2D reaction-diffusion model of quorum sensing characteristics during all phases of bacterial growth

Shuai, Y.; Maslovskaya, A. G.; Kuttler, Christina

doi:10.47910/femj202231

Cited by 1 publication

(2 citation statements)

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“…Taking into consideration the importance of controlling bacterial biofilms, they have become the objects of interdisciplinary research. The most important areas are presented by the modeling of biomass growth (density and rate of progress) [14][15][16][17][18][19][20], the mechanisms of regulation of key chemical compounds related to the quorum sensing [21][22][23][24][25][26][27][28], and the study of the geometric characteristics of the complex morphology of the observed structures [29][30][31].…”

Section: Introductionmentioning

confidence: 99%

“…The present study is dedicated to creating the research framework of mathematical modeling of the bacterial communication process, which, in turn, results in the formation of dense self-similar biofilm structures. In our previous works [24][25][26][27][28] various modifications of the bacterial communication model were proposed with the use of a simplified formalization of the spatio-temporal dynamics of bacterial populations based on approximating dependencies. In this field of study, the formalization of the spatial evolution of bacterial populations is an important subproblem.…”

Section: Introductionmentioning

confidence: 99%

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Three-Dimensional Cellular Automaton for Modeling of Self-Similar Evolution in Biofilm-Forming Bacterial Populations

Sarukhanian,

Maslovskaya,

Kuttler

2023

Mathematics

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Bacterial populations often form colonies and structures in biofilm. The paper aims to design suitable algorithms to simulate self-similar evolution in this context, specifically by employing a hybrid model that includes a cellular automaton for the bacterial cells and their dynamics. This is combined with the diffusion of the nutrient (as a random walk), and the consumption of nutrients by biomass. Lastly, bacterial cells divide when reaching high levels. The algorithm computes the space-time distribution of biomass under limited nutrient conditions, taking into account the collective redistribution of nutrients. To achieve better geometry in this modified model approach, truncated octahedron cells are applied to design the lattice of the cellular automaton. This allows us to implement self-similar realistic bacterial biofilm growth due to an increased number of inner relations for each cell. The simulation system was developed using C# on the Unity platform for fast calculation. The software implementation was executed in combination with the procedure of surface roughness measurements based on computations of fractional dimensions. The results of the simulations qualitatively correspond to experimental observations of the population dynamics of biofilm-forming bacteria. Based on in silico experiments, quantitative dependencies of the geometrical complexity of the biofilm structure on the level of consumed nutrients and oxygen were revealed. Our findings suggest that the more complex structure with a fractal dimension of the biofilm boundaries (around 2.6) corresponds to a certain range of nutrient levels, after which the structure degenerates and the biofilm homogenizes, filling the available space provided and tending towards a strictly 3D structure. The developed hybrid approach allows realistic scenario modeling of the spatial evolution of biofilm-forming bacterial populations and specifies geometric characteristics of visualized self-similar biofilm bacterial structures.

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