Autocatalytic feedback loop

In a network of autocatalytic feedback loops (of which we here do consider only those processes related to Mg) control functions which give rise to either autocatalyst supply (sequestration from the enviromnent) or loss (abstraction or precipitation by parasitic byproducts) several different chemical species may interact or cooperate to achieve the above kinds of control (Eiswirth et al. 1991b), two such side-loops cause somewhat increased topological network complexity rather than fundamentally changing network dynamics. 

Fig. 10 (a). Despite of the autocatalytic feedback loop which is present in (6.1) even for v = 1 we thus have a unique steady state in X > 0 which is globally and asymptotically stable. 

Fig. 1. Positive (autocatalytic) and negative feedback loops between the activator (A) and inhibitor (I) variable.

If a second variable participates in an additional feedback loop with a negative regulation, oscillations become possible. The mutual dependencies of the two variables, which have been coined activator and inhibitor, are depicted in Fig. 1. A, the autocatalytic species is the activator it activates the production of /, and I is the inhibitor because it slows down or inhibits the growth of A [13, 14]. Oscillations arise in activator-inhibitor systems if characteristic changes of the activator occur on a faster time-scale than the ones of the inhibitor. In other words, the inhibitor must respond to a variation of the activator variable with some delay. In fields as diverse as semiconductor physics, chemistry, biochemistry or astrophysics, and also in electrochemistry, most simple periodic oscillations can be traced back to such an activator-inhibitor scheme. 

In this chapter, the experimentally observed wave forms are not reviewed from the point of view of dynamic systems theory. Rather, we focus on the physical mechanisms that cause complex oscillatory behavior. In general, the phenomena considered require the presence of autocatalysis and two negative feedback loops. Recall that simple oscillations are caused by the interaction of an autocatalytic variable and one negative feedback variable. Thus it is plausible to look for an additional variable that introduces a second negative feedback loop into the two mechanisms considered in the last section. 

This reaction scheme implies that an extra source for the intermediates HOBr and HBr02 appears in the BZ system. As HBr02 is the autocatalytic intermediate its production enhances the positive feedback loop, which would lead to an increase in the IP. (This is because turning off the autocatalytic HBr02 production at the end of the IP becomes more difficult.) On the other hand the inflow of HOBr would decrease the IP since HOBr brominates the malonic acid (R31, for the reactions of the unperturbed BZ system we follow the notations of the MBM model) ... 

In the language of network topology, feedback manifests itself as a closed loop of bonds, junctions and elements. The reverse conclusion, however, does not hold the networks of the pore and carrier models and that of active transport in Sections 5.1 to 5.5 actually involve closed loops, but nevertheless show a unique globally and asymptotically stable steady state. The simplest case of a nontrivial feedback loop, i.e., a feedback loop which really leads to multiple steady states or limit cycles, is an autocatalytic reaction... 

The mechanism of the BZ reaction can be considered using a simple Oregonator model, where some intermediates are considered to be quasisteady-state and quasiequilibria, while the others are supposed to constant. The Oregonator model, in its simplified form, contains both an autocatalytic step and a delayed negative feedback loop... 

This is a result of autocatalytic or feedback phenomena in systems where components are extensively coupled, so that collective behavior becomes possible. Servomechanisms in biological systems act as closed loops in which the output feeds back upon the input, modifying the kinetics of the process. Far-from-equilibrium conditions are a prerequisite for any state in which we will encounter oscillatory behavior. The implications seem clear that oscillatory phenomena can propagate signals which can be amplified and can stimulate other, similar systems, which can then act collectively. The occurrence of oscillatory phenomena in biochemical systems has been documented (Chance et al., 1973 Nicolis and Portnow, 1973) however, as yet, there is no conclusive proof that such phenomena actually generate signals responsible for such hierarchical behavior. 

---