Multicellular growth as a dynamic network of cells.

Cell division without cell separation produces multicellular clusters in budding yeast. Two fundamental characteristics of these clusters are their size (the number of cells per cluster) and cellular composition: the fractions of cells with different phenotypes. However, we do not understand how different cellular features quantitatively influence these two phenotypes. Using cells as nodes and links between mother and daughter cells as edges, we model cluster growth and breakage by varying three parameters: the cell division rate, the rate at which intercellular connections break, and the kissing number (the maximum number of connections to one cell). We find that the kissing number sets the maximum possible cluster size. Below this limit, the ratio of the cell division rate to the connection breaking rate determines the cluster size. If links have a constant probability of breaking per unit time, the probability that a link survives decreases exponentially with its age. Modeling this behavior recapitulates experimental data. We then use this framework to examine synthetic, differentiating clusters with two cell types, faster-growing germ cells and their somatic derivatives. The fraction of clusters that contain both cell types increases as either of two parameters increase: the kissing number and difference between the growth rate of germ and somatic cells. In a population of clusters, the variation in cellular composition is inversely correlated (r=0.87) with the average fraction of somatic cells in clusters. Our results show how a small number of cellular features can control the phenotypes of multicellular clusters that were potentially the ancestors of more complex forms of multicellular development, organization, and reproduction.