An Anticipatory Model

An anticipatory system is one in which information is sent from an element in the early stages of a sequence of events to a nonacting element that will arise in that sequence. The information sent ahead prepares the future element to function based on information arising in advance of the normal sequence of events. The unmanifested element anticipates its ultimate manifestation in the sequence. An anticipatory system has been modeled by Kier and Cheng94 using the dynamic characteristics of cellular automata. A concentration of an intermediate product influences the creation of a supplemental enzyme that enhances the competence of an enzyme downstream. This anticipation of a future event creates a condition in which the concentration of a later substrate is suppressed, a property characteristic of the system. 

The anticipatory model employed in this study had the following stepwise reactions. 

Equation [17] is the conversion of A to B, assuming an irreversible first-order reaction catalyzed by the enzyme e. The rules governing the initial encounter, PB(Aei) and J(Ae4), are set at the beginning of each run. The next step in the reaction is modeled as shown in Eqs. [18]. 

If the system is not an anticipatory one, the conversion of Be2 to Ce2 would follow only one route. If the system is anticipatory, as shown, there are two paths for the conversion of Bez- The formation of e24 represents an enzyme that may function upon substrates B or D (Eqs. [19] and [20]). 

Thus the available enzyme to convert B to C is the same for an anticipatory or nonanticipatory system. In the case of an anticipatory system, there is formed, in advance of the creation of substrate D an enzyme, 2,4, that will enhance the 

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Kercel SW, Allgood GO, Dress WB, Hylton JO. An anticipatory model of cavitation. Proceedings of the Society of Photo-Optical Instrumentation Engineers (SPIE) Applications and Science of Computational Intelligence II, Serial Number 0277-786X, 1999 6 224-235. 

In each study, the dynamics revealed concentrations over time that are influenced by the presence or absence of a feed-forward or preadaption state in the system. The concentration of A steadily diminishes as successive concentrations of B, C, and D rise and fall at the same levels. The concentration of E rises at the end of the run, eventually becoming the only ingredient in the system. The concentration of D is ca. 0.25 in a nonanticipatory model. In contrast, with an anticipatory or feed-forward step in the system there is created an additional amount of enzyme specific for substrate D (enzyme, 2,4) that is available at a future time to catalyze the conversion of D to E. This anticipatory attribute creates a property of the system in which the concentration of ingredient D is not allowed to accumulate to its normal level. In contrast, the concentration of D in an anticipatory model is approximately 0.13, about half the D concentrations for the nonanticipatory models. The concentration of B therefore serves as a predictor of the concentration of D at a later time. 

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