Oscillatory, stochastic and chaotic growth rate fluctuations in permittistatically controlled yeast cultures

We describe a continuous culture system related to the turbidostat, but using a feedback system based on biomass estimation from the dielectric permittivity of the cell suspension rather than its optical density. It is shown that this system provides an excellent method of maintaining a constant biomass level within a fermenter. The computer-controlled system was able to effect the essentially continuous registration of growth rate by monitoring the rate of medium addition via the time-dependent activity of the pump. At some biomass setpoints for aerobically grown cultures of baker's yeast substantial time-dependent fluctuations in the growth rate of the culture were thereby observed. At some biomass setpoints, however, or under anaerobic conditions, or when using a non-Crabtree yeast, the growth rate was constant, indicating that the fluctuations were inherent to the biological system and not simply a property of the fermenter and control system. A variety of time series analyses (Fourier transformations, Hurst and Lyapunov exponents, the determination of embedding dimension, and non-linear time series predictions based on the methodology of Sugihara and May) were used to demonstrate, for the first time, that as well as stochastic and periodic components these fluctuations exhibited deterministic chaos. 'Trivial predictors' were unable to give accurate predictions of the growth rate in these cultures. The growth rate fluctuations were studied further by means of offline measurements of changes in percentage viability, bud count, and in the external ethanol and glucose concentrations; these data and other evidence suggested that the growth rate fluctuations were closely linked to the primary respiro-fermentative metabolism of this organism. The identification of chaotic growth rates in cell cultures suggests that there may be novel methods for controlling the growth of such cultures.