The origin of kinetic cooperativity in prehiotic catalysts |
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Authors: | Jacques Ricard Jacques Vergne Jean-Luc Decout Marie-Christine Maurell |
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Institution: | (1) Institut Jacques Monod, Tour 43, 2, place Jussieu-75251, 05 Paris Cedex, France;(2) L.E.D.S.S. 6, Université J. Fourier, BP53 X-38041 Grenoble Cedex, France |
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Abstract: | A polyallylamine carrying long hydrophobic dodecyl groups and adenine residues as side chains (PALAD C12) may be able to catalyze the hydrolysis ofN-carbobenzoxy-l-alaninep-nitrophenyl ester (N-Cbz-Ala) as well asp-nitrophenyl acetate (pNPA). The progress curve of hydrolysis of the former displays a long lag and apparently no steady state.
After this transient the rate falls off due to the accumulation of the products. Conversely, the hydrolysis ofp-nitrophenyl acetate displays classical burst kinetics followed by a slow decline of the reaction rate.
Theoretical considerations show that a steady state may be expected to occur only if the concentration of the free catalyst
is very small during the reaction. This condition is sufficient to allow the rate of disappearance of the substrate to be
equal to the rate of appearance of the products, which is precisely a condition for the existence of a steady state. If the
catalyst is poorly active and has a loose affinity for its substrate and product, the measurement of a significant reaction
rate will require a much larger concentration of the catalyst. Therefore, under these conditions, one cannot expect a steady
state to occur. The mathematical expression of the error made in the steady-state assumption has been derived. This error
increases with the catalyst concentration and decreases if the affinity of the substrate for the catalyst is high. Therefore
the lack of steady state is associated with the affinity (or the dissociation) of the substrate and the product for the catalyst.
When this affinity is low, the free concentration of the catalyst during the reaction is high and one cannot expect a steady
state to occur. This is precisely what takes place with N-Cbz-Ala.
A mathematical expression of the rate of hydrolysis of N-Cbz-Ala and of any reactant that displays this type of kinetics may
be derived at the end of the transient when the rate is close to its maximum value. Under these conditions the rate cannot
follow classical Michaelis-Menten kinetics and displays positive cooperativity.
It may therefore be speculated that primordial template-like catalysts that were displaying a poor affinity for their substrates
and products were already exhibiting apparent positive cooperativity in the kinetic reactions they were able to catalyze.
Correspondence to: J. Ricard |
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Keywords: | Primordial catalysts Template-like catalysts Kinetic cooperativity Ribozymes N 6-substituted adenine derivative |
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