Spatial demixing in microbial colonies with growth delay

Abstract

A microbial colony population expanding in two-dimensions is subject to greater genetic drift compared to well-mixed populations. Time-series fluorescence images of bacteria Escherichia coli and budding yeast Saccharomyces cerevisiae colonies show that during the course of colony growth, a well-mixed population of two fluorescently labeled strains, segregates into well-defined sector-like domains with fractal boundaries (Hallatschek et. al. 2007). The dynamics of these domain boundaries are responsible for the sectoring pattern at large. As the colony grows, these domain boundaries do not propagate linearly, as the cells with different genotypes on either side of the domain boundary undergo neutral competition at this interface. These domain boundaries in the sectoring pattern are akin to trajectories of random walkers undergoing anomalous diffusion. Through previous research, we note that different microbial colonies, such as that of E. coli and S. cerevisiae, differ in the amount of boundary wandering. To answer these questions, we have implemented the Eden Model, a grid based stochastic simulation in Python. This model of microbial colony growth allows us to test models that can give rise to the experimentally observed differences in boundary wandering. We propose a modification of the Eden Model that delays the cell division of newly reproduced cells the model. This is implemented as a two-state process: a newly born cell is in a nascent state for a fixed maturation time after which they reach an active state which can divide. We quantitatively show that by incorporating this growth delay into the Eden Model, the domain boundary wandering becomes less pronounced in our model and consequently, reduces the genetic drift in the growing populations. We discuss how our model integrates biological cell cycle dynamics into colony growth models to predict the genetic drift in colony populations.