Autocatalysis Reversible

If a reaction is reversible and if one has assumed a rate function that does not take the reverse reaction into account, one observes a downward curvature. As equilibrium is approached, the slope of this curve approaches zero. Another cause of curvature is a change in temperature during the course of the experiment. An increase in temperature causes an increase in the reaction rate, leading to an upward curvature. Bunnett (3) has discussed a number of other sources of curvature, including changes in pH and ionic strength, impurity effects, autocatalysis, and side reactions. 

In the 45 years since its proposal, Frank s autocatalytic mechanism (Section 11.3, above) has spawned numerous theoretical refinements including consideration of such factors as reversibility, racemization, environmental noise, and parity-violating energy differences. [100,101] In contrast to the above examples of stereospecific autocatalysis by the SRURC, however, none of these theoretical refinements is supported by experimental evidence. While earlier attempts to validate the Frank mechanism for the autocatalytic amplification of small e.e.s in other experimental systems have generally been unsuccessful, several recent attempts have shown more promising results. [102,104]... 

Fig. 6.22. The 14 different qualitative forms for the stationary-state locus for cubic autocatalysis with reversible reactions and inflow of all species, with c0 < a0 the broken line represents the equilibrium composition which is approached at long residence times. (Reprinted with permission from Balakotaiah, V. (1987). Proc. R. Soc., A41J, 193.)...

If the temperature difference 0C between the heat bath and the inflow is greater than zero, we can have the opposite effect to Newtonian cooling, with a net flow of heat into the reactor through the walls. With his possibility, two more stationary-state patterns can be observed, giving a total of seven different forms—the same seven seen before in cubic autocatalysis with the additional uncatalysed step (the two new patterns then required negative values for the rate constant) or with reverse reactions included and c0 > ja0 ( 6.6). 

Gray, P., Showalter, K., and Scott, S. K. (1987). Propagating reaction-diffusion fronts with cubic autocatalysis the effects of reversibility. J. Chim. Phys., 84, 1329-33. 

Reactions (377) and (378) are usually not ranked among catalytic processes, although they are, as a matter of fact, autocatalytic since they occur on the surface of carbon, one of the participants of the reactions. True, it is more usual to speak of autocatalysis for reactions catalyzed by products rather than by reactants, but it is not essential in our case. Equations (377) and (378) may be read from right to left as the reactions are reversible. 

It is easy to see that such a system has certain advantages in bad times, when food is depleted. Because some key components of the network cannot permeate the membrane, they cannot leak out either, thus a package of metabolites will be preserved in the cell interior (until it is degraded by side reactions). In contrast, a cell whose metabolic network could be re-created entirely from outside could also lose all it metabolites under harsh conditions since they would simply be lost by reactions running in the reverse. We suggest the term endogenous autocatalysis to describe contemporary metabolic networks. 

Autocatalysis in self-complementary systems is generally due to an efficient reaction within the complex T-A-B. If the reaction has no intermediate, or formation of an intermediate is rate limiting, rate enhancement is derived from the reduction in entropy caused by bringing together the reagents on a template. If breakdown of an intermediate is rate limiting (as in the case with our amide-forming replicators), rate enhancement is derived from template stabilization of an intermediate A-B such that product formation is favored over reversion to substrates. 

The unusual reversal of isomers may be rationalized according to Scheme 19, where an equilibrium is proposed between the kinetically controlled anionic C-2 a-adduct 54 and the thermodynamically stable anionic C-6 CT-adduct 55. Another equilibrium exists between the dianionic <7-adducts 56 and 57. Support for the existence of dianionic cr-adducts has been presented by Novikov et al. (76CHE210) and Kessar et al. (73IJC825). The function of the partial pressure of ammonia is to inhibit the formation of the dianionic a-adducts. Once the dianionic cr-adducts are formed, they become good hydride donors and aromatize to products 58 and 59. As the concentration of products slowly becomes significant, the principal amination pathway is taken over by autocatalysis by means of a six-membered transition complex, as described in Section II,A,2 and as shown for the 2,5-isomer in Scheme 20. 

The unrealistic "cubic autocatalysis" form 14.4 was chosen here for simplicity s sake (a "quadratic" form X+Y— 2Y does not produce instability). Gray and Scott [34] discuss this case in much greater detail. They include reverse steps as well as an uncatalyzed, parallel step X— Y the latter keeps the mathematics from... 

Diffusion Fronts with Cubic Autocatalysis The Effeas of Reversibility. 

Three further sets of circumstances are particularly illuminating one where the autocatalytic reaction is reversible (A+2B 3B) one where the catalyst B itself decays according to a first-order or second-order law and finally, one where cubic and quadratic autocatalysis occur simultaneously. The last case is discussed in section 5. 

Lutz F, Igarashi T, Kawasaki T, Soai K (2005) Small amounts of achiral P-amino alcohols reverse the enantioselectivity of chiral catalysts in cooptaative asyrrrmetric autocatalysis. J Am Chem Soc 127 12206-12207. doi 10.1021/ja054323c... 

This method is applicable to all reactions, simple and complex, and is of particular interest at the moment when / = 0 (initial rate), when the initial order is obtained it is often easier to find the initial rate law in the first 10% of the reaction, before products which can influence the rate (reversible reactions, autocatalysis, inhibition, polymerizations, etc.) have been formed in sufficient concentration. 

Very recently, autocatalysis has been foimd in organocatalytic Matmich reactions with chiral amines that are themselves made by catalysis with the amino acid proline (26). So far, no asynunetric amplification was observed but the stereoselectivity of the reaction catalysed by the enantiopure product was still very high. Like other autocatalytic reactions known where the product formed is of lower ee than the initially present product-catalyst, corrsecutive cycles of autoeatalysis will inevitably lead to an erosion of errantiomeric prrrity. Let us therefore look at other means of asynunetric amplification that can provide the reverse from low to high enantiomerio purity. 

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