= Quasi-steady enzyme kinetics at low substrate saturation
{title2=$\varepsilon=e_0/(s_0+K_m)\ll1$}
A <quasi-steady-state approximation> for <enzyme-substrate complexes> can remain useful when total enzyme and initial substrate concentrations are comparable. The relevant parameter can involve the sum $s_0+K_m$, rather than $s_0$ alone. In a <mechanism-based inhibition> model with $s_0/K_m=O(\varepsilon)$, bounded intermediate decay rates and an inactivation rate of order $\varepsilon$, the fast complexes adjust in a layer of scaled width $O(\varepsilon)$. On bounded slow-time intervals the main complex follows the substrate, the later complex and accumulated inactivated enzyme remain $O(\varepsilon)$, and the substrate has leading exponential depletion. An outer algebraic complex concentration does not satisfy the unbound initial condition inside that initial layer.
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