= Mixed inhibition
{wiki}
In the branching model, <mixed inhibition> retains inhibitor binding to both free <enzyme> and the <enzyme-substrate complex>. Unequal $K_i$ and $K_i'$ shift both apparent parameters; their equality gives <pure noncompetitive inhibition>. For the chosen unequal case, $I=30\,\mathrm{\mu M}$ gives $\alpha=4$ and $\alpha'=2$, hence $V_{\max,\rm app}=50\,\mathrm{\mu M\,min^{-1}}$ and $K_{M,\rm app}=40\,\mathrm{\mu M}$. Because $K_i<K_i'$, binding favours free <enzyme>, and the apparent <Michaelis constant> increases. Reversing that inequality decreases it.
The limiting behaviour provides a useful diagnostic within this model:
$$
\lim_{s\to0}\frac{v}{s}=\frac{V_{\max}}{\alpha K_M},\qquad
\lim_{s\to\infty}v=\frac{V_{\max}}{\alpha'}.
$$
Low <substrate> <concentration> isolates $\alpha$ through the initial <slope>; high <substrate> <concentration> isolates $\alpha'$ through the plateau. At $I=30\,\mathrm{\mu M}$, the chosen <competitive inhibition> and unequal <mixed inhibition> examples have the same low-$s$ <slope>, $1.25\,\mathrm{min^{-1}}$, but different plateaus, $100$ and $50\,\mathrm{\mu M\,min^{-1}}$. Measuring only low <substrate> <concentrations> would miss that distinction.
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