A multi-cellular network of metabolically active E. coli as a weak gel of living Janus particles Remigijus Šimkus, * a Romas Baronas b and Žilvinas Ledas b Bioluminescence images of nutrient rich liquid cultures of lux-gene reporter Escherichia coli were recorded for several hours after being placed into small diameter cylindrical containers (glass tubes and microtiter plate wells). It was found that luminous cells distribute near the three-phase contact line forming an irregular array of clumps, channels and plumes at the solid-liquid interface. The experimentally observed quasi-2-dimensional spatiotemporal patterns ('venation patterns') were simulated fairly well by the mean field Keller-Segel equations of chemotactic aggregation. The equations use a logistic cell growth term whose carrying capacity depends on oxygen concentration. The experimental and numerical results are interpreted as follows: (1) the patterns of bioluminescence form due to arrested phase separation in the culture; (2) the luminous phase formed along the upper part of the solid-liquid interface is a weak gel-like network of metabolically active bacteria which exhibit ligand-receptor type cell-cell adhesion and high rates of oxidative phosphorylation; (3) active bacteria in this gel can be viewed as self-generated Janus particles, i.e., polarized particles whose surface is divided into two chemically varying regions, the adhering region and the non-adhering region; (4) the life-time of the metabolically active bacterium (living Janus particle) in the weak gel phase is estimated to be $25 s; (5) the observed network of luminous bacteria can be viewed as a biofilm, in which bacteria move due to self-phoresis by generating pH gradients via metabolic reactions; and (6) the reversible clustering of cells near interfaces is attributed to the bacterial energy-taxis phenomenon.

It has been recently shown that bioluminescence imaging can be usefully applied to provide new insights into bacterial self-organization. In this work we employ bioluminescence imaging to record images of nutrient rich liquid cultures of the lux-gene reporter Escherichia coli in microtiter plate wells. The images show that patterns of inhomogenous bioluminescence form along the three-phase contact lines. The paper analyzes the dependencies of the average number of luminous aggregates (clouds) on various environmental factors. In particular, our results show that optimal (neutral) pH and high aeration rates determine the highest mean number of clouds, and that spatiotemporal patterns do not form in the pH buffered suspensions. In addition, a sigmoidal (switch-like) dependence of the number of aggregates on the rate of aeration was observed. The obtained bioluminescence imaging data was interpreted by employing the Keller-Segel-Fisher (KSF) model of chemotaxis and logistic growth, adapted to systems of metabolically flexible (two-state) bacteria. The modified KSF model successfully simulated the observed switch-like responses. The results of the microtiter plate tests and their simulations indicate that the segregation of bacteria with different activities proceeds in the three-phase contact line region.

A bacterial self-organization in a rounded container as detected by bioluminescence imaging is mathematically modeled by applying the the Keller-Segel approach with logistic growth. The pattern formation in a colony of luminous Escherichia coli is numerically simulated by the nonlinear reaction-advection-diffusion equations. In this work, the pattern formation is studied in 3D and the results are compared with previous and new 2D and 1D simulations. The numerical simulation at transition conditions was carried out using the finite difference technique. The simulation results showed that the developed 3D model captures fairly well the sophisticated patterns observed in the experiments. Since the numerical simulation based on the 3D model is very time-consuming, the reduction of spatial dimension of the model for simulating 1D spatiotemporal patterns is discussed. Due to the accumulation of luminous cells near the top three-phase contact line the experimental patterns of the bioluminescence can be qualitatively described by 1D and 2D models by adjusting values of the diffusion coefficient and/or chemotactic sensitivity.

Bioluminescence imaging experiments were carried out to characterize spatio-temporal patterns of bacterial self-organization in active suspensions (cultures) of bioluminescent Escherichia coli and its mutants. An analysis of the effects of mutations shows that spatio-temporal patterns formed in standard microtitre plates are not related to the chemotaxis system of bacteria. In fact, these patterns are strongly dependent on the properties of mutants that characterize them as self-phoretic (non-flagellar) swimmers. In particular, the observed patterns are essentially dependent on the efficiency of proton translocation across membranes and the smoothness of the cell surface. These characteristics can be associated, respectively, with the surface activity and the phoretic mobility of a colloidal swimmer. An analysis of the experimental data together with mathematical modelling of pattern formation suggests the following: (1) pattern-forming processes can be described by Keller–Segel-type models of chemotaxis with logistic cell kinetics; (2) active cells can be seen as biochemical oscillators that exhibit phoretic drift and alignment; and (3) the spatio-temporal patterns in a suspension of growing E. coli form due to phoretic interactions between oscillating cells of high metabolic activity.

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This paper deals with the computational modeling of the bioluminescence pattern formation in suspensions of Escherichia coli bacteria. The aim was to develop a computational model for simulating the bacterial populations consisting of two subpopulations of active and passive cells. A suitable model based on Keller–Segel and Fisher equations was proposed and the spatiotemporal patterns were simulated using the finite difference technique. The influence of cell activation, deactivation, chemotactic sensitivity, growth rate and saturating signal production parameter values on the pattern formation was investigated. The proposed model can be used to effectively simulate quasi-one-dimensional spatiotemporal patterns. We provide a simple qualitative explanation of the experimental results and estimated model parameters. In particular, it is argued that the effective model simulates patterns of evaporation-driven convection in open-to-air suspensions of cells that can be either active or passive.

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