Cauliflower shapes of bacterial clusters in the off-lattice Eden model for bacterial growth in a Petri dish with an agar layer

TL;DR

This paper introduces a three-dimensional off-lattice Eden model to simulate bacterial colony growth in Petri dishes, revealing complex morphologies, fractal structures, and transport properties influenced by nutrient layer height.

Contribution

The study extends the Eden model to three dimensions with new constraints, providing insights into bacterial cluster morphology and transport properties in realistic settings.

Findings

Cluster morphology depends non-trivially on nutrient layer height.

Clusters exhibit fractal structures with measurable dimensions.

Transport properties like permeability and tortuosity are estimated from density data.

Abstract

We developed the off-lattice Eden model to simulate the growth of bacterial colonies in the three-dimensional geometry of a Petri dish. In contrast to its two-dimensional counterpart, our model takes a three-dimensional set of possible growth directions and employs additional constraints on growth, which are limited by access to the nutrient layer. We rigorously tested the basic off-lattice Eden implementation against literature data for a planar cluster. We then extended it to three-dimensional growth. Our model successfully demonstrated the non-trivial dependency of the cluster morphology, non-monotonous dependency of the cluster density, and power law of the thickness of the boundary layer of clusters as a function of the nutrient layer height. Moreover, we revealed the fractal nature of all the clusters by investigating their fractal dimensions. Our density results allowed us to estimate the basic transport properties, namely the permeability and tortuosity of the bacterial colonies.