Enzyme Kinetics, Inhibition, and Hemoglobin Function: Study Notes for Biochemistry

Enzyme Kinetics

Basic Rate Equations

Enzyme kinetics studies the rates at which enzymatic reactions proceed and the factors affecting these rates. The rate of formation of product is equal to the rate of disappearance of the reactant in a simple reaction:

• Rate of formation of product (d[P]/dt): $d[P]/dt = k[A]$

• Rate constant (k): Determines the speed of the reaction.

• First-order reaction: The rate depends linearly on the concentration of one reactant.

Example: For the reaction A → Products, if 1 mole of A reacts with 1 mole of P, the rate of formation of product equals the rate of disappearance of A.

Michaelis-Menten (MM) Equation

The Michaelis-Menten equation describes the rate of enzymatic reactions by relating reaction rate to substrate concentration:

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

• Assumptions: The concentration of ES (enzyme-substrate complex) is constant (steady-state assumption).

• Rate-limiting step: The slowest step determines the overall rate.

• Neglecting k-2: When product formation is much slower than ES breakdown, k-2 can be ignored.

Example: At high substrate concentrations, the reaction rate approaches Vmax.

Graphical Representation

• Velocity vs. [S] plot: Shows hyperbolic relationship between reaction rate and substrate concentration.

• Double reciprocal (Lineweaver-Burk) plot: Plots 1/v vs. 1/[S] to linearize the MM equation.

• Equation: $\frac{1}{v} = \frac{K_m}{V_{max}} \cdot \frac{1}{[S]} + \frac{1}{V_{max}}$

• Intercepts: y-intercept = 1/Vmax, x-intercept = -1/Km

Example: Increasing total enzyme concentration increases Vmax but does not affect Km.

Enzyme Inhibition and Regulation

Types of Inhibition

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

• Reversible inhibition: Inhibitor binds non-covalently and can dissociate.

• Competitive inhibition: Inhibitor competes with substrate for active site; increases apparent Km, Vmax unchanged.

• Non-competitive inhibition: Inhibitor binds elsewhere; decreases Vmax, Km unchanged.

• Uncompetitive inhibition: Inhibitor binds only to ES complex; decreases both Vmax and Km.

Type	Effect on Vmax	Effect on Km
Competitive	No change	Increases
Non-competitive	Decreases	No change
Uncompetitive	Decreases	Decreases

Example: Addition of a competitive inhibitor can be overcome by increasing substrate concentration.

Enzyme Efficiency

• Turnover number (kcat): Number of substrate molecules converted per enzyme per second.

• Enzyme efficiency: $\text{Efficiency} = \frac{k_{cat}}{K_m}$

• Units: kcat (s-1), Km (M), efficiency (M-1s-1).

Example: If kcat = 100 s-1, Km = 10 nM, efficiency = 1010 M-1s-1.

Protein Function: Hemoglobin and Myoglobin

Oxygen Binding and Allosteric Regulation

• Hemoglobin (Hb): Tetrameric protein responsible for oxygen transport in blood.

• Myoglobin (Mb): Monomeric protein for oxygen storage in muscle.

• Allosteric sites: Regions where effectors bind, altering protein activity.

• Cooperative binding: Hb exhibits positive cooperativity; binding of one O2 increases affinity for others.

• Bohr effect: Decreased pH or increased CO2 reduces Hb's O2 affinity.

Example: O2 saturation curves for Hb are sigmoidal, for Mb are hyperbolic.

Structural Changes in Hemoglobin

• T (tense) state: Deoxy form, lower O2 affinity.

• R (relaxed) state: Oxy form, higher O2 affinity.

• Allosteric transitions: O2 binding triggers conformational change from T to R state.

Example: Allosteric effectors like 2,3-BPG stabilize the T state, reducing O2 affinity.

Oxygen Saturation Curves

• pO2 vs. O2 saturation: Plots show differences between Hb and Mb under various conditions (acidic/alkaline pH, presence of phosphate derivatives).

• Effect of pH: Acidic pH shifts curve right (lower affinity), alkaline pH shifts left (higher affinity).

Additional info:

• MM and LB plots are used to analyze enzyme kinetics and inhibition.

• kcat/Km is a measure of catalytic efficiency, approaching diffusion limit for highly efficient enzymes.

• Graphical differences between enzymatic and non-enzymatic conversion: Enzymatic reactions show saturation kinetics, non-enzymatic are typically linear.