Autocatalytic systems

Response of autocatalytic system to addition of catalytic agent. 

In conclusion, we note that a cell is totally dependent on external supply of nutrients and energy and hence the states of coenzymes frequently depend on external conditions. They are also totally dependent on a central DNA code (see below). As coenzyme activity and DNA expression are concentration dependent, the treatment of them belongs with thermodynamic analysis of the whole controlled autocatalytic system. 

These possibilities rectify the proposed subsequent appearance and amplification of chiral autocatalytic molecules and hypercydes. [190] Any autocatalytic systems would propagate [191] throughout an extensive adjoining hydrated porous network already rich in layered amphiphiles, lipids, polymeric materials, amino acids, thiols, and so forth. In addition, amphiphiles are known to be organized into lipid membranes by interaction with the inner surfaces of porous minerals. [136] It is a small organizational jump from these membranes to frilly formed lipid vesides. 

The peroxides and peracids formed in autocatalytic systems are highly energetic molecules. We now see that the Co/Mn/Br catalyst serves to rapidly relax this energy in increasingly lower steps winding up with a highly selective bromide(O) radical (probably as a complex with the metal). The bromide(O) transient species quickly reacts with methylaromatic compounds to form PhCHj radicals and hence continues to propagate the chain sequence. 

The simplest form of flow system is the continuously fed well-stirred tank reactor or CSTR, represented schematically in Fig. 1.11. The behaviour of typical autocatalytic systems in a CSTR will be considered in chapters 4 and 5, but here we may quickly examine how multistability can arise, even with only one overall chemical reaction. We will take a CSTR in which just the... 

Fig. 6.6. Dependences of reaction rate R on extent of reaction y typical of self-accelerating (autocatalytic) systems (a) prototype quadratic autocatalysis (b) prototype cubic autocatalysis.

The flow diagram technique can also be used to illustrate clearly the rather limited effects on autocatalytic systems which arise from the reversibility of chemical reactions. For this we replace step (6.8) by its reversible counterpart... 

Further comparisons between non-isothermal and autocatalytic systems... 

Now that the recipes for locating the various changes in the qualitative form of the stationary-state locus have been presented, we can go on to examine the origin of the behaviour in the cubic autocatalytic system with the additional uncatalysed step, and for the non-adiabatic non-isothermal CSTR which has been asserted in previous sections. 

OSCILLATORY BEHAVIOUR IN THE ISOTHERMAL CSTR AUTOCATALYTIC SYSTEMS... 

To determine the response of the cubic autocatalytic system to perturbations in the vicinity of a turning point in the locus, we must return to eqn (8.6). The first two terms (not involving A a) again cancel exactly, because of the stationary-state condition. If we are also at an ignition or extinction point, the tangency condition in any of its forms discussed above ensures that the coefficient of the A a term is also zero. Thus the first non-zero term is that involving (Aa)2 ... 

The analyses applied to the simplest two-variable autocatalytic system in the previous sections can obviously be brought to bear on other systems. Much effort has been expended on the first-order non-isothermal model of chapter 7, and very similar ranges of complexity are found. Up to 35 phase portraits have been predicted for the full system with the Arrhenius temperature dependence and forced cooling, with different combinations of one or three stationary states and up to three limit cycles of varying stability. 

In the course of NMR studies of the autocatalytic system in CyDg, several experiments were carried out in which the 2-TMS-alkynylpyrimidine-5-aldehyde was directly mixed with diisopropylzinc at low temperatures and allowed to warm until the reaction was complete. The dimeric product can then be observed directly, and would be expected to be racemic since there are no internal or external chiral influences on the reaction. This was not the case, and an imbalance in favour of the homochiral form was sometimes observed a striking example is shown in Fig. 17. Since there is no workup... 

According to Mislow [70], the spontaneous generation of optical activity in chirally autocatalytic systems is practically unavoidable on statistical grounds alone. In fact, as shown early on by Mills [71], trivial statistical deviations from the racemic state can become significant, especially when the population of the chiral species is small. In a racemic mixture, there is always a tiny ee. Its value is proportional to the reciprocal of the square root of N, the total number of molecules. For instance, the expected ee (eeexp), which will be observed in more than 50% of the cases is given by ... 

One may wonder whether recycling processes such as a linear or a nonlinear back reaction exist in relevant autocatalytic systems. So far, we are not aware of their existence, ft is, however, possible that the back reaction rates k or ji are nonzero but too exceedingly small to be detected in laboratory experiments. Concerning the problem of homo chirality in life, very small A. or // are not unimaginable, considering the geological time scale for its establishment on earth. 

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... 

The essence of our approach to designing new oscillators is choose autocatalytic systems, keep them far from equilibrium, and look for multiple stationary states. Carrying out this program requires specialized experimental and theoretical tools . 

Examples for the many cases where the observed development of optical activity in a reaction could not be reproduced are the photoaddition of H2O2 to diethylfumarate [13] or the thermal decarboxylation of 2-phenyl-2-carboxylbu-tyric acid in cholesteric liquid crystals [14]. On the other hand, spurious optically active impurities may, especially in autocatalytic systems, cause considerable asymmetry effects. This exceptional case was demonstrated by Singleton and Vo... 

The cpl-induced asymmetry in photoreactions as described in Sec. B. of this chapter is not very pronounced. In order to obtain ees in excess of a few percent, photodestruction must be chosen and most of the reactant material must be sacrificed. Therefore amplification mechanisms for all types of cpl-induced asymmetric photoreactions would be highly desirable. Autocatalysis, i.e., an asymmetric synthesis where a chiral product acts as a catalyst for its own production [128], and autoinduction, i.e., the stimulation of a chiral catalyst by a chiral product [44,129], are options. Autocatalytic systems that will tilt to one enantiomeric side were introduced by Frank [130] and Seelig [131]. 

The speculations about bifurcation in autocatalytic systems lead us to conclude that the adaptive natural selection of biological systems analogue may have a primitive in analogue, and even in abiogenic autocatalytic, systems where chemical "mutations" of the autocatalyst may occur [2],... 

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