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{k1} EA \xrightarrow{k3} 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 ( k1 ), dissociation ( k2 ), 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