Relevance of the Computational Models of Bacterial Interactions in the simulation of Biofilm Growth

TL;DR

The paper addresses how different mechanistic models of cell-cell interaction influence the emergence of rod-shaped bacterial microcolonies during early biofilm formation. Using an agent-based Brownian dynamics framework, it systematically compares Hertz, Soft Repulsive Spherocylindrical (SRS), and attractive Kihara potentials within a 2D setting where growth, division, and diffusion compete under the control parameter $\Gamma = t_{dif}/t_{gr}$. The key finding is that interaction strength largely drives colony density, shape, and orientational order, while the specific force law has a secondary effect, with attractive interactions only relevant in non-compact regimes. The results provide practical guidance for parameterizing biofilm simulations and indicate when simplified repulsive models suffice, while acknowledging limitations such as the exclusion of the extracellular matrix and three-dimensional effects, which the authors propose to address in future work.

Abstract

This study explores the application of elongated particle interaction models, traditionally used in liquid crystal phase research, in the context of early bacterial biofilm development. Through computer simulations using an agent-based model, we have investigated the possibilities and limitations of modeling biofilm formation and growth using different models for interaction between bacteria, such as the Hertz model, Soft Repulsive Spherocylindrical (SRS) model, and attractive Kihara model. Our approach focuses on understanding how mechanical forces due to the interaction between cells, in addition to growth and diffusive parameters, influence the formation of complex bacterial communities. By comparing such force models, we evaluate their impact on the structural properties of bacterial microcolonies. The results indicate that, although the specific force model has some effect on biofilm properties, the intensity of the interaction between bacteria is the most important determinant. This study highlights the importance of properly selecting interaction strength in simulations to obtain realistic representations of biofilm growth, and suggests which adapted models of rod-shaped bacterial systems may offer a valid approach to study the dynamics of complex biofilms.

Figures (6)

• Figure 1: (A) Schematic representation of the geometrical parameters of the bacterial model. (B) Parameters involves in the calculation of the forces in SRS, attractive Kihara and Hertz models (see main text for details). (C) Comparison between the modulus of the forces calculated by SRS and attractive Kihara models ($F^K/\varepsilon_K$, black and red line respectively), and Hertz model ($F^H/10^4\varepsilon_H$, blue line) as function of the minimum distance between cells $d_m/\sigma$. The inset shows a zoom to the region of $d_m/\sigma \in [0.5,1.1]$. (D)-(G) Configurations of microcolonies with biomass $m(t)\approx 3500$ obtained with SRS model with $\varepsilon_K/k_BT=1$ (D and F) and $\varepsilon_K/k_BT=100$ (E and G), at $\Gamma=10$ (D and E) and $\Gamma=0.1$ (F and G).
• Figure 2: Position of the first peak of the distribution function in units of bacterial diameter $r_1/\sigma$, for microcolonies with biomass $m(t)=2000$ obtained with the SRS model (black lines and circles), the attractive Kihara model (red lines and triangles) and the Hertz model (blue lines and squares) as a function of the interaction strength ($\varepsilon_{K}/k_BT$ for the SRS and attractive Kihara models and $\varepsilon_H\cdot10^{-4}/k_BT$ for Hertz). The cases with $\Gamma=10$ (open symbols), $1$ (dashed symbols) and $0.1$ (solid symbols) are shown.
• Figure 3: Cell density in reduced units $\rho\sigma^2$ as function of the biomass $m(t)$ for $\Gamma=10$ (top panel) and $\Gamma=0.1$ (bottom panel). In both panels are represented results obtained with SRS model (black lines and circles), attractive Kihara (red lines and triangles) and Hertz model (blue lines and squares). Open, dashed and solid symbols are for $\varepsilon_K= k_BT, 25k_BT$ and $100k_BT$ respectively in the case of SRS and attractive Kihara models, and for $\varepsilon_H= 10^4k_BT, 25\cdot10^4k_BT$ and $100\cdot10^4k_BT$ in the case of Hertz model.
• Figure 4: Square of the eccentricity of the microcolony ($e^2(t)$) and nematic order parameter ($S_2(t)$) as a function of the biomass $m(t)$, for $\Gamma=10$ (A) and (C), and for $\Gamma=0.1$ (B) and (D). The results obtained with SRS, attractive Kihara and Hertz models are represent by the same symbols than in Fig. \ref{['fig2']}.
• Figure 5: Surface coverage profiles $g(r_{cm})$ for microcolonies with $m(t) = 100, 500$ and $2000$ (left, middle and right column, respectively), and $\Gamma = 10$ and $0.1$ (top and and bottom row, respectively) obtained with SRS model (black lines and circles), attractive Kihara (red lines and triangles) and Hertz model (blue lines and squares). Open, dashed and solid symbols are for $\varepsilon_K= k_BT, 25k_BT$ and $100k_BT$ respectively in the case of SRS and attractive Kihara models, and for and $\varepsilon_H= 10^4k_BT, 25\cdot10^4k_BT$ and $100\cdot10^4k_BT$ respectively in the case of Hertz model.