Enzyme Kinetics and Michaelis-Menten Parameters

Enzyme Kinetics I: $\Delta G$, Reaction Rates, and Michaelis-Menten Parameters

Announcements & Project Information

• The 6180 final project information, including all deadlines and instructions, is now posted on Canvas.

Two Different Types of Delta G (Free Energy Change)

1. Overall Delta G ( $\Delta G$ ) for a Reaction (A to P)

• This is the familiar concept, representing the change in free energy between products and reactants.

• It dictates the direction of a reaction.

• The reaction is exergonic if $\Delta G$ is negative, meaning energy is released.

• The reaction is endergonic if $\Delta G$ is positive, meaning energy is required.

2. Delta G Double Dagger ( $\Delta G^{\ddagger}$ ) for Activation Energy

• Designated with a double dagger superscript ( $\ddagger$ ).

• This value is always positive.

• It represents the activation energy, which is the energy barrier a reaction must overcome to proceed from one ground state to another through a transition state.

• Connection to Rate Constant: $\Delta G^{\ddagger}$ is connected to the rate constant for a reaction via the Arrhenius rate concept equation (though the specific equation was not detailed, the conceptual link was emphasized).

• Enzyme Catalysis: A major way enzymes catalyze reactions is by lowering the transition state energy (i.e., reducing $\Delta G^{\ddagger}$ ). This increases the reaction rate without changing the overall $\Delta G$ of the reaction.

Measuring Reaction Rates Experimentally

• Reaction diagrams, such as energy profiles, correspond to measurable phenomena in the lab.

• Methods of Measurement:

  • Decay of Substrate (A): Monitoring the decrease in substrate concentration over time.

  • Appearance of Product (P): Monitoring the increase in product concentration over time.

  • Example: If product P is colored (e.g., blue) and easily detectable by UV-Vis spectroscopy, its rate of appearance can be tracked over time on a plot of concentration vs. time.

Model for Enzyme Catalysis ( $E + A \xleftrightarrow{k<em>1} EA \xrightarrow{k</em>3} E + P$ )

• This simplified model involves an enzyme (E) binding a substrate (A) to form an enzyme-substrate complex (EA), which then converts to product (P), regenerating the free enzyme.

• The steps include association ($k<em>1$), dissociation ($k</em>2$), and catalysis ($k_3$).

• Four Conceptual Phases of an Enzyme Reaction Over Time:

  1. Initial Rush (Pre-Steady State):

     • When enzyme is first mixed with abundant substrate, there's a rapid formation of the enzyme-substrate (EA) complex.

     • This leads to a