OSCILLATORY, STOCHASTIC AND CHAOTIC GROWTH-RATE FLUCTUATIONS IN PERMITTISTATICALLY CONTROLLED YEAST CULTURES

We describe a continuous culture system related to the turbidostat, bu t using a feedback system based on biomass estimation from the dielect ric permittivity of the cell suspension rather than its optical densit y. It is shown that this system provides an excellent method of mainta ining a constant biomass level within a fermenter. The computer-contro lled 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 aerobic ally grown cultures of baker's yeast substantial time-dependent fluctu ations in the growth rate of the culture were thereby observed. At som e biomass setpoints, however, or under anaerobic conditions, or when u sing a non-Crabtree yeast, the growth rate was constant, indicating th at the fluctuations were inherent to the biological system and not sim ply 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 t o demonstrate, for the first time, that as well as stochastic and peri odic components these fluctuations exhibited deterministic chaos. 'Tri vial predictors' were unable to give accurate predictions of the growt h rate in these cultures. The growth rate fluctuations were studied fu rther by means of offline measurements of changes in percentage viabil ity, bud count, and in the external ethanol and glucose concentrations ; these data and other evidence suggested that the growth rate fluctua tions were closely linked to the primary respiro-fermentative metaboli sm of this organism. The identification of chaotic growth rates in cel l cultures suggests that there may be novel methods for controlling th e growth of such cultures.