Article Figures and data Abstract Editor's evaluation Introduction Results Discussion Materials and methods Appendix 1 Data availability References Decision letter Author response Article and author information Metrics Abstract Long-range material transport is essential to maintain the physiological functions of multicellular organisms such as animals and plants. By contrast, material transport in bacteria is often short-ranged and limited by diffusion. Here, we report a unique form of actively regulated long-range directed material transport in structured bacterial communities. Using Pseudomonas aeruginosa colonies as a model system, we discover that a large-scale and temporally evolving open-channel system spontaneously develops in the colony via shear-induced banding. Fluid flows in the open channels support high-speed (up to 450 µm/s) transport of cells and outer membrane vesicles over centimeters, and help to eradicate colonies of a competing species Staphylococcus aureus. The open channels are reminiscent of human-made canals for cargo transport, and the channel flows are driven by interfacial tension mediated by cell-secreted biosurfactants. The spatial-temporal dynamics of fluid flows in the open channels are qualitatively described by flow profile measurement and mathematical modeling. Our findings demonstrate that mechanochemical coupling between interfacial force and biosurfactant kinetics can coordinate large-scale material transport in primitive life forms, suggesting a new principle to engineer self-organized microbial communities. Editor's evaluation Congratulations on a very nice study. We see the discovery of the formation of large self-organized canals within bacterial colonies as a fascinating phenomenon. Furthermore, your thorough analysis describing the capacity of bacteria to employ these canals for rapid long-distance intercellular transportation has major implications for our understanding of bacterial cooperation. We are delighted to have the opportunity to present your fundamental findings to the scientific community. https://doi.org/10.7554/eLife.79780.sa0 Decision letter Reviews on Sciety eLife's review process Introduction Long-range directed material transport is essential to maintain the physiological functions of multicellular organisms; it helps an organism to transport nutrients, metabolic wastes, and signaling molecules, translocate differentiated sub-populations through the body, and maintain pH or temperature homeostasis. Long-range directed transport in multicellular qorganisms is primarily driven by pressure-induced advection and coordinated cilia beating. For example, hydraulic pressure due to active pumping drives the circulation of body fluid in blood and lymph vessel systems of animals (Scallan et al., 2016); transpiration and capillary pressure passively drive the water transport through vascular tissues of plants (Sack and Holbrook, 2006) and cilia beating of epithelial cells drives the cerebrospinal fluid flow in brain ventricles (Faubel et al., 2016) as well as mucus flow in the respiratory tract (Huang and Choma, 2015). Like in animals and plants, any form of long-range directed material transport would undoubtedly bring profound effect to the development, structure, and stress response of bacterial communities. Establishing autonomous long-range material transport will be of particular importance to maintain and control the physiology of engineered functional living materials consisting of large-scale synthetic microbial consortia (Chen et al., 2015b; Rodrigo-Navarro et al., 2021). However, material transport in bacterial world is often short-ranged and limited by diffusion (either passive diffusion due to thermal energy or active diffusion due to self-propulsion of motile cells; Wu and Libchaber, 2000). At the single-cell level, diffusion governs nutrient uptake and sets a fundamental limit on the size of bacterial cells (Berg, 1993; Nelson, 2003; Schulz and Jorgensen, 2001). In bacterial communities, diffusion has been assumed to dominate material transport (Lavrentovich et al., 2013; Pirt, 1967; Shao et al., 2017); long-range directed material transport is deemed unusual, despite the notion that bacterial communities resemble multicellular organisms in many aspects such as coordinated metabolism, communication, and division of labor (Lee et al., 2017; Parsek and Greenberg, 2005; Shapiro, 1998; van Gestel et al., 2015). Intriguingly, a few examples of long-range directed transport in bacterial communities were reported in recent years. Among these examples, it was shown that long-range flows were driven by flagellar motility in sediment biofilms (Fenchel and Glud, 1998; Petroff and Libchaber, 2014) and in bacterial colonies (Wu et al., 2011; Xu et al., 2019), with a typical flow speed comparable to the swimming speed of individual cells; directed transport can also be driven by passive forces such as osmosis and evaporation-induced pressure gradient (Wilking et al., 2013; Wu and Berg, 2012), with a speed of ~0.1–10 µm/s. Nonetheless, these forms of directed material transport all appear to lack autonomous regulation at the community level; the transport is either passive (Wilking et al., 2013; Wu and Berg, 2012) or driven by locally interacting cells (Fenchel and Glud, 1998; Petroff and Libchaber, 2014; Wu et al., 2011; Xu et al., 2019). Intra-colony channel structures have been identified in a few bacterial species (Davey et al., 2003; Drury et al., 1993; Rooney et al., 2020; Stoodley et al., 1994; Xu et al., 2019); these channel structures have a typical persistence length of a few micron to tens of microns, thus not able to support directed transport beyond millimeter scale. In general, active or autonomous long-range directed transport would require a spatially or temporally regulated source of driving force. For bacterial communities, interfacial tension may potentially offer such a driving force because many bacterial species synthesize biosurfactants (i.e., surface active agents that reduce interfacial energy or surface tension Chandler, 1987) in a tightly regulated manner (Ron and Rosenberg, 2001). Here, we report a unique form of active long-range directed transport in structured bacterial communities enabled by spatial-temporal control of interfacial force. Using Pseudomonas aeruginosa colonies as a model system (Ramos et al., 2010), we discovered that large-scale, time-evolving open channels spontaneously emerge in the colony; these centimeter-long channels with a free surface are referred to as ‘bacterial canals.’ Fluid flows in the bacterial canals support high-speed (up to 450 µm/s) transport of cells and outer membrane vesicles (OMVs) over centimeters and help to eradicate colonies of a competing species Staphylococcus aureus. The canal flows are driven by surface tension gradient mediated by the P. aeruginosa-produced biofurfactant rhamnolipids, and the canals presumably emerge via a complex-fluid phenomenon known as shear-induced banding (Divoux et al., 2016; Olmsted, 2008). Overall, our findings demonstrate that mechanochemical coupling between interfacial force and biosurfactant kinetics can coordinate large-scale material transport in primitive life forms, suggesting a new principle to design macroscopic patterns and functions of synthetic microbial communities (Brenner et al., 2008; Chen et al., 2015a; Kong et al., 2018; Luo et al., 2021; Miano et al., 2020). Results P. aeruginosa colonies establish large-scale open channels supporting directed fluid transport We cultured P. aeruginosa PA14 colonies on M9DCAA agar plates (‘Methods’). In the colonies of wildtype and pilB-knockout mutant (PA14 ΔpilB; denoted as non-piliated mutant), we were intrigued to observe rapid cellular flows streaming through the interior of the colonies, while there was little collective directed motion on both sides of the streams (Video 1). The streams were tens of microns in width and up to millimeters in length, but their courses were highly unstable presumably due to continuous disruption by cellular motion driven by flagellar motility. On the other hand, for PA14 mutants without flagellar motility, namely, PA14 flgK::Tn5 ΔpilA (with both flagellar motility and type IV pilus-mediated motility disabled; denoted by ‘non-motile P. aeruginosa’) (Beaussart et al., 2014) and PA14 flgK::Tn5 (without flagellar motility but with functional type IV pilus-mediated motility; denoted by ‘piliated P. aeruginosa’) (Lee et al., 2011; ‘Methods’), we observed by naked eyes that the colonies of both strains presented many low-cell-density valleys extending from colony center to the edge over centimeters with high directional persistence (Figure 1A–D). Under the microscope, we found that these remarkable, centimeter-long valleys were fluid-filled, free-surface channels (i.e., open channels) ~5–10 µm in height and tens to several hundred µm in width, in which cells carried by the fluid flow streamed rapidly at speeds up to hundreds of µm/s in coherent directions (Figure 1E, Appendix 1—figure 1A, Figure 1—video 1). The fluid flow in channels on average went towards the colony edge and stopped abruptly at the very end (i.e., the tip) of a channel, disappearing into the dense layer of cells near the edge (Appendix 1—figure 1B). The fluid flow was sensitive to water content in the air environment, and it was easily disrupted by decrease of humidity. Cells translocating along the channels eventually settled in near the colony edge and they may contribute to colony expansion; however, channel formation does not necessarily coincide with colony expansion (e.g., see ‘Discussion’). Nearby channels could merge with each other while individual channels could split, resulting in a large-scale channel network across the entire colony (Figure 1B and D). These large-scale open channels have a free upper surface, and therefore, they are distinct from the pipe-like closed channels or conduits previously reported in bacterial colonies (Drury et al., 1993; Rooney et al., 2020; Stoodley et al., 1994; Xu et al., 2019). The open channels we found here are reminiscent of human-made canals for cargo transport, so we refer to these open channels as ‘bacterial canals.’ Figure 1 with 2 supplements see all Download asset Open asset Large-scale open channels in non-flagellated P. aeruginosa colonies support directed fluid transport. (A) Colony morphology of non-motile P. aeruginosa (PA14 flgK::Tn5 ΔpilA). The arrow indicates the position where the image in panel (E) was taken. (B) Sketch of the open channels in panel (A) for better visualization. (C) Colony morphology of piliated P. aeruginosa (PA14 flgK::Tn5). (D) Sketch of the open channels in panel (C) for better visualization. Scale bars in A–D, 1 cm. (E) Phase-contrast microscopy image of an open channel with cellular flows in a non-motile P. aeruginosa (PA14 flgK::Tn5 ΔpilA) colony, taken at the location indicated by the arrow in panel (A). Arrows indicate flow direction. Scale bar, 100 μm. Cellular flows in the open channel are better visualized in Figure 1—video 1 because the contrast between the open channel and other regions is low in still images. (F) Time-lapse image sequence showing the development of open channels in branching colonies of piliated P. aeruginosa (PA14 flgK::Tn5). Scale bar, 1 cm. Also see Figure 1—video 2. Video 1 Download asset This video cannot be played in place because your browser does support HTML5 video. You may still download the video for offline viewing. Download as MPEG-4 Download as WebM Download as Ogg Rapid cellular flow streaming through a non-piliated P. aeruginosa (PA14 ΔpilB) colony. Cells are motile outside the stream. Microscopically, the bacterial canals observed in non-motile (PA14 flgK::Tn5 ΔpilA) and piliated (PA14 flgK::Tn5) P. aeruginosa colonies are similar to the unstable streams observed in wildtype P. aeruginosa (PA14) and non-piliated mutant (PA14 ΔpilB) colonies, but the former have more stable courses and are thus able to support sustained long-range directed fluid transport. For this reason, and to exclude any potential contribution of flagellar motility to material transport (Wu et al., 2011; Xu et al., 2019), we focused on bacterial canals in this study. When the amount of surface water on agar plates was reduced by extended drying (‘Methods’), the piliated P. aeruginosa (PA14 flgK::Tn5) colonies displayed a unique branching morphology presumably driven by fingering instability in the presence of surface tension gradient in the colony (Trinschek et al., 2018; Troian et al., 1989; Figure 1F). Interestingly each branch was highly directed and hosted a single canal that ran through the entire branch (Figure 1F, Figure 1—video 2; Appendix 1—figure 1C). The emergence of canals in such branching colonies occurred robustly at ~8 hr (at 30°C) or ~15 hr (at room temperature) after inoculation. Since canals in the branching colonies advanced in a predictable manner without merging, hereinafter we systematically characterized canal development and manipulated this process using branching colonies of piliated P. aeruginosa (PA14 flgk::Tn5). Canal development requires rhamnolipids and is driven by surface tension gradient P. aeruginosa produces the well-characterized biofurfactant (i.e. surface active agents that reduce interfacial energy or surface tension; Chandler, 1987) rhamnolipids (Lang and Wullbrandt, 1999; Müller et al., 2012). Since canal development does not require cell motility, we hypothesized that surface tension gradient (i.e., Marangoni stress; Davey et al., 2003) mediated by rhamnolipids provided the driving force for fluid transport in canals; note that the canal flows cannot be driven by osmotic pressure because osmolarity gradients of cell products (hence the resultant osmotic flows) must be directing toward the colony center. As in situ measurement of rhamnolipid concentration or surface tension within colonies and canals is challenging, to examine our hypothesis, we chose to knock out rhlA gene (encoding a rhamnosyltransferase essential for the production of rhamnolipids; Ochsner et al., 1994) in pilated P. aeruginosa (‘Methods’). We found that this rhamnolipid-deficient mutant (PA14 flgK::Tn5 ΔrhlA) was unable to develop canals (Figure 2A); also the colony showed no sign of any mesoscale flows under the microscope. Next, to show that Marangoni stress could drive canal formation, we established artificial surface tension gradient in colonies by injecting an exogenous source of rhamnolipids via a programmable syringe pump (‘Methods’), and it restored canal formation in colonies of the rhamnolipid-deficient mutant (Figure 2B). We note that the artificial surface tension gradient also promoted colony expansion (Figure 2B), but again canal formation does not necessarily coincide with colony expansion (see ‘Discussion’). On the other hand, to examine whether canal formation involves agar degradation due to any potential agarase or hydrolase activities, we measured the height profile of the colony and agar with laser scanning confocal microscopy (‘Methods’). We found that while the colony thickness above agar had an abrupt drop near canals, the height of agar under canals and other regions of the colony was uniform and there was no sign of agar degradation (Appendix 1—figure 2). Taken together, these results show that canal development requires rhamnolipids but not agar degradation, and they provide strong evidence that fluid flows in canals are driven by rhamnolipids-mediated surface tension gradient. Figure 2 Download asset Open asset Role of rhamnolipids in canal development. (A) Image of a representative colony of the rhamnolipid-deficient mutant (PA14 flgK::Tn5 ΔrhlA) after 20 hr growth. The colony failed to develop canals and microscopic flows. (B) Surface tension gradient established by 1 hr injection of exogenous rhamnolipids at the colony center following 20 hr growth (schematics shown as left panel; ‘Methods’) restored the formation of canals (right panel). Scale bars in (A, B), 1 cm. (C) Fluorescence image sequences showing promoter activity of rhamnolipid synthesis at the early stage of canal development. The images were taken at the center of representative canal-forming P. aeruginosa colonies (PA14 flgK::Tn5) grown at room temperature. The upper row shows GFP(ASV) fluorescence from the rhamnolipid synthesis reporter PrhlA-gfp(ASV) (‘Methods’), and the lower row shows red fluorescence of the membrane dye FM 4-64, which serves as a proxy of cell number in the colony. Scale bar, 1 mm. (D) Temporal dynamics of rhamnolipid synthesis level measured by the fluorescence of PrhlA-gfp(ASV) reporter during canal development. Solid and dashed lines represent the overall fluorescence count of the rhamnolipid synthesis reporter and the FM 4-64 dye, respectively (‘Methods’). The colony started to expand at T = ~10 hr, and the expansion caused a slight drop of overall FM 4-64 fluorescence count during T = ~10–12 hr. Three replicate experiments were performed, and they showed the same temporal dynamics. When we applied a counteracting surface tension gradient directing toward the colony center by placing an agar patch containing surfactant Tween 20 (50 mg/mL, surface tension ~4 × 10-2 N/m) ~1 cm in front of a colony branch, fluid flows in the canal gradually ceased and the canal (but not the colony branch) slowly retracted (Video 2; ‘Methods’), suggesting that the driving force of canal flows is comparable in magnitude to that provided by a surface tension gradient of ~ 103 mN·m–2. Moreover, using a previously developed fluorescence reporter PrhlA-gfp(ASV) for rhamnolipids synthesis (Yang et al., 2009) GFP-ASV is a short-lived derivative of GFP and its fluorescence intensity reflects the current rate of biosynthesis (Andersen et al., 1998; ‘Methods’), we found that the rhlA promoter activity was azimuthally symmetric in early-stage colonies and the overall PrhlA-gfp(ASV) fluorescence increased monotonically until canals emerged (Figure 2C and D). The result shows that rhamnolipids in the colony center were continuously synthesized, thus generating a radial gradient of surface tension. Video 2 Download asset This video cannot be played in place because your browser does support HTML5 video. You may still download the video for offline viewing. Download as MPEG-4 Download as WebM Download as Ogg Effect of externally applied counteracting surface tension gradient on fluid transport in canals. An agar patch infused with surfactant Tween 20 (50 mg/mL) was placed at ~1 cm in front of a colony branch of piliated P. aeruginosa (PA14 flgK::Tn5); see ‘Methods’. As shown in the video, immediately following this operation, fluid flows in the canal gradually ceased and the canal slowly retracted. Time label shows the elapsed time from placing the agar patch (mm:ss). Flow profiles reveal shear-induced banding and surface tension distribution during canal development The temporal dynamics of fluorescence reporter PrhlA-gfp(ASV) described in Figure 2D indicated continuous accumulation of rhamnolipids in the colony center, which would generate a radial surface tension gradient with azimuthal symmetry at the initial stage of canal development. It is then intriguing why rapid flows only emerge in certain regions of the colony (i.e., in canals), even though at the initial stage of canal development every part of the colony at the same distance to the colony center should experience similar Marangoni stress; for instance, canals had already emerged while the colony was still nearly symmetric at T = 15 hr in Figure 2C. Flow speed measurement by particle image velocimetry (PIV) analysis (‘Methods’) in colonies before canals became visible to naked eyes revealed that the flow speed profile in regions with homogeneous cell density distribution displayed flow regimes with distinct shear rates (Figure 3A and B, Figure 3—video 1; ‘Methods’). The course of those high-shear-rate domains were initially unstable (Figure 3C, 0–24 min) and similar to the unstable streams observed in wildtype P. aeruginosa (PA14) and non-piliated mutant (PA14 ΔpilB) colonies; as time went by, fluid flows in the high shear domains carried away cells in nearby areas, and the course got widened and gradually became fixed canals (Figure 3C, 32–56 min, Figure 3—video 2). The presence of distinct flow regimes under presumably uniform shear stress (Figure 3A and B) and the instability of flow courses (Figure 3C) are hallmarks of shear-induced banding, a phenomenon often seen in complex fluids (Divoux et al., 2016; Olmsted, 2008; Ovarlez et al., 2009). These results suggest that canals emerge via the onset of shear-induced banding in the colony fluids (see more in ‘Discussion’). Figure 3 with 2 supplements see all Download asset Open asset Shear-induced banding during canal development and flow speed profile in canals. (A) Collective velocity field of cells in a region with homogeneous cell density distribution prior to canal formation. The collective velocity field was measured by particle image velocimetry (PIV) analysis on phase-contrast image sequence and averaged over a time window of 4 s (‘Methods’). Arrows in left panel and colormap in right panel represent collective velocity direction and magnitude, respectively. The velocity direction field in left panel is superimposed onto the phase-contrast image of this region. Both panels share the same scale bar (100 µm). Also see Figure 3—video 1. (B) Probability distributions of phase-contrast image intensity (upper panel) and flow speed (lower panel) associated with panel (A). Unimodal distribution of phase-contrast intensity indicates a homogeneous distribution of cell density. The bimodal distribution of flow speeds shows the occurrence of a high-speed flow regime. (C) Image sequence showing the course of a developing canal in a colony. Cells in the colony hosted the GFP-reporter plasmid expressing PrhlA-gfp(ASV) and the colony was imaged by fluorescence microscopy (‘Methods’). The course of the canal (across the center of each image) had lower cell density due to flushing by rapid flows and thus appeared darker than other areas. The red trace in each image starting from T = 8 min indicates the course of the canal in the previous image (8 min earlier). Scale bar, 125 µm. Also see Figure 3—video 2. (D) The fluorescence image of a canal in a P. aeruginosa colony seeded with ~1% GFP-expressing cells. The image was taken at a distance of ~12.5 mm from the tip of a canal. Colored traces show the trajectories of 38 fluorescent cells being transported in the canal, which were recorded during 0.5 s exposure time of a single image frame. Scale bar, 100 μm. Different colors serve to distinguish trajectories of different cells. (E) Peak flow speed at different locations of canals. The horizontal axis indicates the distance from the canal tips to the measuring position. Horizontal error bars indicate the uncertainty of canal position measurement (1 mm). Vertical error bars indicate the full range of peak speeds measured from >20 cell trajectories. Data from independent experiments are presented in different colors. After the onset of canals, due to the coupling of rhamnolipid transport, cellular transport and quorum-sensing (QS) (Mukherjee and Bassler, 2019) regulation of rhamnolipid synthesis (Lang and Wullbrandt, 1999; Müller et al., 2012), rhamnolipid distribution or surface tension along the canals may vary in space and time, giving rise to a complex and dynamic profile of surface tension gradient that drives fluid flows in canals. To characterize the spatial distribution of surface tension gradient, we sought to measure the flow speed profile in canals because flow speed is linearly proportional to Marangoni stress. PIV analysis as performed in Figure 3A can only yield the spatially averaged collective speed, so we switched to local velocity measurement with fluid tracers. In order to avoid perturbing canal flows by introducing external fluid tracers, we took advantage of the fact that some cells being transported along the canals were well isolated from others and these isolated cells could be used as natural fluid tracers. We seeded the colony with a small proportion of GFP(ASV)-expressing cells (PA14 flgK::Tn5 PlasB-gfp(ASV); ‘Methods’), and measured the flow speed in canals by tracking the movement of these fluorescent cells. The speed of cells being transported by canals were too fast to resolve cellular positions in a single-image frame, so we computed the time-averaged speed of cells based on the long-exposure-time trajectories of cells in order to reduce the error in speed measurement (Figure 3D; ‘Methods’). The speed of these cells varied significantly along a canal cross section; it peaked near the canal center and was attenuated near the canal boundaries. We found that the time-averaged peak cell speed near the center of canals was ~200 µm/s (with transient speeds up to 450 µm/s) (Figure 3D), higher than other reported forms of bacterial long-range directed transport (Fenchel and Glud, 1998; Petroff and Libchaber, 2014; Wilking et al., 2013; Wu et al., 2011; Xu et al., 2019) and most forms of active bacterial motility (Mitchell and Kogure, 2006). Note that the type IV pilus-mediated motility did not contribute to the movement of these isolated cells being transported in canals since type IV pilus-mediated motility requires surface attachment and the resultant speed is only a few µm/s (Talà et al., 2019), so the movement of cells indeed followed fluid motion in canals. We further measured the peak flow speed at different locations of canals. As shown by the plateau in Figure 3E, we found a high-flow-speed region spanning ~20 mm from the canal tip toward the colony center, and the flow speed diminished further toward the colony center. This result reveals the spatial distribution of Marangoni stress and suggests that the surface tension near the colony center has decreased to a steady-state level, presumably due to the saturated concentrations of rhamnolipids there. Spatial-temporal dynamics of fluid transport in canals Measuring the speed profile as shown in Figure 3E along a typical ~3-cm-long canal is challenging; it requires scanning over at least ~10 locations, with each location taking ~5 min and the entire measurement taking >~1 hr (‘Methods’). The trade-off between the large spatial scale of canals (centimeters) and the microscopic nature of speed-profile measurement makes it even more difficult to measure the temporal evolution of canal flows in experiment, so we resorted to mathematical modeling for understanding the spatial-temporal dynamics of canal flows. First of all, we used finite-element simulation of Navier–Stokes equation in a simplified canal geometry (Figure 4A; ‘Methods’) to estimate that the Marangoni stress in canals was on the order of ~1000 mN·m–2 in order to support a peak flow speed of ~400 µm/s. This magnitude roughly corresponds to the surface tension gradient established between a saturated source of rhamnolipids (surface tension ~30 mN/m; Appendix 1—figure 3) and a surfactant-free region (surface tension ~70 mN/m; Appendix 1—figure 3) over a distance of ~4 cm, which is consistent with the notion that the colony center has saturated concentrations of rhamnolipids as revealed in Figure 3E. Figure 4 Download asset Open asset Modeling fluid transport and spatial-temporal dynamics of surface tension gradient in canals. (A) Hydrodynamic simulation of fluid transport in a simplified canal geometry. The cross-sectional profile of the canal was modeled as a half ellipse with the major and minor axis being 150 μm and 10 μm, respectively. Note that the vertical and horizontal length scales are different. Red arrows indicate the direction of surface tension gradient ∇γ. Black arrows and colormap show the surface and the bulk flow speed profiles, respectively, generated by a surface tension gradient of 1000 mN∙m-2 imposed at the canal’s upper surface (liquid–air boundary). (B) Schematic showing the key processes involved in the establishment of surface tension gradient in canals. Major constituents of the colony are represented by symbols of different colors: surfactant molecules, orange dots; QS molecule, blue dots; cells, green rods. The key processes are labeled by numbers: ‘1,’ transport of bacteria and biosurfactant at the liquid–air interface driven by surface tension gradient ∇γ; ‘2,’ biosurfactant exchange between the liquid–air interface and the bulk phase; ‘3,’ growth of bacteria and the production of biosurfactant under QS regulation; ‘4,’ diffusion of biosurfactant, QS molecules, and nutrient. Arrows indicate the direction of material transport. (C) Schematic showing the coupling of the key processes described in panel (A) and in main text. See Appendix 1 for details. (D, E) Spatio-temporal dynamics of surface-associated surfactant concentration Γ and surface tension gradient ∇γ obtained by numerical simulations of the mathematical model, as shown in panels (D) and (E), respectively. Also see Appendix 1—figure 4 for the numerical result of the spatial-temporal evolution of other quantities in the model. We then built a model to describe the mechanochemical coupling between interfacial force and biosurfactant kinetics, which involve the transport processes of colony constituents (including rhamnolipids, cell mass, QS molecules and nutrients) and QS regulation of rhamnolipid synthesis (Figure 4B and C; Appendix 1). Surface tension (γ) is a function of surface density (Γ) of rhamnolipids at the liquid–air interface: (1) γ(Γ)=Πmaxexp(−AΓ2/Γc2)+γ∞

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