Michaelis-Menten Equation

#Biochemistry

Related

• Lineweaver-Burk Plot
• Turnover Number
• Catalytic Efficiency

$\displaystyle \ce{E + S <=>[k_{1}][k_{-1}] ES <=>[k_{2}][k_{-2}] E + P}$

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

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

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