The origin of kinetic cooperativity in prebiotic catalysts

A polyallylamine carrying long hydrophobic dodecyl groups and adenine residues as side chains (PALAD C12) may be able to catalyze the hydrolysis of N-carbobenzoxy-l-alanine p-nitrophenyl ester (N-Cbz-Ala) as well as p-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 of p-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.