Mathematical modeling of dispersal phenomenon in biofilms

Abstract

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.

Modeling biological systems with an improved fractional Gompertz law

“…This is usually justified by the assumption that bacterial cells live suspended in the bulk liquid. Nonetheless, it was recently observed that bacteria tend to organize themselves in biofilm form [27], which are aggregates of cells enclosed in a self-produced matrix [28,29]. Then diffusion phenomena at micro-scale turn out to be of paramount importance for such systems.…”

The influence of substrate surface conditioning and biofilm age on the composition of Enterococcus faecalis biofilms

“…This draws attention to biofilm dispersal, during which the metabolic activity of the active biofilm cells may be modelled to switch to inactive status (D'Acunto et al . ).…”

“…The number of viable cells in multispecies biofilms has been reported to increase gradually during the first 72 h, after which the cell numbers remained constant (Wake et al 2016). This draws attention to biofilm dispersal, during which the metabolic activity of the active biofilm cells may be modelled to switch to inactive status (D'Acunto et al 2019).…”

Flux-Balance Based Modeling of Biofilm Communities

“…conversion between active and inactive material), diffusive or other forms of mobility, etc. [15,16,27], as well as the possibility for different material types to move with different velocities [13,25,38]. Upon summing equations (2), we obtain the volume conservation constraint…”

“…From left to right: glucose respiration, glucose to lactate fermentation, and lactate respiration. See(16) for the corresponding flux vectors including stoichiometry.…”