In the growth of bacterial colonies, a great variety of complex patterns are observed in experiments, depending on external conditions and the bacterial species. Typically, existing models employ systems of reaction-diffusion equations or consist of growth processes based on rules, and are limited to a discrete lattice. In contrast, the two-dimensional model proposed here is an off-lattice simulation, where bacteria are modelled as rigid circles and nutrients are point-like, Brownian particles. Varying the nutrient diffusion and concentration, we simulate a wide range of morphologies compatible with experimental observations, from round and compact to extremely branched patterns. A scaling relationship is found between the number of cells in the interface and the total number of cells, with two characteristic regimes. These regimes correspond to the compact and branched patterns, which are exhibited for sufficiently small and large colonies, respectively. In addition, we characterise the screening effect observed in the structures by analysing the multifractal properties of the growth probability.
Bacteria commonly live in structured communities that affect human health and influence ecological systems. Heterogeneous populations, such as motile and non-motile populations, often coexist in bacteria communities. Motile subpopulations in microbial communities are believed to be important to dispersal, quest for food, and material transport. However, except in circumstances where motile cells drive colony expansion (e.g. bacterial swarming), the physiological functions of motile subpopulations in bacterial communities are largely unclear. Here we discovered that motile cells in routinely cu…
The front of a compact bacterial colony growing on a Petri dish is a paradigmatic instance of non-equilibrium fluctuations in the celebrated Eden, or Kardar-Parisi-Zhang (KPZ), universality class. While in many experiments the scaling exponents crucially differ from the expected KPZ values, the source of this disagreement has remained poorly understood. We have performed growth experiments with B. subtilis 168 and E. coli ATCC 25922 under conditions leading to compact colonies in the classically-alleged Eden regime, where individual motility is suppressed. Non-KPZ scaling is indeed observed fo…
Bacteria can adjust the structure of colonies and biofilms to enhance their survival rate under external stress. Here, we explore the link between bacterial interaction forces and colony structure. We show that the activity of extracellular pilus motors enhances local ordering and accelerates fusion dynamics of bacterial colonies. The radial distribution function of mature colonies shows local fluid-like order. The degree and dynamics of ordering are dependent on motor activity. At a larger scale, the fusion dynamics of two colonies shows liquid-like behavior whereby motor activity strongly af…
Commenting on the paper "Swarming Ring Patterns in Bacterial Colonies Exposed to Ultraviolet Radiation" of A.M. Delprato et al., Phys. Rev. Lett 87, 158102 (2001) we point out that their observed ring pattern formation by colonies of soil bacteria Bacillus subtilis exposed to ultra violet (UV) radiation might be caused by the artificial confinement of motile bacteria evolved to live in a 3-dimensional environment to a 2-dimensional geometry. We propose that to investigate the reaction of Bacillus subtilis to UV radiation coming from above, a seminal experiment should have a 3-dimensional setup…
We discuss the structure of the equilibrium states of a regularized Keller-Segel model describing the chemotaxis of bacterial populations. We consider the limit of high degradation of the secreted chemical where analytical results can be obtained. Below a critical effective temperature, the system experiences a second order phase transition from a homogeneous phase to an inhomogeneous phase formed by two domains with uniform concentration separated by a thin interface (domain wall). We study the properties of the interface and determine the bifurcation between a circular shape (spot) and a str…
We study the spreading of a bacterial colony undergoing turbulent like collective motion. We present two minimalistic models to investigate the interplay between population growth and coherent structures arising from turbulence. Using Direct Numerical Simulation (DNS) of the proposed models we find that turbulence has two prominent effects on the spatial growth of the colony: (a) the front speed is enhanced, and (b) the front gets crumpled. Both these effects, which we highlight by using statistical tools, are markedly different in our two models. We also show that the crumpled front structure…
External control of the swimming speed of `active particles' can be used to self assemble designer structures in situ on the micrometer to millimeter scale. We demonstrate such reconfigurable templated active self assembly in a fluid environment using light powered strains of Escherichia coli. The physics and biology controlling the sharpness and formation speed of patterns is investigated using a bespoke fast-responding strain.
Anaerobic processes (e.g., methanogenesis and fermentation) largely contribute to element cycling and natural contaminant attenuation/mobilization, even in well-oxygenated porous environments, such as shallow aquifers. This paradox is commonly explained by the occurrence of small-scale anoxic microenvironments generated by the coupling of bacterial respiration and the heterogeneous oxygen (O2) transport by porewater. Such microenvironments allow facultatively and obligately anaerobic bacteria to proliferate in oxic environments. Microenvironment dynamics are still poorly understood due to the …
We investigate the emergence of global alignment in colonies of dividing rod-shaped cells under confinement. Using molecular dynamics simulations and continuous modeling, we demonstrate that geometrical anisotropies in the confining environment give rise to imbalance in the normal stresses, which, in turn, drives a collective rearrangement of the cells. This behavior crucially relies on the colony's solid-like mechanical response at short time scales and can be recovered within the framework of active hydrodynamics upon modeling bacterial colonies as growing viscoelastic gels characterized by …
Colonies of bacteria endowed with a pili-based self-propulsion machinery are ideal models for investigating the structure and dynamics of active many-particle systems. We study Neisseria gonorrhoeae colonies with a molecular-dynamics-based approach. A generic, adaptable simulation method for particle systems with fluctuating bond-like interactions is devised. The simulations are employed to investigate growth of bacterial colonies and the dependence of the colony structure on cell-cell interactions. In colonies, pilus retraction enhances local ordering. For colonies consisting of different typ…
Bacterial conglomerates such as biofilms and microcolonies are ubiquitous in nature and play an important role in industry and medicine. In contrast to well-mixed, diluted cultures routinely used in microbial research, bacteria in a microcolony interact mechanically with one another and with the substrate to which they are attached. Despite their ubiquity, little is known about the role of such mechanical interactions on growth and biological evolution of microbial populations. Here we use a computer model of a microbial colony of rod-shaped cells to investigate how physical interactions betwe…
Many bacteria rely on active cell appendages, such as type IV pili, to move over substrates and interact with neighboring cells. Here, we study the motion of individual cells and bacterial colonies, mediated by the collective interactions of multiple pili. It was shown experimentally that the substrate motility of Neisseria gonorrhoeae cells can be described as a persistent random walk with a persistence length that exceeds the mean pili length. Moreover, the persistence length increases for a higher number of pili per cell. With the help of a simple, tractable stochastic model, we test whethe…
Engineering spatially organized biofilms for creating adaptive and sustainable biomaterials is a forthcoming mission of synthetic biology. Existing technologies of patterning biofilm materials suffer limitations associated with the high technical barrier and the requirements of special equipment. Here we present controlled meniscus-driven fluidics, MeniFluidics; an easily implementable technique for patterning living bacterial populations. We demonstrate multiscale patterning of living-colony and biofilm formation with submillimetre resolution. Relying on fast bacterial spreading in liquid cha…
We show, using differential dynamic microscopy, that the diffusivity of non-motile cells in a three-dimensional (3D) population of motile E. coli is enhanced by an amount proportional to the active cell flux. While non-motile mutants without flagella and mutants with paralysed flagella have quite different thermal diffusivities and therefore hydrodynamic radii, their diffusivities are enhanced to the same extent by swimmers in the regime of cell densities explored here. Integrating the advective motion of non-swimmers caused by swimmers with finite persistence-length trajectories predicts our …
Mixtures of active and passive particles are predicted to exhibit a variety of nonequilibrium phases. Here we report a dynamic clustering phase in mixtures of colloids and motile bacteria. We show that colloidal clustering results from a balance between bond breaking due to persistent active motion and bond stabilization due to torques that align active particle velocity tangentially to the passive particle surface. Furthermore, dynamic clustering spans a broad regime between diffusivity-based and motility-induced phase separation that subsumes typical bacterial motility parameters.
We present a new reaction-diffusion model for chiral branching growth of colonies of the bacteria Paenibacillus dendritiformis. In our model the bacteria are represented by a density field with non-linear diffusion and a complex scalar field which represents bacterial orientation. The orientation field introduces anisotropy into the flux of bacteria, representing self-propulsion along their long axes. The model can also reproduce tip-splitting growth of other strains (shorter bacteria) of the same species. The model can capture changes of small number of bacteria, thus it can be used to study …
We study the clustering of a model cyanobacterium \textit{Synechocystis} into microcolonies. The bacteria are allowed to diffuse onto surfaces of different hardness, and interact with the others by aggregation and detachment. We find that soft surfaces give rise to more microcolonies than hard ones. This effect is related to the amount of heterogeneity of bacteria's dynamics as given by the proportion of motile cells. A kinetic model that emphasizes specific interactions between cells, complemented by extensive numerical simulations considering various amounts of motility, describes the experi…
The spreading of bacterial colonies at solid-air interfaces is determined by the physico-chemical properties of the involved interfaces. The production of surfactant molecules by bacteria is a widespread strategy that allows the colony to efficiently expand over the substrate. On the one hand, surfactant molecules lower the surface tension of the colony, effectively increasing the wettability of the substrate, which facilitates spreading. On the other hand, gradients in the surface concentration of surfactant molecules result in Marangoni flows that drive spreading. These flows may cause an in…
The role of activity on the hydrodynamic dispersion of bacteria in a model porous medium is studied by tracking thousands of bacteria in a microfluidic chip containing randomly placed pillars. We first evaluate the spreading dynamics of two populations of motile and non-motile bacteria injected at different flow rates. In both cases, we observe that the mean and the variance of the distances covered by the bacteria vary linearly with time and flow velocity, a result qualitatively consistent with the standard geometric dispersion picture. However, quantitatively, the motiles bacteria display a …
How motile bacteria move near a surface is a problem of fundamental biophysical interest and is key to the emergence of several phenomena of biological, ecological and medical relevance, including biofilm formation. Solid boundaries can strongly influence a cell's propulsion mechanism, thus leading many flagellated bacteria to describe long circular trajectories stably entrapped by the surface. Experimental studies on near-surface bacterial motility have, however, neglected the fact that real environments have typical microstructures varying on the scale of the cells' motion. Here, we show tha…
Segregation of populations is a key question in evolution theory. One important aspect is the relation between spatial organization and the population's composition. Here we study a specific example -- sectors in expanding bacterial colonies. Such sectors are spatially segregated sub-populations of mutants. The sectors can be seen both in disk-shaped colonies and in branching colonies. We study the sectors using two models we have used in the past to study bacterial colonies -- a continuous reaction-diffusion model with non-linear diffusion and a discrete ``Communicating Walkers'' model. We fi…
We characterize cell motion in experiments and show that the transition to collective motion in colonies of gliding bacterial cells confined to a monolayer appears through the organization of cells into larger moving clusters. Collective motion by non-equilibrium cluster formation is detected for a critical cell packing fraction around 17%. This transition is characterized by a scale-free power-law cluster size distribution, with an exponent $0.88\pm0.07$, and the appearance of giant number fluctuations. Our findings are in quantitative agreement with simulations of self-propelled rods. This s…
The emergent spatial patterns generated by growing bacterial colonies have been the focus of intense study in physics during the last twenty years. Both experimental and theoretical investigations have made possible a clear qualitative picture of the different structures that such colonies can exhibit, depending on the medium on which they are growing. However, there are relatively few quantitative descriptions of these patterns. In this paper, we use a mechanistically detailed simulation framework to measure the scaling exponents associated with the advancing fronts of bacterial colonies on h…
We study spreading of a non-motile bacteria colony on a hard agar plate by using agent-based and continuum models. We show that the spreading dynamics depends on the initial nutrient concentration, the motility and the inherent demographic noise. Population fluctuations are inherent in an agent based model whereas, for the continuum model we model them by using a stochastic Langevin equation. We show that the intrinsic population fluctuations coupled with non-linear diffusivity lead to a transition from Diffusion Limited Aggregation (DLA) type morphology to an Eden-like morphology on decreasin…
Colonies of rod-shaped bacteria constitute a system of colloidal active matter with nematic properties. As a single initial bacterium multiplies through repeated divisions, the resulting colony quickly loses long-range orientational order, but retains locally ordered domains. At the boundaries of these domains, topological defects emerge, which move around randomly as the colony grows. In both experiments and simulations, we find that these defects are created at a rate that corresponds to the exponential growth of the colony, resulting in a stable defect density. Both this defect density and …
Bacterial colonies are abundant on living and nonliving surfaces and are known to mediate a broad range of processes in ecology, medicine, and industry. Although extensively researched, from single cells to demographic scales, a comprehensive biomechanical picture, highlighting the cell-to-colony dynamics, is still lacking. Here, using molecular dynamics simulations and continuous modeling, we investigate the geometrical and mechanical properties of a bacterial colony growing on a substrate with a free boundary and demonstrate that such an expanding colony self-organizes into a "mosaic" of mic…
Microbiology is the science of microbes, particularly bacteria. Many bacteria are motile: they are capable of self-propulsion. Among these, a significant class execute so-called run-and-tumble motion: they follow a fairly straight path for a certain distance, then abruptly change direction before repeating the process. This dynamics has something in common with Brownian motion (it is diffusive at large scales), and also something in contrast. Specifically, motility parameters such as the run speed and tumble rate depend on the local environment and hence can vary in space. When they do so, eve…
The transition from monolayers to multilayered structures in bacterial colonies is a fundamental step in biofilm development. Observed across different morphotypes and species, this transition is triggered within freely growing bacterial microcolonies comprising a few hundred cells. Using a combination of numerical simulations and analytical modeling, here we demonstrate that this transition originates from the competition between growth-induced in-plane active stresses and vertical restoring forces, due to the cell-substrate interactions. Using a simple chainlike colony of laterally confined …
Microbial colonies cultured on agar Petri dishes have become a model system to study biological evolution in populations expanding in space. Processes such as clonal segregation and gene surfing have been shown to be affected by interactions between microbial cells and their environment. In this work we investigate the role of mechanical interactions such as cell-surface adhesion. We compare two strains of the bacterium E. coli: a wild-type strain and a "shaved" strain that adheres less to agar. We show that the shaved strain has a selective advantage over the wild type: although both strains …
We study colonies of non-motile, rod-shaped bacteria growing on solid substrates. In our model, bacteria interact purely mechanically, by pushing each other away as they grow, and consume a diffusing nutrient. We show that mechanical interactions control the velocity and shape of the advancing front, which leads to features that cannot be captured by established Fisher-Kolmogorov models. In particular, we find that the velocity depends on the elastic modulus of bacteria or their stickiness to the surface. Interestingly, we predict that the radius of an incompressible, strictly two-dimensional …
In nature, bacterial collectives typically consist of multiple species, which are interacting both biochemically and physically. Nonetheless, past studies on the physical properties of swarming bacteria were focused on axenic (single species) populations. In bacterial swarming, intricate interactions between the individuals lead to clusters, rapid jets and vortices that depend on cell characteristics such as speed and length. In this work, we show the first results of rapidly swarming mixed-species populations of {\sl Bacillus subtilis} and {\sl Serratia marcescens}, two model swarm species th…
Various bacterial strains (e.g. strains belonging to the genera Bacillus, Paenibacillus, Serratia and Salmonella) exhibit colonial branching patterns during growth on poor semi-solid substrates. These patterns reflect the bacterial cooperative self-organization. Central part of the cooperation is the collective formation of lubricant on top of the agar which enables the bacteria to swim. Hence it provides the colony means to advance towards the food. One method of modeling the colonial development is via coupled reaction-diffusion equations which describe the time evolution of the bacterial de…
Adhesion of bacteria to liquid-liquid interfaces can play a role in the biodegradation of dispersed hydrocarbons and in biochemical and bioprocess engineering. Whereas thermodynamic factors underpinning adhesion are well studied, the role of bacterial activity on adhesion is less explored.Here, we show that bacterial motility enhances adhesion to surfactant-decorated oil droplets dispersed in artificial sea water. Motile Halomonas titanicae adhered to hexadecane droplets stabilized with dioctyl sodium sulfosuccinate (DOSS) more rapidly and at greater surface densities compared to nonmotile H. …
Many mature bacterial colonies and biofilms are complex three-dimensional (3D) structures. One key step in their developmental program is a transition from a two-dimensional (2D) monolayer into a 3D architecture. Despite the importance of controlling the growth of microbial colonies and biofilms in a variety of medical and industrial settings, the underlying physical mechanisms behind single-cell dynamics, collective behaviors of densely-packed cells, and 3D complex colony expansion remain largely unknown. In this work, we explore the mechanisms behind the 2D-to-3D transition of motile Pseudom…
Colonies of bacteria grown on thin agar plate exhibit fractal patterns as a result of adaptation to their environments. The bacterial colony pattern formation is regulated crucially by chemotaxis, the movement of cells along a chemical concentration gradient. Here, the dynamics of pattern formation in bacterial colony is investigated theoretically through a continuum model that considers chemotaxis. In the case of the gradient sensed by the bacterium is nearly uniform, the bacterial colony patterns are self-similar, which they look the same at every scale. The scaling law of the bacterial colo…
Deep learning-enhanced Lagrangian 3D Tracking of motile microorganisms
Laboratoire PMMH-ESPCI Paris, PSL Research University, Sorbonne Université and Denis Diderot（巴黎PM MH实验室、PSL研究大学、索邦大学和狄德罗大学）；University of Gothenburg（哥德堡大学）；Science for Life Laboratory（科学生命实验室）；Institut Universitaire de France (IUF)（法国高等研究院）
We demonstrate 'differential dynamic microscopy' (DDM) for the fast, high throughput characterization of the dynamics of active particles. Specifically, we characterize the swimming speed distribution and the fraction of motile cells in suspensions of Escherichia coli bacteria. By averaging over ~10^4 cells, our results are highly accurate compared to conventional tracking. The diffusivity of non-motile cells is enhanced by an amount proportional to the concentration of motile cells.
It is widely accepted that population genetics theory is the cornerstone of evolutionary analyses. Empirical tests of the theory, however, are challenging because of the complex relationships between space, dispersal, and evolution. Critically, we lack quantitative validation of the spatial models of population genetics. Here we combine analytics, on and off-lattice simulations, and experiments with bacteria to perform quantitative tests of the theory. We study two bacterial species, the gut microbe Escherichia coli and the opportunistic pathogen Pseudomonas aeruginosa, and show that spatio-ge…
We present a study about AFM imaging of living, moving or self-immobilized, bacteria in their genuine physiological liquid medium. No external immobilization protocol, neither chemical nor mechanical, was needed. For the first time, the native gliding movements of Gram-negative Nostoc cyanobacteria upon the surface, at speeds up to 900microns/h, were studied by AFM. This was possible thanks to an improved combination of a gentle sample preparation process and an AFM procedure based on fast and complete force-distance curves made at every pixel, drastically reducing lateral forces. No limitatio…
Non-motile active matter exhibits a wide range of non-equilibrium collective phenomena yet examples are crucially lacking in the literature. We present a microscopic model inspired by the bacteria {\it Neisseria Meningitidis} in which diffusive agents feel intermittent attractive forces. Through a formal coarse-graining procedure, we show that this truly scalar model of active matter exhibits the time-reversal-symmetry breaking terms defining the {\it Active Model B+} class. In particular, we confirm the presence of microphase separation by solving the kinetic equations numerically. We show th…
Aerotaxis is the ability of motile cells to navigate toward oxygen. A key question is the dependence of the aerotactic velocity with the local oxygen concentration c. Here we combine simultaneous bacteria tracking and local oxygen concentration measurements using Ruthenium encapsulated in micelles to characterize the aerotactic response of Burkholderia contaminans, a motile bacterium ubiquitous in the environment. In our experiments, an oxygen gradient is produced by the bacterial respiration in a sealed glass capillary permeable to oxygen at one end, producing a bacterial band traveling towar…
Rod-shaped bacteria, such as Escherichia coli, commonly live forming mounded colonies. They initially grow two-dimensionally on a surface and finally achieve three-dimensional growth. While it was recently reported that three-dimensional growth is promoted by topological defects of winding number $+1/2$ in populations of motile bacteria, how cellular alignment plays a role in non-motile cases is largely unknown. Here, we investigate the relevance of topological defects in colony formation processes of non-motile E. coli populations, and found that both $\pm 1/2$ topological defects contribute …
This paper studies a two-dimensional chemotactic model for two species in which one of them produces a chemo-repellent for the other. It is shown asymptotically and numerically how the chemical inhibits the invasion of a moving front for the second species and how stable steady states, which depend on the chemical concentration, can be reached. The results qualitatively explain experimental observations by Swain and Ray (Microbiol. Res. 164(2), 2009), where colonies of bacteria produce metabolite agents which prevent the invasion of fungi.
Optical tweezers are a versatile tool that can be used to manipulate small particles including both motile and non-motile bacteria and cells. The orientation of a non-spherical particle within a beam depends on the shape of the particle and the shape of the light field. By using multiple beams, sculpted light fields or dynamically changing beams, it is possible to control the orientation of certain particles. In this paper we discuss the orientation of the rod-shaped bacteria Escherichia coli (E. coli) using dynamically shifting annular beam optical tweezers. We begin with examples of differen…
