Competitive inhibition

In the model of reversible enzyme inhibition, competitive inhibition makes substrate binding and inhibitor binding mutually exclusive: $EI$ is allowed but $ESI$ is absent. Set ${\alpha }^{\prime }=1$, equivalently take $K_i^{\prime }\to \infty$. ThenFor the chosen $I=30\mu \mathrm{M}$, $\alpha =4$: the half-limiting substrate concentration rises from $20$ to $80\mu \mathrm{M}$, while the limiting reaction rate remains $100\mu \mathrm{M}\mathrm{mi}{\mathrm{n}}^{-1}$. At $s=200\mu \mathrm{M}$ the inhibited reaction rate is $500/7\approx 71.43\mu \mathrm{M}\mathrm{mi}{\mathrm{n}}^{-1}$, compared with the uninhibited $1000/11\approx 90.91\mu \mathrm{M}\mathrm{mi}{\mathrm{n}}^{-1}$. “Overcome by substrate” means that their ratio tends to one as $s\to \infty$, not that any finite addition removes the difference.