Michaelis-Menten Equation

Related

• Lineweaver-Burk Plot
• Turnover Number
• Catalytic Efficiency

$\mathrm{E}+\mathrm{S}\underset{\mathrm{k}{}_{-1}}{\overset{\mathrm{k}{}_1}{\rightleftharpoons }}\mathrm{ES}\underset{\mathrm{k}{}_{-2}}{\overset{\mathrm{k}{}_2}{\rightleftharpoons }}\mathrm{E}+\mathrm{P}$

• $\mathrm{E}$ is the enzyme
• $\mathrm{S}$ is the substrate
• $k_1$ is the association rate into ES from E + S
• $k_{-1}$ is the disassociation rate into ES from E + S
• $k_2$ is the association rate into ES from E + P
• $k_{-2}$ is the disassociation rate into ES from E + P

$v=\frac{v_{\text{max}}[S]}{K_{\text{m}}+[S]}$

• Assumes:
  1. Second step above is rate-limiting
  2. $[P]\approx 0$
  3. Reaction is in Steady State such that $[\text{ES}]$ is constant and influx of ES equals efflux
• $v$ is the velocity of substrate conversion commonly in units of $\frac{\mu \mathrm{M}}{\min }$
• $v_{\text{max}}$ is the max reaction velocity
• $[S]$ is the concentration of substrate commonly in units of $\mathrm{mM}$
• $K_m$ is the Michaelis constant
• When $[S]\ll K_m$, the slope is the catalytic efficiency times $[E]$, or the enzyme concentration
• Desmos Graph