Mathematical analysis of a quorum sensing induced biofilm dispersal model and numerical simulation of hollowing effects

Emerenini, Blessing O.; Sonner, Stefanie; Eberl, Hermann J.

doi:10.3934/mbe.2017036

Cited by 14 publications

(6 citation statements)

References 40 publications

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“…In Figure 2, we illustrate the behavior of S and M along time for a mesh of Ω = (0, 1) 2 composed of 3584 triangles. We observe, as in [14,15,16], that after a transient time, the two colonies merge. After this stage, we observe an expansion of the region {M > 0} due to the porous-medium type degeneracy for the equation of M , which implies a finite speed of propagation of the interface between {M > 0} and {M = 0}.…”

Section: Numerical Experimentssupporting

confidence: 68%

“…To this purpose, we choose the coefficients d 1 = 4.1667, d 2 = 4.2, κ 1 = 793.65, κ 2 = 0.067, κ 3 = 1, κ 4 = 0.4 and M D = 0. These values are close to those used in [16]. We take a = 2 and b = 1 such that, after elementary computations,…”

Section: Numerical Experimentssupporting

confidence: 55%

“…Remark 5. We could adapt the construction of scheme ( 15)-( 18) and the proofs of our main results, Theorem 2 and Theorem 4, for the approximation of the solution to a quorumsensing-induced biofilm dispersal model introduced in [16], which can be seen as a generalization of ( 1)-( 6).…”

Section: Resultsmentioning

confidence: 99%

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Analysis of a finite-volume scheme for a single-species biofilm model

Helmer¹,

Jüngel²,

Zurek³

2021

Preprint

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An implicit Euler finite-volume scheme for a parabolic reaction-diffusion system modeling biofilm growth is analyzed and implemented. The system consists of a degenerate-singular diffusion equation for the biomass fraction, which is coupled to a diffusion equation for the nutrient concentration, and it is solved in a bounded domain with Dirichlet boundary conditions. By transforming the biomass fraction to an entropy-type variable, it is shown that the numerical scheme preserves the lower and upper bounds of the biomass fraction. The existence and uniqueness of a discrete solution and the convergence of the scheme are proved. Numerical experiments in one and two space dimensions illustrate, respectively, the rate of convergence in space of our scheme and the temporal evolution of the biomass fraction and the nutrient concentration.

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Section: Numerical Experimentssupporting

confidence: 68%

Section: Numerical Experimentssupporting

confidence: 55%

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Analysis of a finite-volume scheme for a single-species biofilm model

Helmer¹,

Jüngel²,

Zurek³

2021

Preprint

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“…This process is necessary for biofilm survival and part of a repetitive cycle phase for keeping the biofilm at optimal size in which the availability and access to nutrients, surface and other factors cope with the colony's requirements 150 . In this regard, the mathematical models proposed by Emerinini et al 151137 suggest that the central hollowing caused by biofilm detachment is regulated by the same biofilm, followed by subsequent biomass growth to repeat the process. The authors suggest biofilm detachment can be continuous or oscillating, for example, biofilm can continuously release single‐cell bacteria or program self‐cleavage.…”

Section: Bacterial Biofouling Process the Science Behindmentioning

confidence: 99%

The biofouling process: The science behind a valuable phenomenon for aquaculture

Garibay-Valdez

Martínez‐Córdova

Vargas‐Albores

et al. 2022

Reviews in Aquaculture

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Biofouling, the biological process leading to the accumulation of microorganisms, has been promoted for over a decade in aquaculture, particularly in biofloc technology, biofilm-based systems and recently aquamimicry. However, the science behind biofouling is largely unknown in aquaculture. This document brings the science behind the biofouling process, reviews and analyses available information about the different phases of such a unique natural process. In aquatic or high humidity environments, substrata rapidly become colonized by microbes. After molecules form a thin film on any surface, bacterial adhesions occur and bacteria-bacteria, bacteria-eukaryotes and bacteria-substrate interactions take place; bacterial adhesion entails the production of adhesins and polysaccharides production. Coaggregation continues after irreversible adhesion, but the activated genes during the adhesion process associated with flagella and pili are suppressed in this stage. Throughout the process, bacteria communicate by excreting signalling or self-inducing molecules, and other bacteria recognize these molecules that serve as a sort of checkpoint associated with their accumulation. Thereafter, the maturation phase is achieved and usually characterized by a colony equilibrium; some bacteria and other microorganisms achieve prominence in the colony, and many of the members have their functions and contributions to the microbial community. Finally, the detachment involves a complex but coordinated process involving several environmental signals, signal transduction pathways and effectors, promoting biofilm or biofloc split and dispersal to start the process again. In conclusion, biofouling is a complex, multifaceted process, but a deeper understanding of it and its consequent regulation would benefit microorganismbased aquaculture.

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“…A partial differential equation based model for cells dispersal was presented in [17], where the authors modeled the dynamics of quorum sensing induced bacterial cell dispersal in growing biofilms. Qualitative analysis of this model has been recently presented in [18]. Here, a mathematical model able to describe dispersal phenomenon as a response to diverse external stress cues, is presented.…”

Section: Introductionmentioning

confidence: 99%

Mathematical modeling of dispersal phenomenon in biofilms

D’Acunto

Frunzo

Klapper

et al. 2019

Mathematical Biosciences

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A mathematical model for dispersal phenomenon in multispecies biofilm based on a continuum approach and mass conservation principles is presented. The formation of dispersed cells is modeled by considering a mass balance for the bulk liquid and the biofilm. Diffusion of these cells within the biofilm and in the bulk liquid is described using a diffusion-reaction equation. Diffusion supposes a random character of mobility. Notably, biofilm growth is modeled by a hyperbolic partial differential equation while the diffusion process of dispersed cells by a parabolic partial differential equation. The two are mutually connected but governed by different equations that are coupled by two growth rate terms. Three biological processes are discussed. The first is related to experimental observations on starvation induced dispersal [1]. The second considers diffusion of a non-lethal antibiofilm agent which induces dispersal of free cells. The third example considers dispersal induced by a self-produced biocide agent.

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Mathematical analysis of a quorum sensing induced biofilm dispersal model and numerical simulation of hollowing effects

Cited by 14 publications

References 40 publications

Analysis of a finite-volume scheme for a single-species biofilm model

Analysis of a finite-volume scheme for a single-species biofilm model

The biofouling process: The science behind a valuable phenomenon for aquaculture

Mathematical modeling of dispersal phenomenon in biofilms

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