  We analyse the mechanism of enzyme-substrate catalysis from the perspective
of minimizing the load on the enzymes through sequestration, whilst maintaining
at least a minimum reaction flux. In particular, we ask: which binding free
energies of the enzyme-substrate and enzyme-product reaction intermediates
minimize the fraction of enzymes sequestered in complexes, while sustaining at
a certain minimal flux? Under reasonable biophysical assumptions, we find that
the optimal design will saturate the bound on the minimal flux, and reflects a
basic trade-off in catalytic operation. If both binding free energies are too
high, there is low sequestration, but the effective progress of the reaction is
hampered. If both binding free energies are too low, there is high
sequestration, and the reaction flux may also be suppressed in extreme cases.
The optimal binding free energies are therefore neither too high nor too low,
but in fact moderate. Moreover, the optimal difference in substrate and product
binding free energies, which contributes to the thermodynamic driving force of
the reaction, is in general strongly constrained by the intrinsic free-energy
difference between products and reactants. Both the strategies of using a
negative binding free-energy difference to drive the catalyst-bound reaction
forward, and of using a positive binding free-energy difference to enhance
detachment of the product, are limited in their efficacy.
