A new mathematical model of bacterial interactions in two-species oral biofilms

Abstract

Periodontitis are bacterial inflammatory diseases, where the bacterial biofilms present on the tooth-supporting tissues switch from a healthy state towards a pathogenic state. Among bacterial species involved in the disease, Porphyromonas gingivalis has been shown to induce dysbiosis, and to induce virulence of otherwise healthy bacteria like Streptococcus gordonii. During biofilm development, primary colonizers such as S. gordonii first attach to the surface and allow the subsequent adhesion of periodontal pathogens such as P. gingivalis. Interactions between those two bacteria have been extensively studied during the adhesion step of the biofilm. The aim of the study was to understand interactions of both species during the growing phase of the biofilm, for which little knowledge is available, using a mathematical model. This two-species biofilm model was based on a substrate-dependent growth, implemented with damage parameters, and validated thanks to data obtained on experimental biofilms. Three different hypothesis of interactions were proposed and assayed using this model: independence, competition between both bacteria species, or induction of toxicity by one species for the other species. Adequacy between experimental and simulated biofilms were found with the last hypothetic mathematical model. This new mathematical model of two species bacteria biofilms, dependent on different substrates for growing, can be applied to any bacteria species, environmental conditions, or steps of biofilm development. It will be of great interest for exploring bacterial interactions in biofilm conditions.

Pore‐scale modeling of competition and cooperation of multispecies biofilms for nutrients in changing environments

“…It can be found that all models reach the maximum concentration after about 30 days (Figure 2b) and all models show higher concentration for nitrite oxidizer (Figure 2(c)). Hereafter we selected double Monod kinetics due to its better numerical behavior during simulations, besides it was more commonly used in previous studies …”

Challenges of biofilm control and utilization: lessons from mathematical modelling

“…It is therefore mixed-species biofilms that are mostly apparent in situ, and thus the study of inter-species interactions within a biofilm is of great importance in addressing the challenges associated with biofilm control. Studying the role of mixed species interactions on biofilm growth is experimentally challenging [44] and mathematical models can be of great help [44,46,60]. In particular, we describe two recent applications of mathematical models which reveal key mechanisms in biofilm communities involving multiple species.…”

“…Recently, a new 2D cellular automata (discrete space and time) model has been developed to study biofilm formation of two species of bacteria, Streptococcus gordonii and Porphyromonas gingivalis [44]. These two species have been identified as the leading causes of periodontitis, commonly referred to as gum infection, which can lead to tooth loss around the infected area.…”

Un modèle mathématique pour l’étude des interactions bactériennes en biofilm

“…La procédure adoptée pour l'étude des interactions entre S. gordonii et P. gingivalis a consisté en 2 grandes étapes (Figure 2A et B [5]. La croissance des bactéries en biofilm est modélisée au moyen d'un automate cellulaire à 2 dimensions (largeur x hauteur) dans lequel chaque bactérie est considérée comme un individu caractérisé par un comportement qui lui est propre (Figure 1) [6].…”