Mixed Inhibition

Inhibitor binds allosterically to either the enzyme or ES complex. We define $K_I$ to be the dissociation constant for the free $\mathrm{EI}$ complex (equilibrium constant for converting $\mathrm{EI}\to \mathrm{E}+\mathrm{I}$) and $K_I^{\prime }$ to be dissociation constant for the $\mathrm{ESI}$ complex

• $K_m$ increased if $K_I<K_I^{\prime }$ where $K_m$ is the Michaelis constant
  • If the inhibitor binds more strongly to E than it does to ES, binding affinity of E to S decreases, so $K_m$ increases
  • This is kind of analogous to competitive inhibition since for lower relative $K_I$, we’ll have less free $E$, which is kind of how the competitive inhibitor takes away free $E$. Competitive inhibition also increases $Km$
• $K_m$ decreased if $K_I>K_I^{\prime }$
  • If the inhibitor binds more strongly to ES than it does to E, binding affinity of E to S increases, so $K_m$ decreases
• $v_{\text{max}}$ decreased due to general inhibition
• Desmos Graph of Lineweaver-Burk Plot for Mixed Inhibition

Lineweaver-Burk Plot