Modeling the bacterial self-organization in a circular container along the contact line as detected by bioluminescence imaging

Baronas, Romas; Šimkus, Remigijus

doi:10.15388/na.16.3.14093

Cited by 12 publications

(38 citation statements)

References 30 publications

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“…Similar behaviour has been observed in a number of specific applications of models incorporating chemotaxis processes, such as models for tumour-macrophage interactions [21], tumour invasion [2] and host-parasitoid dynamics [23]. Furthermore, cultured Eschirichia coli bacteria populations can also exhibit highly dynamic patterning, the nature of which has been shown to be well replicated by models of the form (2): see [24,5] for details.…”

Section: Statistical Analysis a Pde Model Such Assupporting

confidence: 60%

“…In [22] the authors studied a specific form of chemotaxis model incorporating logistic cell growth, revealing spatio-temporal dynamics ranging from stationary patterns to periodic solutions and chaotic behaviour. Notably, this complex spatio-temporal patterning phenomenon has also been reported in cultured Eschirichia coli populations, for example see [24,5]. Examples of these various patterns are demonstrated in Figure 1; details of the chemotaxis model itself will be provided in Section 1.1.…”

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confidence: 59%

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Merging-emerging systems can describe spatio-temporal patterning in a chemotaxis model

Hillen

Zielinski

Painter³

2013

Discrete &Amp; Continuous Dynamical Systems - B

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In a recent study (K.J. Painter and T. Hillen, Spatio-temporal chaos in a chemotaxis model, Physica D, 240 (4), 363-375, 2011) a model for chemotaxis incorporating logistic growth was investigated for its pattern formation properties. In particular, a variety of complex spatio-temporal patterning was found, including stationary, periodic and chaotic. Complicated dynamics appear to arise through a sequence of "merging and emerging" events: the merging of two neighbouring aggregates or the emergence of a new aggregate in an open space. In this paper we focus on a time-discrete dynamical system motivated by these dynamics, which we call the merging-emerging system (MES). We introduce this new class of set-valued dynamical systems and analyse its capacity to generate similar "pattern formation" dynamics. The MES shows remarkably close correspondence with patterning in the logistic chemotaxis model, strengthening our assertion that the characteristic length scales of merging and emerging are responsible for the observed dynamics. Furthermore, the MES describes a novel class of pattern-forming discrete dynamical systems worthy of study in its own right.2010 Mathematics Subject Classification. Primary: 92C17, 35B36; Secondary: 37N25.

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Section: Statistical Analysis a Pde Model Such Assupporting

confidence: 60%

mentioning

confidence: 59%

Merging-emerging systems can describe spatio-temporal patterning in a chemotaxis model

Hillen

Zielinski

Painter³

2013

Discrete &Amp; Continuous Dynamical Systems - B

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“…It has been recently shown that bioluminescence imaging can be employed to validate mathematical models of bacterial self‐organization. In particular, the abovementioned merging–emerging patterns were, to the best of our knowledge, for the first time observed experimentally in cylindrical samples of liquid cultures of bioluminescent Escherichia coli . The imagining showed luminous aggregates of bacteria merging and emerging along the three‐phase contact lines.…”

Section: Introductionmentioning

confidence: 55%

“…Optical density measurements at 600 nm (OD 600 ) were used to monitor the concentration of cells. The freshly harvested mid‐log phase cultures (OD 600 = 0.4), corresponding to the cell density of ~1.08 × 10 8 cells/mL were chosen for examination . The induction of the culture was provided by adding a stock solution IPTG into LB medium up to the final concentration of 1 mM.…”

Section: Methodsmentioning

confidence: 99%

Microtiter plate tests for segregation of bioluminescent bacteria

et al. 2015

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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.

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“…Computational modeling was also applied to investigate the bacterial self-organization in small rounded containers near the three-phase contact line as detected by quasi-onedimensional bioluminescence imaging [2,40]. The spatiotemporal patterns in the fluid cultures of luminous E. coli were numerically simulated on the basis of a 1D mathematical model of chemotaxis taking into consideration the cell growth and death.…”

Section: Introductionmentioning

confidence: 99%

Computational modeling of the bacterial self-organization in a rounded container: The effect of dimensionality

Baronas

Ledas

Šimkus

2015

NAMC

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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.

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Modeling the bacterial self-organization in a circular container along the contact line as detected by bioluminescence imaging

Cited by 12 publications

References 30 publications

Merging-emerging systems can describe spatio-temporal patterning in a chemotaxis model

Merging-emerging systems can describe spatio-temporal patterning in a chemotaxis model

Microtiter plate tests for segregation of bioluminescent bacteria

Computational modeling of the bacterial self-organization in a rounded container: The effect of dimensionality

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