Lattice Gas Model for Budding Yeast: A New Approach for Density Effects

Abstract

Yeasts in culture media grow exponentially in early period but eventually stop growing. The saturation of population growth is due to “density effect”. The budding yeast, Saccharomyces cerevisiae, is known to exhibit an age-dependent cell division. Daughter cell, which gives no birth, has longer generation time than mother, because daughter needs maturing period. So far, investigations in exponential growth period have been intensively accumulated, but very little is known for the stage dependence of density effect. Here we present an “in vivo” study of density effect, applying a lattice gas model to explore the age-structure dynamics. It is, however hard to solve basic equations, because they have an infinite number of variables and parameters. The basic equations are constructed from several simplified models which have few variables and parameters. These simplified models are compared with experimental data to report two findings for stage-dependent density effect: 1) paradox of decline birthrate (PDB), and 2) mass suicide of aged mothers. These events suddenly and temporarily occur at early stage of density effect. The mother-daughter model leads to PDB. Namely, when the birthrate of population is decreased, then the fraction of daughter is abruptly increased. Moreover, we find the average age of yeast population suddenly decreases at the inflection point. This means the mass apoptosis of aged mothers. Our results for density effect imply the existence of several types of “pheromones” that specifically inhibit the population growth.