= Sequential-enzyme Hill limit
{title2=$\rho=E_0 k_n^+S^n/(\prod_iK_i+S^n)$}
For sequential <enzyme> binding, a <quasi-steady-state approximation> gives occupied-state weights $\phi_jS^j$, $\phi_j=\prod_{i=1}^jK_i^{-1}$, relative to free <enzyme>. If all intermediate weights tend to zero while the terminal weight remains nonzero, <enzyme conservation> leaves only unbound and fully bound states, and the production rate becomes the displayed <Hill equation>. One realization holds other rates fixed while the first binding rate tends to zero and the last tends to infinity with positive finite product. A statement merely bounding that product does not by itself specify this nontrivial <distinguished limit>.
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