains used in this study.
| Strain | Parent | Operation | Genotype |
|---|---|---|---|
| BAK132 | PN | Isolated from environmental samples, transformed pUCP18-MCSgfpmut3 | ampR |
| BAK133 | PA14 | Received from F. M. Ausubel lab | |
| BAK134 | LD2222 | Received from Lars Dietrich Lab (Hölscher et al., 2015) | PA14 ΔpilB |
| BAK135 | LD2221 | Received from Lars Dietrich Lab (Hölscher et al., 2015) | PA14 ΔflgK |
| BAK136 | PAO1 PilH | Received from Joanne Engel | ΔPilH |
| BAK | PAO1 | Received from DSMZ 10145GFP |
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Controlling the synchronization and symmetry breaking of coupled bacterial pili on active biofilm carpets
eLife 14:RP107609.
https://doi.org/10.7554/eLife.107609.3
