Abstract

This paper explores the consequences of the theoretical forward activation enzymatic pathway A 0 A 1 A 2 A 3 where E 1 convents A 0 to A 1, E 2 converts A 1 to A 2 and E 3 converts A 2 to A 3. A 0, which is environmentally determined, also serves to activate (or modulate) the activity of E 3 in such a way as to keep the concentration of A 2 ([A 2]) constant at a particular set-point value. For mathematical simplicity, first order rate kinetics are used where k 1, k 2 and k 3 are the rate constants for E 1, E 2, and E 3 respectively. It is shown that if k 3 is modulated appropriately so as keep [A 2] at the setpoint value with a changing upstream [A 0], then the modulation of k 3 must be anticipatory of the dynamics of the biochemical pathway. In other words, the rate of change of k 3, will be a function of [A 0], k 1, k 2, k 3, and the set-point value of [A 2]. If the modulation of k 3 does not perfectly model (anticipate) the reaction pathway of which it is a part, then the actual [A 2] will deviate from the set-point value. This type of anticipatory feed-forward activation may represent an important aspect of biological organization.