= DNAzyme product-release limitation
{c}
\b[DNAzyme product-release limitation] is a kinetic regime in which slow departure of cleaved products delays reuse of a <DNAzyme>, even when the chemical cleavage step is fast. Product formation and regeneration of free catalyst are separate events. A <DNAzyme turnover experiment> must therefore distinguish one cleavage per catalyst from repeated cycles.
Consider an intentionally simplified saturated-substrate cycle,
$$
ES\xrightarrow{k_{\rm chem}}EP\xrightarrow{k_{\rm rel}}E+P.
$$
Here $ES$ is an <enzyme-substrate complex> and $EP$ a catalyst–product complex. If the two irreversible steps have exponential waiting times and binding of fresh substrate is effectively immediate, the mean <DNAzyme catalytic-cycle waiting time> is the sum of their means:
$$
\tau_{\rm cycle}=\frac1{k_{\rm chem}}+\frac1{k_{\rm rel}},\qquad
k_{\rm turn}=\frac{k_{\rm chem}k_{\rm rel}}{k_{\rm chem}+k_{\rm rel}}.
$$
With stipulated $k_{\rm chem}=1\,\mathrm{s^{-1}}$ and $k_{\rm rel}=0.01\,\mathrm{s^{-1}}$, the average cycle takes 101 s and $k_{\rm turn}\approx0.00990\,\mathrm{s^{-1}}$. Making chemistry ten times faster reduces the cycle only to 100.1 s. The slow release dominates this model; the numbers are not measurements of a particular DNAzyme.
Under those assumptions a rapid first cleavage can precede much slower continued production. A burst alone is not a unique identification of slow release: catalyst inactivation or mixed active populations can also change the trace. Comparing chemical cleavage with independent product-dissociation observations is more informative than assigning a mechanism from curve shape alone.
The regime is not a definition of every DNAzyme. The primary kinetic analysis by <S. W. Santoro> and <Gerald F. Joyce> instead reported substrate-binding limitation of catalytic efficiency for their RNA-cleaving DNA enzyme under the studied conditions.<Mechanism and utility of an RNA-cleaving DNA enzyme by S. W. Santoro and G. F. Joyce>[Abstract: kinetic measurements and substrate-binding limit]{ref} Different concentrations and measured quantities can expose different limiting steps; a claim about efficiency at low substrate is not automatically a claim about the slowest saturated turnover step.
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