Hydrodynamics of bacterial colonies: a model

Biophysical metabolic modeling of complex bacterial colony morphology

Microbial colony growth is shaped by the physics of biomass propagation and nutrient diffusion, and by the metabolic reactions that organisms activate as a function of the surrounding environment. While microbial colonies have been explored using minimal models of growth and motility, full integration of biomass propagation and metabolism is still lacking. Here, building upon our framework for Computation of Microbial Ecosystems in Time and Space (COMETS), we combine dynamic flux balance modeling of metabolism with collective biomass propagation and demographic fluctuations to provide nuanced simulations of E. coli colonies. Simulations produced realistic colony morphology, consistent with our experiments. They characterize the transition between smooth and furcated colonies and the decay of genetic diversity. Furthermore, we demonstrate that under certain conditions, biomass can accumulate along "metabolic rings" that are reminiscent of coffee-stain rings, but have a completely different origin. Our approach is a key step towards predictive microbial ecosystems modeling.

Single Nanoparticle Tracking Reveals Efficient Long-Distance Undercurrent Transport in Upper Fluid of Bacterial Swarms

Flagellated bacteria move collectively in a swirling pattern on agar surfaces immersed in a thin layer of viscous "swarm fluid," but the role of this fluid in mediating the cooperation of the bacterial population is not well understood. Herein, we use gold nanorods (AuNRs) as single particle tracers to explore the spatiotemporal structure of the swarm fluid. Individual AuNRs are moving in a plane of ∼2 μm above swarms, traveling for long distances in high speed without interferences from bacterial movements. The particles are lifted and transported by collective mixing of small vortices around bacteria during localized clustering and de-clustering of motile cells. Their motions fit the Lévy walk model, revealing efficient fluidic flows above the swarms. These flows provide obstacle-free highways for long-range material transportations, allow swarming bacteria to perform population-level communications, and imply the essential role of the fluid phase on the emergence of large-scale synergy.

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.

Ecology of Contaminant Biotransformation in the Mycosphere: Role of Transport Processes

Fungi and bacteria often share common microhabitats. Their co-occurrence and coevolution give rise to manifold ecological interactions in the mycosphere, here defined as the microhabitats surrounding and affected by hyphae and mycelia. The extensive structure of mycelia provides ideal "logistic networks" for transport of bacteria and matter in structurally and chemically heterogeneous soil ecosystems. We describe the characteristics of the mycosphere as a unique and highly dynamic bacterial habitat and a hot spot for contaminant biotransformation. In particular, we emphasize the role of the mycosphere for (i) bacterial dispersal and colonization of subsurface interfaces and new habitats, (ii) matter transport processes and contaminant bioaccessibility, and (iii) the functional stability of microbial ecosystems when exposed to environmental fluctuations such as stress or disturbances. Adopting concepts from ecological theory, the chapter disentangles bacterial-fungal impacts on contaminant biotransformation in a systemic approach that interlinks empirical data from microbial ecosystems with simulation data from computational models. This approach provides generic information on key factors, processes, and ecological principles that drive microbial contaminant biotransformation in soil. We highlight that the transport processes create favorable habitat conditions for efficient bacterial contaminant degradation in the mycosphere. In-depth observation, understanding, and prediction of the role of mycosphere transport processes will support the use of bacterial-fungal interactions in nature-based solutions for contaminant biotransformation in natural and man-made ecosystems, respectively.

Collective chemotaxis and segregation of active bacterial colonies

Still recently, bacterial fluid suspensions have motivated a lot of works, both experimental and theoretical, with the objective to understand their collective dynamics from universal and simple rules. Since some species are active, most of these works concern the strong interactions that these bacteria exert on a forced flow leading to instabilities, chaos and turbulence. Here, we investigate the self-organization of expanding bacterial colonies under chemotaxis, proliferation and eventually active-reaction. We propose a simple model to understand and quantify the physical properties of these living organisms which either give cohesion or on the contrary dispersion to the colony. Taking into account the diffusion and capture of morphogens complicates the model since it induces a bacterial density gradient coupled to bacterial density fluctuations and dynamics. Nevertheless under some specific conditions, it is possible to investigate the pattern formation as a usual viscous fingering instability. This explains the similarity and differences of patterns according to the physical bacterial suspension properties and explain the factors which favor compactness or branching.

Branching instability in expanding bacterial colonies

Self-organization in developing living organisms relies on the capability of cells to duplicate and perform a collective motion inside the surrounding environment. Chemical and mechanical interactions coordinate such a cooperative behaviour, driving the dynamical evolution of the macroscopic system. In this work, we perform an analytical and computational analysis to study pattern formation during the spreading of an initially circular bacterial colony on a Petri dish. The continuous mathematical model addresses the growth and the chemotactic migration of the living monolayer, together with the diffusion and consumption of nutrients in the agar. The governing equations contain four dimensionless parameters, accounting for the interplay among the chemotactic response, the bacteria-substrate interaction and the experimental geometry. The spreading colony is found to be always linearly unstable to perturbations of the interface, whereas branching instability arises in finite-element numerical simulations. The typical length scales of such fingers, which align in the radial direction and later undergo further branching, are controlled by the size parameters of the problem, whereas the emergence of branching is favoured if the diffusion is dominant on the chemotaxis. The model is able to predict the experimental morphologies, confirming that compact (resp. branched) patterns arise for fast (resp. slow) expanding colonies. Such results, while providing new insights into pattern selection in bacterial colonies, may finally have important applications for designing controlled patterns.

Mechanically driven branching of bacterial colonies

A continuum mathematical model with sharp interface is proposed for describing the occurrence of patterns in initially circular and homogeneous bacterial colonies. The mathematical model encapsulates the evolution of the chemical field characterized by a Monod-like uptake term, the chemotactic response of bacteria, the viscous interaction between the colony and the underlying culture medium and the effects of the surface tension at the boundary. The analytical analysis demonstrates that the front of the colony is linearly unstable for a proper choice of the parameters. The simulation of the model in the nonlinear regime confirms the development of fingers with typical wavelength controlled by the size parameters of the problem, whilst the emergence of branches is favored if the diffusion is dominant on the chemotaxis or for high values of the friction parameter. Such results provide new insights on pattern selection in bacterial colonies and may be applied for designing engineered patterns.

Laser-induced speckle scatter patterns in Bacillus colonies

Label-free bacterial colony phenotyping technology called BARDOT (Bacterial Rapid Detection using Optical scattering Technology) provided successful classification of several different bacteria at the genus, species, and serovar level. Recent experiments with colonies of Bacillus species provided strikingly different characteristics of elastic light scatter (ELS) patterns, which were comprised of random speckles compared to other bacteria, which are dominated by concentric rings and spokes. Since this laser-based optical sensor interrogates the whole volume of the colony, 3-D information of micro- and macro-structures are all encoded in the far-field scatter patterns. Here, we present a theoretical model explaining the underlying mechanism of the speckle formation by the colonies from Bacillus species. Except for Bacillus polymyxa, all Bacillus spp. produced random bright spots on the imaging plane, which presumably dependent on the cellular and molecular organization and content within the colony. Our scatter model-based analysis revealed that colony spread resulting in variable surface roughness can modify the wavefront of the scatter field. As the center diameter of the Bacillus spp. colony grew from 500 to 900 μm, average speckles area decreased two-fold and the number of small speckles increased seven-fold. In conclusion, as Bacillus colony grows, the average speckle size in the scatter pattern decreases and the number of smaller speckle increases due to the swarming growth characteristics of bacteria within the colony.

Micro-environmentally restricted cell growth dynamics - modeling considerations

Various modeling approaches have been applied to describe the rearrangement of immobilized cell clusters within the extracellular matrix. The cell rearrangement has been related with the micro-environmental restrictions to cell growth. Herein, an attempt is made to discuss and connect various modeling approaches on various time scales which have been proposed in the literature in order to shed further light to this complex phenomenon which induces micro-environmental restrictions to cell growth. The rearrangement is driven by internal stress generated within the cluster. The internal stress represents a consequence of the matrix rheological response to cell expansion. The rearrangement includes the interplay between the processes of: (1) single and collective cell migrations, (2) cell deformation and orientation, (3) decrease of cell-to-cell separation distances and (4) cell growth. It has been considered on two time scales: a short time scale (i.e. the rearrangement time) and a long time scale (i.e. the growing time). The results indicate that short and long times cell rearrangement induces energy dissipation. The dissipation provokes biological responses of cells which cause the resistance effects to cell growth. Deeper insight in the anomalous nature of the energy dissipation would be useful for understanding the biological mechanisms which causes the resistance effects to cell growth.

Dynamics of self-organized rotating spiral-coils in bacterial swarms

Self-propelled particles (SPP) exhibit complex collective motions, mimicking autonomous behaviors that are often seen in the natural world, but essentially are generated by simple mutual interactions. Previous research on SPP systems focuses on collective behaviors of a uniform population. However, very little is known about the evolution of individual particles under the same global influence. Here we show self-organized rotating spiral coils in a two-dimensional (2D) active system. By using swarming bacteria Vibrio alginolyticus as an ideal experimental realization of a well-controlled 2D self-propelled system, we study the interaction between ultra-long cells and short background active cells. The self-propulsion of long cells and their interactions with neighboring short cells leads to a self-organized, stable spiral rotational state in 2D. We find four types of spiral coils with two main features: the rotating direction (clockwise or counter-clockwise) and the central structure (single or double spiral). The body length of the spiral coils falls between 32 and 296 μm and their rotational speed is within a range from 2.22 to 22.96 rad s(-1). The dynamics of these spiral coils involves folding and unfolding processes, which require local velocity changes of the long bacterium. This phenomenon can be qualitatively replicated by a Brownian dynamics simulation using a simple rule of the propulsion thrust, imitating the reorientation of bacterial flagella. Apart from the physical and biological interests in swarming cells, the formation of self-organized spiral coils could be useful for the next generation of microfabrication.

Modeling the role of water in Bacillus subtilis colonies

We propose a simple cellular automaton model for the description of the evolution of a colony of Bacillus subtilis. The originality of our model lies in the fact that the bacteria can move in a pool of liquid. We assume that each migrating bacterium is surrounded by an individual pool, and the overlap of the latter gives rise to a collective pool with a higher water level. The bacteria migrate collectively when the level of water is high enough. When the bacteria are far enough from each other, the level of water becomes locally too low to allow migration, and the bacteria switch to a proliferating state. The proliferation-to-migration switch is triggered by high levels of a substance produced by proliferating bacteria. We show that it is possible to reproduce in a fairly satisfactory way the various forms that make up the experimentally observed morphological diagram of B. subtilis. We propose a phenomenological relation between the size of the water pool used in our model and the agar concentration of the substrate on which the bacteria migrate. We also compare experimental results from cutting the central part of the colony with the results of our simulations.

The relevance of conditional dispersal for bacterial colony growth and biodegradation

Bacterial degradation is an ecosystem service that offers a promising method for the remediation of contaminated soils. To assess the dynamics and efficiency of bacterial degradation, reliable microbial simulation models, along with the relevant processes, are required. We present an approach aimed at improving reliability by studying the relevance and implications of an important concept from theoretical ecology in the context of a bacterial system: conditional dispersal denoting that the dispersal strategy depends on environmental conditions. Different dispersal strategies, which either incorporate or neglect this concept, are implemented in a bacterial model and results are compared to data obtained from laboratory experiments with Pseudomonas putida colonies growing on glucose agar. Our results show that, with respect to the condition of resource uptake, the model's correspondence to experimental data is significantly higher for conditional than for unconditional bacterial dispersal. In particular, these results support the hypothesis that bacteria disperse less when resources are abundant. We also show that the dispersal strategy has a considerable impact on model predictions for bacterial degradation of resources: disregarding conditional bacterial dispersal can lead to overestimations when assessing the performance of this ecosystem service.

A bidirectional interface growth model for cranial interosseous suture morphogenesis

Interosseous sutures exhibit highly variable patterns of interdigitation and corrugation. Recent research has identified fundamental molecular mechanisms of suture formation, and computer models have been used to simulate suture morphogenesis. However, the role of bone strain in the development of complex sutures is largely unknown, and measuring suture morphologies beyond the evaluation of fractal dimensions remains a challenge. Here we propose a morphogenetic model of suture formation, which is based on the paradigm of Laplacian interface growth. Computer simulations of suture morphogenesis under various boundary conditions generate a wide variety of synthetic sutural forms. Their morphologies are quantified with a combination of Fourier analysis and principal components analysis, and compared with natural morphological variation in an ontogenetic sample of human interparietal suture lines. Morphometric analyses indicate that natural sutural shapes exhibit a complex distribution in morphospace. The distribution of synthetic sutures closely matches the natural distribution. In both natural and synthetic systems, sutural complexity increases during morphogenesis. Exploration of the parameter space of the simulation system indicates that variation in strain and/or morphogen sensitivity and viscosity of sutural tissue may be key factors in generating the large variability of natural suture complexity.

Generalized nonlinear Schrodinger equation as a model for turbulence, collapse, and inverse cascade

A two-dimensional generalized cubic nonlinear Schrödinger equation with complex coefficients for the group dispersion and nonlinear terms is used to investigate the evolution of a finite-amplitude localized initial perturbation. It is found that modulation of the latter can lead to sideband formation, wave condensation, collapse, turbulence, and inverse energy cascade, although not all together and not in that order.

On the sensitivity of forward scattering patterns from bacterial colonies to media composition

Morphology of colonies is important for taxonomy and diagnostics in microbiology where the response to environmental factors is sensitive enough to support discrimination. In this research, we analyzed the forward scattering patterns of individual Escherichia coli K12 colonies when agar hardness and nutrition levels were varied from the control sample. As the agar concentration increased from 1.2% to 1.8%, the diameter of the forward scattering patterns also increased for the same experimental condition which reflects that the colony thickness at the apex is greater for increased agar concentrations. Regarding nutrition, increasing dextrose resulted in smaller mean colony diameters while the mean diameters of the colonies were proportional to the yeast extract concentration up to 0.5%. The result reveals that ±0.3% agar concentration from the control sample is sufficient to create variations in the scattering patterns. For nutrition -0.25% of yeast extract showed significant variations while +0.25% from control sample showed minimal variations.

Suspension biomechanics of swimming microbes

Micro-organisms play a vital role in many biological, medical and engineering phenomena. Some recent research efforts have demonstrated the importance of biomechanics in understanding certain aspects of micro-organism behaviours such as locomotion and collective motions of cells. In particular, spatio-temporal coherent structures found in a bacterial suspension have been the focus of many research studies over the last few years. Recent studies have shown that macroscopic properties of a suspension, such as rheology and diffusion, are strongly affected by meso-scale flow structures generated by swimming microbes. Since the meso-scale flow structures are strongly affected by the interactions between microbes, a bottom-up strategy, i.e. from a cellular level to a continuum suspension level, represents the natural approach to the study of a suspension of swimming microbes. In this paper, we first provide a summary of existing biomechanical research on interactions between a pair of swimming micro-organisms, as a two-body interaction is the simplest many-body interaction. We show that interactions between two nearby swimming micro-organisms are described well by existing mathematical models. Then, collective motions formed by a group of swimming micro-organisms are discussed. We show that some collective motions of micro-organisms, such as coherent structures of bacterial suspensions, are satisfactorily explained by fluid dynamics. Lastly, we discuss how macroscopic suspension properties are changed by the microscopic characteristics of the cell suspension. The fundamental knowledge we present will be useful in obtaining a better understanding of the behaviour of micro-organisms.

Hydrodynamic interactions between two swimming bacteria

This article evaluates the hydrodynamic interactions between two swimming bacteria precisely. We assume that each bacterium is force free and torque free, with a Stokes flow field around it. The geometry of each bacterium is modeled as a spherical or spheroidal body with a single helical flagellum. The movements of two interacting bacteria in an infinite fluid otherwise at rest are computed using a boundary element method, and the trajectories of the two interacting bacteria and the stresslet are investigated. The results show that as the two bacteria approach each other, they change their orientations considerably in the near field. The bacteria always avoided each other; no stable pairwise swimming motion was observed in this study. The effects of the hydrodynamic interactions between two bacteria on the rheology and diffusivity of a semidilute bacterial suspension are discussed.

Magnetic Resonance Imaging of Flow-Distributed Oscillations

The formation of stationary concentration patterns in a packed-bed reactor (PBR), using a manganese-catalyzed Belousov-Zhabotinsky (BZ) reaction in a mixed sulfuric-phosphoric acid medium, was studied using magnetic resonance imaging (MRI). The PBR was composed of a column filled with glass beads, which was fed by a continuous stirred tank reactor (CSTR). As the reactor is optically opaque, investigation of the three-dimensional (3D) structure of these reaction-diffusion-advection waves is not possible using conventional image capture techniques. MRI has been used to probe this system and the formation, 3D structure, and development of these waves has been studied. At reactor startup, traveling waves were observed. After this initial period the waves stabilized and became stationary. Once fixed, they were found to be remarkably stable. There was significant heterogeneity of the reaction fronts, which were not flat, as would be expected from a plug-flow reactor. Instead, the reaction wave fronts were observed to be conical in shape due to the local hydrodynamics of the bed and specifically the higher velocities and therefore lower residence times close to the wall of the reactor.

Hydrodynamics of bacterial colonies: phase diagrams

We present numerical simulations of a recent hydrodynamic model describing the growth of bacterial colonies on agar plates. We show that this model is able to qualitatively reproduce experimentally observed phase diagrams, which relate a colony shape to the initial quantity of nutrients on the plate and the initial wetness of the agar. We also discuss the principal features resulting from the interplay between hydrodynamic motions and colony growth, as described by our model.

Accurate discretization of advection-diffusion equations

We present an exact mathematical transformation which converts a wide class of advection-diffusion equations into a form allowing simple and direct spatial discretization in all dimensions, and thus the construction of accurate and more efficient numerical algorithms. These discretized forms can also be viewed as master equations which provide an alternative mesoscopic interpretation of advection-diffusion processes in terms of diffusion with spatially varying hopping rates.

A new interpretation of the Keller-Segel model based on multiphase modelling

In this paper an alternative derivation and interpretation are presented of the classical Keller-Segel model of cell migration due to random motion and chemotaxis. A multiphase modelling approach is used to describe how a population of cells moves through a fluid containing a diffusible chemical to which the cells are attracted. The cells and fluid are viewed as distinct components of a two-phase mixture. The principles of mass and momentum balance are applied to each phase, and appropriate constitutive laws imposed to close the resulting equations. A key assumption here is that the stress in the cell phase is influenced by the concentration of the diffusible chemical. By restricting attention to one-dimensional cartesian geometry we show how the model reduces to a pair of nonlinear coupled partial differential equations for the cell density and the chemical concentration. These equations may be written in the form of the Patlak-Keller-Segel model, naturally including density-dependent nonlinearities in the cell motility coefficients. There is a direct relationship between the random motility and chemotaxis coefficients, both depending in an inter-related manner on the chemical concentration. We suggest that this may explain why many chemicals appear to stimulate both chemotactic and chemokinetic responses in cell populations. After specialising our model to describe slime mold we then show how the functional form of the chemical potential that drives cell locomotion influences the ability of the system to generate spatial patterns. The paper concludes with a summary of the key results and a discussion of avenues for future research.