Enzyme Kinetics & Inhibition

🧪 Enzyme Kinetics & Catalysis: Master Guide

Advanced CSIR-NET, GATE & DBT-BET Revision Notes

1. Enzyme Catalytic Strategies

Enzymes employ highly specific chemical strategies to lower the activation energy (ΔG^‡) of a reaction.

• Acid-Base Catalysis: Amino acid side chains (like Histidine) act as proton donors (acids) or acceptors (bases) to stabilize the transition state. Example: RNase A.
• Covalent Catalysis: A transient, highly reactive covalent bond forms between the enzyme and substrate. Example: Serine proteases (Chymotrypsin) using the catalytic triad.
• Metal Ion Catalysis: Metals (Zn²⁺, Mg²⁺, Fe²⁺) facilitate catalysis by orienting substrates, mediating redox reactions, or shielding negative charges. Example: Carbonic anhydrase (Zn²⁺).
• Proximity & Orientation: Enzymes bind substrates in the exact spatial orientation and close proximity required for the reaction to occur, drastically increasing the effective concentration.

2. Michaelis-Menten Kinetics

The fundamental model of enzyme kinetics. It assumes a rapid, reversible formation of an Enzyme-Substrate (ES) complex, followed by a slower rate-limiting breakdown into Enzyme + Product.

V₀ = (V_max × [S]) / (K_m + [S])

• V_max (Maximum Velocity): Reached when all enzyme active sites are saturated with substrate.
• K_m (Michaelis Constant): The substrate concentration [S] at which the reaction velocity is exactly half of V_max. It is an inverse measure of affinity. (Low K_m = High affinity).
• k_cat (Turnover Number): The number of substrate molecules converted to product per enzyme molecule per second at saturation. (k_cat = V_max / [E]_total).
• Catalytic Efficiency: Measured by the ratio k_cat / K_m. An enzyme is "catalytically perfect" when this ratio approaches the diffusion limit (~10⁸ - 10⁹ M^-1s^-1).

3. Linearizing Kinetic Data: LB, HW, & EF Plots

Lineweaver-Burk (Double Reciprocal)

1/V₀ = (K_m/V_max)(1/[S]) + 1/V_max

• Y-intercept: 1 / V_max
• X-intercept: -1 / K_m
• Slope: K_m / V_max
• Note: Highly sensitive to errors at low [S].

Hanes-Woolf Plot

[S]/V₀ = (1/V_max)[S] + K_m/V_max

• Y-axis: [S] / V₀ | X-axis: [S]
• Y-intercept: K_m / V_max
• Slope: 1 / V_max
• Note: Statistically more accurate than LB plot.

Eadie-Hofstee Plot

V₀ = -K_m(V₀/[S]) + V_max

• Y-axis: V₀ | X-axis: V₀ / [S]
• Y-intercept: V_max
• Slope: -K_m

4. Enzyme Inhibitors

A. Irreversible Inhibitors

Bind covalently (or very tightly) to the enzyme, permanently destroying its activity.
Examples: Suicide Inhibitors (Penicillin targeting transpeptidase) and DIPF (nerve gas modifying catalytic Serine).

B. Reversible Inhibitors

Type	Binding Site	Effect on Vmax	Effect on Km
Competitive	Active Site (E only)	Unchanged	Increases (αKm)
Uncompetitive	Allosteric (ES complex only)	Decreases (Vmax/α')	Decreases (Km/α')
Non-competitive	Allosteric (E and ES equally)	Decreases	Unchanged

Competitive (LB Plot)

Non-Competitive (LB Plot)

5. The Dixon Plot

The Dixon plot is specifically used to determine the inhibition constant (K_i) of a competitive or mixed inhibitor.

• Y-axis: 1 / V₀
• X-axis: Inhibitor Concentration [I]
• Method: Data is plotted at two or more different fixed substrate concentrations [S].
• Result: The lines intersect in the upper-left quadrant (for competitive inhibition). Dropping a perpendicular from the intersection point to the X-axis gives the value of -K_i.