Double autocatalysis

A second type of negative feedback is double autocatalysis. The essence of this pattern is that a species generated autocatalytically, often explosively, in the primary autocatalysis is consumed by a second autocatalytic reaction in which it serves as the precursor. As the primary autocatalyst builds up, the second autocatalytic reaction accelerates, consuming the primary species at an ever-faster rate and ultimately terminating the explosion. Franck (1985) constructed a modified version of the original Lotka-Volterra model that nicely illustrates double autocatalysis ... 

Variants of the double autocatalysis mechanism occur in the Limited Explodator model of the BZ reaction (Noszticzius et al., 1984a) and the Briggs-Rauscher oscillator (De Kepper and Epstein, 1982). 

This dilemma could be overcome by the hypercycle model hypercycles are in fact not theoretical concepts, but can be observed (in a simple form) in today s organisms, where an RNA virus transfers the information for an enzyme in the host cell, which is able to carry out the preferred synthesis of new virus RNA. This RNA synthesis is supported by host factors, and an RNA minus-strand is formed. The following RNA replication affords a plus-strand. The process corresponds to a double feedback loop and involves the enzyme coded by the RNA matrix and the information present in the matrix in the form of a nucleotide sequence. Both factors contribute to the replication of the matrix, so that there is second-order autocatalysis (Eigen et al., 1982). 

Returning to the simple cubic autocatalysis model above, we shall be more interested later in the relationship between the rate and the extent of conversion. This is shown for various values of b0 in Fig. 1.7. If b0 = 0 (Fig. 1.7(a)), the rate curve is both a minimum and zero at no conversion (i.e. there is a double root at the origin) and has a further zero at complete conversion (a = 0, a0 — a = a0). The rate has a maximum value of (4/27)/ccao occurring two-thirds of the way across the diagram (a = a0). There is also a point of inflection at 50 per cent conversion, a0 — a — a0. 

Fig. 8.9. The locus A of double-zero eigenvalue degeneracies of the Hopf bifurcation for cubic autocatalysis with decay. Also shown, as broken curves, are the loci of stationary-state degeneracies, corresponding to the boundaries for isola and mushroom patterns. The curve A lies completely within the parameter regions for multiple stationary states.

For every 10 °C increase in temperature, the rate of decomposition is approximately doubled, but may increase as much as 50 times if the explosive is in the molten state. The rates of decomposition depend on the condition of storage and the presence of impurities which may act as catalysts. For example, nitroglycerine and nitrocellulose decompose at an accelerated rate due to autocatalysis, whereas the decomposition rate of TNT, picric acid and tetryl can be reduced by removing the impurities which are usually less stable than the explosive itself. With many of the explosives the presence of moisture increases the rate of decomposition. 

There is a theoretical study on the asymptotic shape of probability distribution for nonautocatalytic and linearly autocatalytic systems with a specific initial condition of no chiral enantiomers [35,36]. Even though no ee amplification is expected in these cases, the probability distribution with a linear autocatalysis has symmetric double peaks at 0 = 1 when ko is far smaller than k -,kototal number of all reactive chemical species, A, R, and S. This can be explained by the single-mother scenario for the realization of homo chirality, as follows From a completely achiral state, one of the chiral molecules, say R, is produced spontaneously and randomly after an average time l/2koN. Then, the second R is produced by the autocatalytic process, whereas for the production of the first S molecule the... 

Thus, autocatalysis occurs in biology across various levels of structural and functional hierarchies, from a complete plant (or fungus, animal) over single cells down to such molecules which take part in metabolism and get doubled in cell budding and reproduction also. Both the... 

The general consensus is to assume that the first active macromolecular species would be capable of self-reproduction, namely capable to induce the synthesis of copies of themselves via an autocatalytic step. Self-reproduction is in fact always to be connected with autocatalysis. Shnerior Lifson provides a nice numerical example to understand the importance of self-reproduction and autocatalysis suppose having a process which produces one molecule of product each microsecond. In a heterocataly tic reactions scheme, to produce one mole of product, 6 x 1 microseconds would be necessary, i.e. more than the age of the universe. Conversely, in an autocatalytic reaction scheme, where the number of reacting species would double every microsecond, the total time to attain a mole of product would be 79 microseconds. 

Under less than ideal conditions, a variety of complications attend the oxidation of cyclohexene including complex termination under low oxygen pressure, autocatalysis owing to thermal dissociation of the hydroperoxide into radicals, and a competitive propagation step in which the R02 radical adds to the double bond. 

Phosphorylation-dephosphorylation see also Period-doubling bifurcations Cascade model for mitotic oscillator, 418-44 arresting the mitotic oscillator, 438-45 double oscillator model, 448-51 extended model with autocatalysis,... 

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