A thin-film extensional flow model for biofilm expansion by sliding motility

Abstract

In the presence of glycoproteins, bacterial and yeast biofilms are hypothesized to expand by sliding motility. This involves a sheet of cells spreading as a unit, facilitated by cell proliferation and weak adhesion to the substratum. In this paper, we derive an extensional flow model for biofilm expansion by sliding motility to test this hypothesis. We model the biofilm as a two-phase (living cells and an extracellular matrix) viscous fluid mixture, and model nutrient depletion and uptake from the substratum. Applying the thin-film approximation simplifies the model, and reduces it to one-dimensional axisymmetric form. Comparison with Saccharomyces cerevisiae mat formation experiments reveals good agreement between experimental expansion speed and numerical solutions to the model with O ( 1 ) parameters estimated from experiments. This confirms that sliding motility is a possible mechanism for yeast biofilm expansion. Having established the biological relevance of the model, we then demonstrate how the model parameters affect expansion speed, enabling us to predict biofilm expansion for different experimental conditions. Finally, we show that our model can explain the ridge formation observed in some biofilms. This is especially true if surface tension is low, as hypothesized for sliding motility.

Quantifying the role of different surface coatings in experimental models of wound healing

“…Mathematical models have been applied to mimic both in vitro and in vivo experiments to test biological hypotheses and to predict experimental outcomes (Jin et al, 2018a;Jove et al, 2019;Nardini et al, 2016;Sheardown and Cheng, 1996;Tam et al, 2019;Villella et al, 2019). One of the most commonly used models to study collective cell migration is the Fisher-Kolmogorov model (Fisher, 1937;Maini et al, 2004;Sherratt and Murray, 1990;Simpson et al, 2006).…”

Vertical growth dynamics of biofilms

“…However, while the logistic growth curve captures these qualitative features, it is unclear if logistic growth is quantitatively accurate. To address this issue, many multi-phase, spatial models have been developed ( Alpkvist et al, 2006 ; Zhang et al, 2008 ; Hartmann et al, 2019 ; Warren et al, 2019 ; Srinivasan et al, 2019 ; Fei et al, 2020 ; Jin et al, 2020 ), with a smaller subset of these models explicitly addressing vertical growth, or colony thickness ( Wang et al, 2017 ; Tam et al, 2019 ; Hughes, 2020 ). Even if these models are highly accurate, reliance on many precisely measured parameters limits the practical and heuristic utility of such models.…”

“…To address this issue, many multi-phase, spatial models have been developed (Alpkvist et al, 2006;Zhang et al, 2008;Hartmann et al, 2019;Warren et al, 2019;Srinivasan et al, 2019;Fei et al, 2020;Jin et al, 2020), with a smaller subset of these models explicitly addressing vertical growth, or colony thickness (Wang et al, 2017;Tam et al, 2019;Hughes, 2020). Even if these models are highly accurate, reliance on many precisely measured parameters limits the practical and heuristic utility of such models.…”

Biofilm Growth Under Elastic Confinement

“…Building on important work on osmotically-driven spreading [1], a biofilm has often been modelled as a viscous, Newtonian fluid mixture (nutrient rich water and biomass), neglecting the matrix elasticity. The effects of surface tension [10], osmotic pressure [11], and the interplay between nutrients, cell growth, and electrical signaling in response to metabolic stress have all been studied recently [2].…”

“…While previous analyses have focused on the experimentally tractable cases of unconfined and unsubmerged biofilms [1,2,10,11], they do not accurately reflect the conditions in which many biofilms grow; they thrive in confined micro-spaces [13] between flexible elastic boundaries such as vessel walls or soil pores [14], and indeed in the human body, where they account for over 80% of microbial infections [15]. Biofilms are difficult to treat with antibiotics, being thousands of times more resistant than the constituent microorganisms in isolation [16] due to a range of mechanical and biological processes [17,18].…”