Enzyme Kinetics and Regulation: Structured Study Notes

Reaction Kinetics

Introduction to Reaction Kinetics

Reaction kinetics studies the rates at which chemical processes occur, focusing on the sequence of elementary reactions and the molecularity of each step. In biochemistry, understanding kinetics is essential for analyzing enzyme-catalyzed reactions.

• Elementary Reaction: A reaction involving a specific number of molecules (molecularity) that must collide simultaneously to generate a product.

• Order of Reaction: Determined experimentally; relates to the sum of exponents of concentration terms in the rate equation.

First Order Reactions

• Definition: Rate depends linearly on the concentration of one reactant.

• Rate Law: $v = k[A]$

• Integrated Rate Law: $[A] = [A]_0 e^{-kt}$

• Graph: Plot of ln[A] vs. time yields a straight line with slope -k.

Second Order Reactions

• Definition: Rate depends on the concentration of two reactants or the square of one reactant.

• Rate Law: $v = k[A]^2$

• Integrated Rate Law: $\frac{1}{[A]} = \frac{1}{[A]_0} + kt$

• Graph: Plot of 1/[A] vs. time yields a straight line with slope k.

Sample Calculation: Half-life of First Order Reaction

• Formula: $t_{1/2} = \frac{0.693}{k}$

• Application: Used to determine the time required for half of a sample to decay.

Enzyme Kinetics

Enzyme Catalysis Summary

Enzymes catalyze reactions via different mechanisms, often involving substrate binding and transition state stabilization. All enzyme-catalyzed reactions can be quantified using kinetic parameters.

• Enzymes may use combinations of five basic catalytic mechanisms.

• Some act on a single substrate; others on two or more.

• Enzyme-substrate complexes are transient and can be measured.

Michaelis-Menten Equation

• General Reaction: $E + S \rightleftharpoons ES \rightarrow E + P$

• Assumptions: Substrate binds reversibly, product formation is irreversible, steady-state conditions apply.

• Rate Equation: $v = \frac{V_{max}[S]}{K_m + [S]}$

• Michaelis Constant ($K_m$): $K_m = \frac{k_{-1} + k_2}{k_1}$

• Maximum Velocity ($V_{max}$): $V_{max} = k_2[E]_{total}$

Graphical Representation

• Michaelis-Menten plot: Hyperbolic curve of velocity vs. substrate concentration.

• Lineweaver-Burk plot: Double reciprocal plot for linear estimation of $K_m$ and $V_{max}$.

Sample Calculations

• Calculating reaction velocity for given $K_m$, $V_{max}$, and substrate concentration.

• Determining $K_m$ and $V_{max}$ from Lineweaver-Burk plot slope and intercept.

Enzyme Inhibition

Types of Inhibition

• Reversible Inhibition: Inhibitor binds and can dissociate from the enzyme.

• Irreversible Inhibition: Inhibitor binds covalently, permanently inactivating the enzyme.

Competitive Inhibition

• Definition: Inhibitor competes with substrate for the active site.

• Effect: Increases apparent $K_m$, $V_{max}$ unchanged.

• Equation: $K_m^{app} = K_m (1 + \frac{[I]}{K_i})$

Uncompetitive Inhibition

• Definition: Inhibitor binds only to the enzyme-substrate complex.

• Effect: Both $K_m$ and $V_{max}$ decrease.

Noncompetitive (Mixed) Inhibition

• Definition: Inhibitor binds to either enzyme or enzyme-substrate complex.

• Effect: $V_{max}$ decreases; $K_m$ may increase or decrease depending on binding.

Table: Effects of Reversible Inhibitors on Apparent $V_{max}$ and $K_m$

Inhibitor Type	Apparent $V_{max}$	Apparent $K_m$
None	$V_{max}$	$K_m$
Competitive	$V_{max}$	$K_m^{app}$
Uncompetitive	$V_{max}^{app}$	$K_m^{app}$
Mixed	$V_{max}^{app}$	$K_m^{app}$

Control of Enzyme Activity

Mechanisms of Control

• Enzyme Availability: Regulated by synthesis and degradation rates.

• Allosteric Regulation: Enzyme activity modulated by structural alterations due to effector binding.

Allosteric Effects

• Allosteric Inhibition: Effector binds to a site other than the active site, reducing activity.

• Allosteric Activation: Effector increases enzyme activity.

Feedback Inhibition

Definition and Example

• Feedback Inhibitor: End product of a pathway inhibits an earlier enzyme, regulating pathway flux.

• Example: CTP inhibits ATCase in pyrimidine biosynthesis.

Summary Table: Key Equations

Equation	Description
$v = k[A]$	First order rate law
$v = k[A]^2$	Second order rate law
$t_{1/2} = \frac{0.693}{k}$	First order half-life
$v = \frac{V_{max}[S]}{K_m + [S]}$	Michaelis-Menten equation
$K_m = \frac{k_{-1} + k_2}{k_1}$	Michaelis constant
$V_{max} = k_2[E]_{total}$	Maximum velocity

Additional info:

• Notes include graphical representations and sample calculations to reinforce concepts.

• Tables and diagrams are described in text for clarity.