Maintaining maximal metabolic flux by gene expression control
Fig 4
The dynamics are illustrated for the network shown in A. The green box depicts a varying external concentration, the blue box denotes the sensor concentration. B: the optimal input-output relations, showing enzyme synthesis rates as a function of changing sensor concentration C′. In plots C1 to C4, the external C concentration is changed after 50 time units, and again after 100 time units. C1: The optimal C concentration predicted by the sensor (red line) converges to the real external C concentration (blue), even when the external concentration changes at t = 50 and t = 100. C2: enzyme dynamics equilibrate after each change in external conditions, and reach their optimal levels. C3: the steered metabolic pathway reaches the optimum after each external change, as the distance to the (periodically changing) optimum reaches zero after some time. C4: flux dynamics equilibrate, showing that the pathway has reached steady state each time the external conditions change. Full equations are given in Box 2, code is given in the SI.