Modelling of surfactant-driven front instabilities in spreading bacterial colonies

Microscopic derivation of the thin film equation using the Mori-Zwanzig formalism

The hydrodynamics of thin films is typically described using macroscopic models whose connection to the microscopic particle dynamics is a subject of ongoing research. Existing methods based on density functional theory provide a good description of static thin films but are not sufficient for understanding nonequilibrium dynamics. In this work, we present a microscopic derivation of the thin film equation using the Mori-Zwanzig projection operator formalism. This method allows to directly obtain the correct gradient dynamics structure along with microscopic expressions for mobility and free energy. Our results are verified against molecular dynamics simulations for both simple fluids and polymers.

Active interface bulging in Bacillus subtilis swarms promotes self-assembly and biofilm formation

Microbial communities such as biofilms are commonly found at interfaces. However, it is unclear how the physical environment of interfaces may contribute to the development and behavior of surface-associated microbial communities. Combining multimode imaging, single-cell tracking, and numerical simulations, here, we found that activity-induced interface bulging promotes colony biofilm formation in Bacillus subtilis swarms presumably via segregation and enrichment of sessile cells in the bulging area. Specifically, the diffusivity of passive particles is ~50% lower inside the bulging area than elsewhere, which enables a diffusion-trapping mechanism for self-assembly and may account for the enrichment of sessile cells. We also uncovered a quasilinear relation between cell speed and surface-packing density that underlies the process of active interface bulging. Guided by the speed-density relation, we demonstrated reversible formation of liquid bulges by manipulating the speed and local density of cells with light. Over the course of development, the active bulges turned into striped biofilm structures, which eventually give rise to a large-scale ridge pattern. Our findings reveal a unique physical mechanism of biofilm formation at air-solid interface, which is pertinent to engineering living materials and directed self-assembly in active fluids.

Spontaneous Multi-scale Supramolecular Assembly Driven by Noncovalent Interactions Coupled with the Continuous Marangoni Effect

Reported herein is the multi-scale supramolecular assembly (MSSA) process along with redox reactions driven by supramolecular interactions coupled with the spontaneous Marangoni effect in ionic liquid (IL)-based extraction systems. The black powder, the single sphere with a black exterior, and the single colorless sphere were formed step by step at the interface when an aqueous solution of KMnO4 was mixed with the IL phase 1-(2-hydroxyethyl)-3-methylimidazolium bis(trifluoromethylsulfonyl) imide (C2OHmimNTf2) bearing octyl(phenyl)-N,N-diisobutylcarbamoylmethylphosphine oxide (CMPO). The mechanism of the whole process was studied systematically. The phenomena were related closely to the change in the valence state of Mn. The MnO4- ion could be reduced quickly to δ-MnO2 and further to Mn2+ slowly by the hydroxyl-functionalized IL C2OHmimNTf2. Based on Mn2+, Mn(CMPO)32+, elementary building blocks (EBBs), and [EBB]n clusters were generated step by step. The [EBB]n clusters with the large enough size that were transferred to the interface, together with the remaining δ-MnO2, assembled into the single sphere with a black exterior, driven by supramolecular interactions coupled with the spontaneous Marangoni effect. When the remaining δ-MnO2 was used up, the mixed single sphere turned completely colorless. It was found that the reaction site of C2OHmim+ with Mn(VII) and Mn(IV) was distributed mainly at the side chain with a hydroxyl group. The MSSA process presents unique spontaneous phase changes. This work paves the way for the practical application of the MSSA-based separation method developed recently. The process also provides a convenient way to observe in situ and characterize directly the continuous Marangoni effect.

Mechanical constraints to unbound expansion of B. subtilis on semi-solid surfaces

IMPORTANCE

How bacterial cells colonize new territory is a problem of fundamental microbiological and biophysical interest and is key to the emergence of several phenomena of biological, ecological, and medical relevance. Here, we demonstrate how bacteria stuck in a colony of finite size can resume exploration of new territory by aquaplaning and how they fine tune biofilm viscoelasticity to surface material properties that allows them differential mobility. We show how changing local interfacial forces and colony viscosity results in a plethora of bacterial morphologies on surfaces with different physical and mechanical properties.

Interplay of bulk soluble surfactants and interfacial kinetics governs the stability of two-layer channel flows

The linear stability of two-layer channel flows in the presence of bulk-soluble surfactants is investigated here, taking into account the rheological properties of the interface. The interfacial stresses are quantified using the Boussinesq-Scriven model, while the surfactant kinetics is assumed to follow the Frumkin isotherm, which accounts for their non-ideal behavior. Our results show that in general, the bulk solubility of surfactants has a stabilizing effect on the interface, both with and without the presence of inertia. On the other hand, the interfacial viscosities play a more complex role, depending on the viscosity ratios of the two fluids, the thickness of the fluid layers, the strength of the surface tension gradients, and the extent of inertia. We show that depending on the strength of inertia and the variability in the surface tension, the interfacial rheology may either stabilize or destabilize the base flow. However, for sufficiently small Reynolds numbers, the surface viscosity always has a stabilizing influence. Our results may be used to better design stable co-flow systems with applications in various processes such as surface coating, preparation of fluid lenses, as well as in a host of multi-purpose microfluidic devices.

Swarming of P. aeruginosa: Through the lens of biophysics

Swarming is a collective flagella-dependent movement of bacteria across a surface that is observed across many species of bacteria. Due to the prevalence and diversity of this motility modality, multiple models of swarming have been proposed, but a consensus on a general mechanism for swarming is still lacking. Here, we focus on swarming by Pseudomonas aeruginosa due to the abundance of experimental data and multiple models for this species, including interpretations that are rooted in biology and biophysics. In this review, we address three outstanding questions about P. aeruginosa swarming: what drives the outward expansion of a swarm, what causes the formation of dendritic patterns (tendrils), and what are the roles of flagella? We review models that propose biologically active mechanisms including surfactant sensing as well as fluid mechanics-based models that consider swarms as thin liquid films. Finally, we reconcile recent observations of P. aeruginosa swarms with early definitions of swarming. This analysis suggests that mechanisms associated with sliding motility have a critical role in P. aeruginosa swarm formation.

Geometrical control of interface patterning underlies active matter invasion

Interaction between active materials and the boundaries of geometrical confinement is key to many emergent phenomena in active systems. For living active matter consisting of animal cells or motile bacteria, the confinement boundary is often a deformable interface, and it has been unclear how activity-induced interface dynamics might lead to morphogenesis and pattern formation. Here, we studied the evolution of bacterial active matter confined by a deformable boundary. We found that an ordered morphological pattern emerged at the interface characterized by periodically spaced interfacial protrusions; behind the interfacial protrusions, bacterial swimmers self-organized into multicellular clusters displaying +1/2 nematic defects. Subsequently, a hierarchical sequence of transitions from interfacial protrusions to creeping branches allowed the bacterial active drop to rapidly invade surrounding space with a striking self-similar branch pattern. We found that this interface patterning is geometrically controlled by the local curvature of the interface, a phenomenon we denote as collective curvature sensing. Using a continuum active model, we revealed that the collective curvature sensing arises from enhanced active stresses near high-curvature regions, with the active length scale setting the characteristic distance between the interfacial protrusions. Our findings reveal a protrusion-to-branch transition as a unique mode of active matter invasion and suggest a strategy to engineer pattern formation of active materials.

Long-range alteration of the physical environment mediates cooperation between Pseudomonas aeruginosa swarming colonies

Pseudomonas aeruginosa makes and secretes massive amounts of rhamnolipid surfactants that enable swarming motility over biogel surfaces. But how these rhamnolipids interact with biogels to assist swarming remains unclear. Here, I use a combination of optical techniques across scales and genetically engineered strains to demonstrate that rhamnolipids can induce agar gel swelling over distances >10,000× the body size of an individual cell. The swelling front is on the micrometric scale and is easily visible using shadowgraphy. Rhamnolipid transport is not restricted to the surface of the gel but occurs through the whole thickness of the plate and, consequently, the spreading dynamics depend on the local thickness. Surprisingly, rhamnolipids can cross the whole gel and induce swelling on the opposite side of a two-face Petri dish. The swelling front delimits an area where the mechanical properties of the surface properties are modified: water wets the surface more easily, which increases the motility of individual bacteria and enables collective motility. A genetically engineered mutant unable to secrete rhamnolipids (ΔrhlA), and therefore unable to swarm, is rescued from afar with rhamnolipids produced by a remote colony. These results exemplify the remarkable capacity of bacteria to change the physical environment around them and its ecological consequences.

Exact solutions for viscous Marangoni spreading

When surface-active molecules are released at a liquid interface, their spreading dynamics is controlled by Marangoni flows. Though such Marangoni spreading was investigated in different limits, exact solutions remain very few. Here we consider the spreading of an insoluble surfactant along the interface of a deep fluid layer. For two-dimensional Stokes flows, it was recently shown that the nonlinear transport problem can be exactly mapped to a complex Burgers equation [D. Crowdy, SIAM J. Appl. Math. 81, 2526 (2021)]SMJMAP0036-139910.1137/21M1400316. We first present a very simple derivation of this equation. We then provide fully explicit solutions and find that varying the initial surfactant distribution-pulse, hole, or periodic-results in distinct spreading behaviors. By obtaining the fundamental solution, we also discuss the influence of surface diffusion. We identify situations where spreading can be described as an effective diffusion process but observe that this approximation is not generally valid. Finally, the case of a three-dimensional flow with axial symmetry is briefly considered. Our findings should provide reference solutions for Marangoni spreading that may be tested experimentally with fluorescent or photoswitchable surfactants.

Self-organized canals enable long-range directed material transport in bacterial communities

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.

Cellular Sensing Governs the Stability of Chemotactic Fronts

In contexts ranging from embryonic development to bacterial ecology, cell populations migrate chemotactically along self-generated chemical gradients, often forming a propagating front. Here, we theoretically show that the stability of such chemotactic fronts to morphological perturbations is determined by limitations in the ability of individual cells to sense and thereby respond to the chemical gradient. Specifically, cells at bulging parts of a front are exposed to a smaller gradient, which slows them down and promotes stability, but they also respond more strongly to the gradient, which speeds them up and promotes instability. We predict that this competition leads to chemotactic fingering when sensing is limited at too low chemical concentrations. Guided by this finding and by experimental data on E. coli chemotaxis, we suggest that the cells' sensory machinery might have evolved to avoid these limitations and ensure stable front propagation. Finally, as sensing of any stimuli is necessarily limited in living and active matter in general, the principle of sensing-induced stability may operate in other types of directed migration such as durotaxis, electrotaxis, and phototaxis.

Chemotactic smoothing of collective migration

Collective migration-the directed, coordinated motion of many self-propelled agents-is a fascinating emergent behavior exhibited by active matter with functional implications for biological systems. However, how migration can persist when a population is confronted with perturbations is poorly understood. Here, we address this gap in knowledge through studies of bacteria that migrate via directed motion, or chemotaxis, in response to a self-generated nutrient gradient. We find that bacterial populations autonomously smooth out large-scale perturbations in their overall morphology, enabling the cells to continue to migrate together. This smoothing process arises from spatial variations in the ability of cells to sense and respond to the local nutrient gradient-revealing a population-scale consequence of the manner in which individual cells transduce external signals. Altogether, our work provides insights to predict, and potentially control, the collective migration and morphology of cellular populations and diverse other forms of active matter.

Thin-film lubrication model for biofilm expansion under strong adhesion

Understanding microbial biofilm growth is important to public health because biofilms are a leading cause of persistent clinical infections. In this paper, we develop a thin-film model for microbial biofilm growth on a solid substratum to which it adheres strongly. We model biofilms as two-phase viscous fluid mixtures of living cells and extracellular fluid. The model explicitly tracks the movement, depletion, and uptake of nutrients and incorporates cell proliferation via a nutrient-dependent source term. Notably, our thin-film reduction is two dimensional and includes the vertical dependence of cell volume fraction. Numerical solutions show that this vertical dependence is weak for biologically feasible parameters, reinforcing results from previous models in which this dependence was neglected. We exploit this weak dependence by writing and solving a simplified one-dimensional model that is computationally more efficient than the full model. We use both the one- and two-dimensional models to predict how model parameters affect expansion speed and biofilm thickness. This analysis reveals that expansion speed depends on cell proliferation, nutrient availability, cell-cell adhesion on the upper surface, and slip on the biofilm-substratum interface. Our numerical solutions provide a means to qualitatively distinguish between the extensional flow and lubrication regimes, and quantitative predictions that can be tested in future experiments.

Use of Alternative Gelling Agents Reveals the Role of Rhamnolipids in Pseudomonas aeruginosa Surface Motility

Pseudomonas aeruginosa is a motile bacterium able to exhibit a social surface behaviour known as swarming motility. Swarming requires the polar flagellum of P. aeruginosa as well as the secretion of wetting agents to ease the spread across the surface. However, our knowledge on swarming is limited to observed phenotypes on agar-solidified media. To study the surface behaviour and the impact of wetting agents of P. aeruginosa on other surfaces, we assessed surface motility capabilities of the prototypical strain PA14 on semi-solid media solidified with alternative gelling agents, gellan gum and carrageenan. We found that, on these alternative surfaces, the characteristic dendritic spreading pattern of P. aeruginosa is drastically altered. One striking feature is the loss of dependence on rhamnolipids to spread effectively on plates solidified with these alternative gelling agents. Indeed, a rhlA-null mutant unable to produce its wetting agents still spreads effectively, albeit in a circular shape on both the gellan gum- and carrageenan-based media. Our data indicate that rhamnolipids do not have such a crucial role in achieving surface colonization of non-agar plates, suggesting a strong dependence on the physical properties of the tested surface. The use of alternative gelling agent provides new means to reveal unknown features of bacterial surface behaviour.

The spatial organization of microbial communities during range expansion

Microbes in nature often live in dense and diverse communities exhibiting a variety of spatial structures. Microbial range expansion is a universal ecological process that enables populations to form spatial patterns. It can be driven by both passive and active processes, for example, mechanical forces from cell growth and bacterial motility. In this review, we provide a taste of recent creative and sophisticated efforts being made to address basic questions in spatial ecology and pattern formation during range expansion. We especially highlight the role of motility to shape community structures, and discuss the research challenges and future directions.

Collective colony growth is optimized by branching pattern formation in Pseudomonas aeruginosa

Branching pattern formation is common in many microbes. Extensive studies have focused on addressing how such patterns emerge from local cell-cell and cell-environment interactions. However, little is known about whether and to what extent these patterns play a physiological role. Here, we consider the colonization of bacteria as an optimization problem to find the colony patterns that maximize colony growth efficiency under different environmental conditions. We demonstrate that Pseudomonas aeruginosa colonies develop branching patterns with characteristics comparable to the prediction of modeling; for example, colonies form thin branches in a nutrient-poor environment. Hence, the formation of branching patterns represents an optimal strategy for the growth of Pseudomonas aeruginosa colonies. The quantitative relationship between colony patterns and growth conditions enables us to develop a coarse-grained model to predict diverse colony patterns under more complex conditions, which we validated experimentally. Our results offer new insights into branching pattern formation as a problem-solving social behavior in microbes and enable fast and accurate predictions of complex spatial patterns in branching colonies.

An expanding bacterial colony forms a depletion zone with growing droplets

Many species of bacteria have developed effective means to spread on solid surfaces. This study focuses on the expansion of Pseudomonas aeruginosa on an agar gel surface under conditions of minimal evaporation. We report the occurrence and spread of a depletion zone within an expanded colony, where the bacteria laden film becomes thinner. The depletion zone is colocalized with a higher concentration of rhamnolipids, the biosurfactants that are produced by the bacteria and accumulate in the older region of the colony. With continued growth in population, dense bacterial droplets occur and coalesce in the depletion zone, displaying remarkable fluid dynamic behavior. Whereas expansion of a central depletion zone requires activities of live bacteria, new zones can be seeded elsewhere by adding rhamnolipids. These depletion zones due to the added surfactants expand quickly, even on plates covered by bacteria that have been killed by ultraviolet light. We explain the observed properties based on considerations of bacterial growth and secretion, osmotic swelling, fluid volume expansion, interfacial fluid dynamics involving Marangoni and capillary flows, and cell-cell cohesion.

Bacterial surface motility is modulated by colony-scale flow and granular jamming

Microbes routinely face the challenge of acquiring territory and resources on wet surfaces. Cells move in large groups inside thin, surface-bound water layers, often achieving speeds of 30 µm s^-1 within this environment, where viscous forces dominate over inertial forces (low Reynolds number). The canonical Gram-positive bacterium Bacillus subtilis is a model organism for the study of collective migration over surfaces with groups exhibiting motility on length-scales three orders of magnitude larger than themselves within a few doubling times. Genetic and chemical studies clearly show that the secretion of endogenous surfactants and availability of free surface water are required for this fast group motility. Here, we show that: (i) water availability is a sensitive control parameter modulating an abiotic jamming-like transition that determines whether the group remains fluidized and therefore collectively motile, (ii) groups self-organize into discrete layers as they travel, (iii) group motility does not require proliferation, rather groups are pulled from the front, and (iv) flow within expanding groups is capable of moving material from the parent colony into the expanding tip of a cellular dendrite with implications for expansion into regions of varying nutrient content. Together, these findings illuminate the physical structure of surface-motile groups and demonstrate that physical properties, like cellular packing fraction and flow, regulate motion from the scale of individual cells up to length scales of centimetres.

Active modulation of surfactant-driven flow instabilities by swarming bacteria

Models based on surfactant-driven instabilities have been employed to describe pattern formation by swarming bacteria. However, by definition, such models cannot account for the effect of bacterial sensing and decision making. Here we present a more complete model for bacterial pattern formation which accounts for these effects by coupling active bacterial motility to the passive fluid dynamics. We experimentally identify behaviors which cannot be captured by previous models based on passive population dispersal and show that a more accurate description is provided by our model. It is seen that the coupling of bacterial motility to the fluid dynamics significantly alters the phase space of surfactant-driven pattern formation. We also show that our formalism is applicable across bacterial species.

A thin-film extensional flow model for biofilm expansion by sliding motility

In the presence of glycoproteins, bacterial and yeast biofilms are hypothesized to expand by sliding motility. This involves a sheet of cells spreading as a unit, facilitated by cell proliferation and weak adhesion to the substratum. In this paper, we derive an extensional flow model for biofilm expansion by sliding motility to test this hypothesis. We model the biofilm as a two-phase (living cells and an extracellular matrix) viscous fluid mixture, and model nutrient depletion and uptake from the substratum. Applying the thin-film approximation simplifies the model, and reduces it to one-dimensional axisymmetric form. Comparison with Saccharomyces cerevisiae mat formation experiments reveals good agreement between experimental expansion speed and numerical solutions to the model withO ( 1 ) parameters estimated from experiments. This confirms that sliding motility is a possible mechanism for yeast biofilm expansion. Having established the biological relevance of the model, we then demonstrate how the model parameters affect expansion speed, enabling us to predict biofilm expansion for different experimental conditions. Finally, we show that our model can explain the ridge formation observed in some biofilms. This is especially true if surface tension is low, as hypothesized for sliding motility.

Rivalry in Bacillus subtilis colonies: enemy or family?

Two colonies of Bacillus subtilis of identical strains growing adjacent to each other on an agar plate exhibit two distinct types of interactions: they either merge as they grow or demarcation occurs leading to formation of a line of demarcation at the colony fronts. The nature of this interaction depends on the agar concentration in the growth medium and the initial separation between the colonies. When the agar concentration was 0.67% or lower, the two sibling colonies were found to always merge. At 1% or higher concentrations, the colonies formed a demarcation line only when their initial separation was 20 mm or higher. Interactions of a colony with solid structures and liquid drops have indicated that biochemical factors rather than the presence of physical obstacles are responsible for the demarcation line formation. A reaction diffusion model has been formulated to predict if two sibling colonies will form a demarcation line under given agar concentration and initial separation. The model prediction agrees well with experimental findings and generates a dimensionless phase diagram containing merging and demarcation regimes. The phase diagram is in terms of a dimensionless initial separation, d[combining macron], and a dimensionless diffusion coefficient, D[combining macron], of the colonies. The phase boundary between the two interaction regimes can be described by a power law relation between d[combining macron] and D[combining macron].

A multiphase theory for spreading microbial swarms and films

Bacterial swarming and biofilm formation are collective multicellular phenomena through which diverse microbial species colonize and spread over water-permeable tissue. During both modes of surface translocation, fluid uptake and transport play a key role in shaping the overall morphology and spreading dynamics. Here we develop a generalized two-phase thin-film model that couples bacterial growth, extracellular matrix swelling, fluid flow, and nutrient transport to describe the expansion of both highly motile bacterial swarms, and sessile bacterial biofilms. We show that swarm expansion corresponds to steady-state solutions in a nutrient-rich, capillarity dominated regime. In contrast, biofilm colony growth is described by transient solutions associated with a nutrient-limited, extracellular polymer stress driven limit. We apply our unified framework to explain a range of recent experimental observations of steady and unsteady expansion of microbial swarms and biofilms. Our results demonstrate how the physics of flow and transport in slender geometries serve to constrain biological organization in microbial communities.

Bacteria can grow and thrive in many different environments. Although we usually think of bacteria as single-celled organisms, they are not always solitary; they can also form groups containing large numbers of individuals. These aggregates work together as one super-colony, allowing the bacteria to feed and protect themselves more efficiently than they could as isolated cells.

These colonies move and grow in characteristic patterns as they respond to their environment. They can form swarms, like insects, or biofilms, which are thin, flat structures containing both cells and a film-like substance that the cells secrete. Availability of food and water influences the way colonies spread; however, since movement and growth are accompanied by mechanical forces, physical constraints are also important. These include the ability of the bacteria to change the water balance and their local mechanical environment, and the forces they create as they grow and move.

Previous research has used a variety of experimental and theoretical approaches to explain the dynamics of bacterial swarms and biofilms as separate phenomena. However, while they do differ biologically, they also share many physical characteristics.

Srinivasan et al. wanted to exploit these similarities, and use them to predict the growth and shape of biofilms and bacterial swarms under different conditions. To do this, a unified mathematical model for the growth of both swarms and biofilms was created. The model accounted for various factors, such as the transport of nutrients into the colony, the movement of water between the colony and the surface on which it grew, and mechanical changes in the environment (e.g. swelling/softening). The theoretical results were then compared with results from experimental measurements of different bacterial aggregates grown on a soft, hydrated gel. For both swarms and biofilms, the model correctly predicted how fast the colony expanded overall, as well as the shape and location of actively growing regions.

Biofilms and other bacterial aggregates can cause diseases and increase inflammation in tissues, and also hinder industrial processes by damage to submerged surfaces, such as ships and waterpipes. The results described here may open up new approaches to restrict the spreading of bacterial aggregates by focusing on their physical constraints.