A coarse-grain model of growth and cell cycle in Saccharomyces cerevisiae: a mathematical analysis

In this paper a coarse-grain model is presented that describes the major features of cell growth and cell cycle in Saccharomyces cerevisiae. Central for the construction of the growth and cell cycle model has been the large amount of scientific papers covering the description of cellular growth in steady-state and perturbed growth conditions, describing ribosome and protein contents, and the description of cell cycle progression as percentage of budded cells (cells that have entered S-phase). The coarse model is composed by i) a growth module, i.e. a set of ODEs representing the dynamics of synthesis/degradation of ribosomes and proteins, and ii) a cell cycle module, i.e. a set of three consecutive timers (T1, T2 and TB ) that temporally accounts for the yeast cell cycle, underlying the length of the G1 phase (timer T1 plus T2 ) and of the budded phase (timer TB ) entailing S, G2 and M phases. The growth module acts as a master, setting the length of the first of the three sequential timers. Main results coming from the mathematical analysis involve the qualitative behavior of the system, constraining ribosome synthesis and growth to the set of model parameters. Further results involve the generalization of a known constraint that involves the lengths of the cycles of parent and daughter cells, and accounts for the genealogical age heterogeneity, typical of budding yeast Saccharomyces cerevisiae.