Michaelis-Menten kinetics

2017-10-20

What do enzymes do to the reaction coordianate to speed up reactions?

They lower the activation energy by stabilizing the transition state

_____________ changes in activation energy lead to ____________ changes in rate.

1. Small, large
2. Small, Small
3. Large, Small
4. Large, Large

1 and 4

Stabilizing TS by $67 \ kJ \cdot mol^{-1}$ gives a 100-billion fold increase in rate!

What part of the serine protease enzymatic mechanism does the most to speed up the reaction?

Oxyanion hole: 2 hydrogen bonds to the negatively charged intermediate

How do organisms regulate the rates at which they do chemistry?

Conceptual goals

• Understand the properties of Michaelis-Menten enzymes
• Understand how experimental rate measurements allow determination of MM parameters
• Understand how cells tweak these parameters to achieve regulated activity

Skill goals

• Interpret experimental graphs for MM enzymes in terms of altered MM parameters.
• Interpret changes to those parameters in terms of altered underlying chemistry.

Resources

Homework (do it...)

Lab 5

Practice problems later

Simulator http://aclarke.uoregon.edu:8000

$E \cdot S \color{red}{\rightarrow} E + P$

$E \cdot S \color{red}{\overset{k_{cat}}{\rightarrow}} E + P$

$k_{cat}$ is the rate constant for the reaction once substrate is bound

$velocity = V = [E \cdot S] k_{cat}$

What determines $[E \cdot S]$?

• $[E]_{T}$: the total enzyme concentration
• $[S]$: the substrate concentration
• $K_{M}$: the "affinity" of the enzyme for substrate

$V = [E \cdot S] k_{cat} = [E]_{T} \theta_{ES} k_{cat}$

What is $\theta_{ES}$?

$K_{M}$ (the Michaelis constant) is basically a $K_{D}$. It measures the affinity of the enzyme for substrate.

The Michaelis-Menten equation:

$V_{0} = k_{cat}[E]_{T}\frac{1}{1 + K_{M}/[S]_{0}}$

The velocity of a reaction is determined by:

• The rate constant for the enzyme when bound to substrate ($k_{cat}$)
• And the concentration of substrate bound to enzyme. This is determined by $K_{M}$, $[S]_{0}$, and $[E]_{T}$.

$E + S \color{blue}{\overset{K_{M}}{\rightleftarrows}} E \cdot S \color{red}{\overset{k_{cat}}{\rightarrow}} E + P$

Would a mutation to serine protease disrupting the oxanion hole alter $k_{cat}$ or $K_{M}$?

$k_{cat}$ would go down. It would disrupt ability to hop over transition state.

How would it alter the $V$ vs. $S$ curve?

It would lower the maximum rate, but leave shape unchanged.

$E + S \color{blue}{\overset{K_{M}}{\rightleftarrows}} E \cdot S \color{red}{\overset{k_{cat}}{\rightarrow}} E + P$

Would a mutation to serine protease disrupting binding of the peptide alter $k_{cat}$ or $K_{M}$?

$K_{M}$ would go up. It would disrupt ability to bind substrate.

How would it alter the $V$ vs. $S$ curve?

It would raise the $K_{M}$, but leave the maximum rate unchanged.

Summary I

• Enzyme chemistry can be described by:
  $E + S \rightleftarrows ES \rightarrow E + P$
• Initial enzyme velocity ($V_{0}$) is:
  $V_{0} = k_{cat} \times [E]_{T} \times \theta$
• $k_{cat}$ is the "intrinisic enzyme rate" in $s^{-1}$
• $[E]_{T}$ is the total enzyme concentration
• $\theta$ is the fractional saturation of the enzyme with substrate
• $\theta = \frac{[S]_{0}}{K_{M}+[S]_{0}} = \frac{1}{1 + K_{M}/[S]_{0}}$
• $K_{M} \approx K_{D}$ for substrate

Summary II

• Michaelis-Menten equation is:
  $V_{0} = k_{cat} [E]_{T} \frac{[S]_{0}}{K_{M} + [S]_{0}} $
• Mucking up enzyme chemistry lowers $k_{cat}$
• Mucking up substrate binding increases $K_{M}$