Enzyme system, mathematical

The quantitative data and observations discussed above appear to be consistent with the qualitative concepts put forward by Mosbach and others to explain the behavior of multistep enzyme systems. Mathematical modelling of gel entrapped, multistep, immobilized enzyme systems, using the collocation technique, is quite straightforward and provides the opportunity not only to compare experiment with theory but also to explore the effect of parameters of the system which are experimentally inaccessible. 

The homogeneous hydrogenation systems discussed in this paper may be treated as analogues of enzyme systems with the rhodium catalyst as the enzyme (E), hydrogen (Si) and cyclohexene (S2) as the substrates, and excess ligand or other donor site as the inhibitor (I). The well-established mathematical operations of enzyme kinetics (12) can then be used to derive rate equations for various possible mechanisms. 

Are these phenomena unique, or are they typical of biological systems From a mathematical perspective, enzyme systems fall into a class of nonlinear organization, and a chain of enzyme reactions with negative feedback easily can demonstrate oscillatory behavior [520]. Glass has noted that in general, any nonlinear system with multiple negative feedback may demonstrate oscillations that lead to chaotic behavior [595]. 

Ref 1. Reagan R. 1977. Mathematical Modelling in Enzyme Systems Some Effects of Dlffusional Limitation. 1977 International Biochemical Symposium, Toronto. 

In a self-reproducing, catalytic hypercycle (second order, because of its double function of protein and RNA synthesis) the polynucleotides Ni contained not only the information necessary for their own autocatalytic self-replication but also that required for the synthesis of the proteins Ei. The hypercycle is closed only when the last enzyme in the cycle catalyses the formation of the first polynucleotide. Hypercycles can be described mathematically by a system of non-linear differential equations. In spite of all its scientific elegance and general acceptance (with certain limitations), the hypercycle does not seem to be relevant for the question of the origin of life, since there is no answer to the question how did the first hypercycle emerge in the first place (Lahav, 1999). 

A mathematical simplification of rate behavior of a multistep chemical process assuming that over a period of time a system displays little or no change in the con-centration(s) of intermediate species (i.e., d[intermedi-ate]/df 0). In enzyme kinetics, the steady-state assumption allows one to write and solve the differential equations defining fhe rafes of inferconversion of various enzyme species. This is especially useful in initial rate studies. 

A particular model, the adsorbed enzyme model, was developed, as it often provides a more realistic approach to such a system. However, both models (mass transfer and adsorbed enzyme) may coexist simultaneously, a matching of the quantitative mathematical descriptions being required to rule out one of the models [6]. 

It is interesting to note that a number of researchers have attempted, more or less successfully, to construct reliable mathematical models which combine structural elements and experimental data to predict the toxicities of new substances not yet experimentally tested for humans and other species.110152 Furthermore pharmacology, toxicity, metabolism and enzyme-inhibiting effects of fluorine-containing aromatic systems (e.g., anilines, ben-zothiadiazines, butyrophenones, corticoids, phenothiazines, steroids, uracils) have been discussed in depth in the literature.153-156... 

The similarities between enzymes and receptors allow both systems to be modeled with many of the same mathematical equations. Most treatments of receptors and enzymes appear to be very different, but the derivations and theories can largely be recycled between the two topics. 

---