The Diversity of Biochemical Time Patterns

The effects of coupling of oscillating glycolysis and oscillating substrate supply are investigated with a two‐enzyme model using detailed two‐substrate rate laws for both enzymes. Under a sinusoidal substrate supply rate, a profusion of entrained, quasiperiodic and chaotic regimes is obtained. Periodic modulation of the sinusoidal supply rate may lead to a considerable enhancement of the degree of randomness in the chaotic regime. Up to four coexisting attractors are found in phase space for a given set of control parameters, having complicatedly interleaved basins of attraction. Switching between such coexisting attractors is accomplished by pulsed substrate fluctuations that drive the system from one basin of attraction to the other. The effect of a series of substrate fluctuations with randomly distributed amplitudes is investigated, allowing the following distinction of cases: 1. For small fluctuations, the system stays within a given basin thus preserving the initial time pattern. 2. For larger fluctuations, an evolution takes place by which the system reaches a basin that cannot be left, thus displaying a time pattern that is fittest to withstand the external stochasticity. 3. For even larger fluctuations, the system is driven back and forth between the basins, displaying an intermittent switching between time patterns. 4. For still larger fluctuations, the system is switched between the basins, staying always so far from the attractors that it can be considered as an amplifier of random fluctuations.