Properties of strange attractors in yeast glycolysis.

The properties of periodic and aperiodic glycolytic oscillations observed in yeast extracts under sinusoidal glucose input were analyzed by the following methods. (1) Spectral analysis, rendering sharp peaks for periodic responses and enhanced broad-band noise for aperiodic oscillations. (2) Phase plane analysis, leading to closed and to open trajectories for periodic and aperiodic oscillations, respectively. (3) Rotation of a phase plane proportionally to time, revealing strange attractors associated with the aperiodic oscillations. (4) Stroboscopic plot on the phase plane, showing that the strange attractors follow a stretch-fold-press process, if the stroboscoping phase is varied. (5) Stroboscopic transfer plot, admitting a period of three transfer processes and thus implying chaos according to the Li-Yorke theorem. (6) Determination of the rate of information production by differentiation of the transfer plot, yielding approx. 0.21 bits per min for the chaotically glycolyzing yeast extract.