Fluid-derived lattices for unbiased modeling of bacterial colony growth
Authors: Verhoef Bryan , Hermsen Rutger , de Graaf Joost 
Published: December 2024

Bacterial colonies can form a wide variety of shapes and structures based on ambient and internal conditions. To help understand the mechanisms that determine the structure of and the diversity within these colonies, various numerical modeling techniques have been applied. The most commonly used ones are continuum models, agent-based models, and lattice models. Continuum models are usually computationally fast, but disregard information at the level of the individual, which can be crucial to understanding diversity in a colony. Agent-based models resolve local details to a greater level, but are computationally costly. Lattice-based approaches strike a balance between these two limiting cases. However, this is known to come at the price of introducing undesirable artifacts into the structure of the colonies. For instance, square lattices tend to produce square colonies even where an isotropic shape is expected. Here, we aim to overcome these limitations and therefore study lattice-induced orientational symmetry in a class of hybrid numerical methods that combine aspects of lattice-based and continuum descriptions. We characterize these artifacts and show that they can be circumvented through the use of a disordered lattice which derives from an unstructured fluid. The main advantage of this approach is that the lattice itself does not imbue the colony with a preferential directionality. We demonstrate that our implementation enables the study of colony growth involving millions of individuals within hours of computation time on an ordinary desktop computer, while retaining many of the desirable features of agent-based models. Furthermore, our method can be readily adapted for a wide range of applications, opening up new avenues for studying the formation of colonies with diverse shapes and complex internal interactions.

Author summary

Bacterial colonies develop highly diverse shapes, ranging from branches to disks and concentric rings. These structures are important because they affect competition between bacteria and evolution in the population. To study the origins and consequences of bacterial colony structures, computational models have been used to great success. However, to speed up simulations, many such models approximate continuous space using regular lattices even though this is known to cause artifacts in the resulting colony shapes. To address this, we explored the use of disordered lattices. We compared two methods from the literature for perturbing a square reference lattice. In some cases, these appeared to work, yet, when the distance between lattice sites, the contact area between cells, and the size of the cells were incorporated into the model, the symmetries of the square reference lattice reappeared. We therefore came up with a method that uses the structure of a dense fluid of disks to generate a disordered lattice. This fluid-derived lattice did not impose undesirable orientational symmetries in any of the models that we tested. Lastly, we show that our approach is very efficient, enabling the simulation of bacterial populations containing millions of individuals on a regular desktop computer.