ANALYSIS OF SYNCHRONOUS GROWTH OF BAKERS-YEAST .1. DEVELOPMENT OF A THEORETICAL-MODEL FOR SUSTAINED OSCILLATIONS

A deterministic population balance model for synchronous growth of baker's yeast with asymmetric budding cycle is developed and solved analytically. The model is able to describe sustained oscillations with constant shape and amplitude in the number of cells in different intervals of the cell cycle. It is shown that many characteristics of the oscillations are already completely determined by the population balances and are independent of cell metabolism. The model predicts that the oscillation period is proportional to the average doubling time, but multiple modes of oscillation with different frequency exist. The oscillation period is always smaller or at least equal to the doubling time. Under synchronized growth, the length of the parent and daughter cycles are multiples of the oscillation period and deviate from asynchronous growth. Expressions for the development in time of averaged population variables, such as the cell number in different intervals of the cell cycle, are derived for an arbitrary shape of the age distribution. Completely synchronized growth with Dirac delta age distribution is considered in more detail. It is shown that the average fraction of budding cells during synchronized growth is increased over the value for asynchronous growth. The amplitude of the oscillation on population variables decreases with increasing frequency.