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

Abstract

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.

Mathematical models for chemotaxis and their applications in self-organisation phenomena

“…Consequently, many of the even more spectacular observations could be captured. An apparently chaotic pattern of E. coli merging/emerging events has been modelled via a PKS system in Baronas et al (2015). 10 Figure 4: An expanding pattern of spotted rings in the model (B1), where we set χ = 3, k 1 = 2, k 2 = 0.03, k 3 = 1, s = 2, k 4 = 0.5, k 5 = 1, k 6 = p = 0, D u = 0.1 and D v = 0.3.…”

“…for g(u) = (1 + tanh(k 2 (u − k 3 ))/2. Baronas et al (2015) for E. coli pattern formation, for bacteria (n), nutrient (succinate, s) and chemoattractant (aspartate, c): n t = ∇ · D n ∇n − χn∇c + k 1 n (1 − n/k 2 s) , c t = D c ∇ 2 c + k 3 n k 4 +n − k 5 c , s t = D s ∇ 2 s − k 6 n .…”

“…Consequently, many of the even more spectacular observations could be captured. An apparently chaotic pattern of E. coli merging/emerging events has been modelled via a PKS system in Baronas et al (2015). Bacillus subtilis swimming within fluid environments can create highly intriguing dynamics, such as falling plumes and aggregates at the contact lines of thin fluid layers separating a solid substrate and air (Hillesdon et al, 1995;Tuval et al, 2005).…”

“…(B3) Polezhaev et al (2006) model for bacteria pattern formation, for vegetative bacteria (n), anabiotic bacteria (a), chemoattractant (c) and nutrient (s): Baronas et al (2015) for E. coli pattern formation, for bacteria (n), nutrient (succinate, s) and chemoattractant (aspartate, c):…”

Nonlinear chemical reaction induced abnormal pattern formation of chemotactic particles

“…The first one is derived from the behavior of bacteria in nature. [10][11][12][13][14][15] Keller and Segel's early research 16 suggested that the positive feedback loop between the signal release and chemotaxis of particles was the key to the formation of clusters. It has become a very popular direction to discuss the patterns formed by chemotactic particles under different chemical stimuli through the Keller-Segel approach.…”