Input-response relationships in the dynamics of glycolysis

The dynamic response of glycolysis is investigated using a two-enzyme model with three different type of input flux time dependences: constant, sinusoidal, and amplitude or frequency modulated (AM or FM) input flux. The analysis reveals that the system acts as a device which transduces amplitudes and frequencies of the input function into complex and remarkably diverse response patterns. This device may have more than one response possibilities for a single input function, owing to the coexistence of attractors in phase space. In such a case one response function can be switched over into the other by short substrate pulses. Stroboscopic plots reveal that chaotic regimes obtained under sinusoidal input flux obey a stretch-fold-press process, similar to the baker's transformation, upon a change of the stroboscoping phase. Chaotic oscillations obtained under AM or FM conditions often show a much higher degree of randomness than those obtained under sinusoidal input. This is expressed quantitatively by an enhanced Liapunov dimension of the attractors.