Enzyme Kinetics & Regulation

Enzymes are biological catalysts — they accelerate chemical reactions without being consumed in the process. The vast majority of enzymes are proteins, though some RNA molecules (ribozymes) also have catalytic activity.

How Enzymes Work

Enzymes lower the activation energy (Ea) of a reaction, making it proceed faster. They do not change the equilibrium of the reaction or the overall free energy change (ΔG) — they simply allow the reaction to reach equilibrium more quickly.

The active site is a specific three-dimensional pocket or cleft on the enzyme where the substrate binds and catalysis occurs. Two models describe substrate binding:

• Lock and Key Model — The active site has a rigid shape perfectly complementary to the substrate. This model is oversimplified but useful for understanding specificity.
• Induced Fit Model (more accurate) — The active site changes shape upon substrate binding, wrapping around the substrate for optimal catalysis. This conformational change can strain the substrate, stabilize the transition state, or bring catalytic residues into position.

Cofactors and Coenzymes

Many enzymes require non-protein helpers to function:

• Cofactors — Inorganic ions such as Zn²⁺, Mg²⁺, Fe²⁺, or Cu²⁺ that assist in catalysis.
• Coenzymes — Organic molecules, often derived from vitamins, that serve as carriers of chemical groups. Examples include NAD⁺ (from niacin/B3), FAD (from riboflavin/B2), coenzyme A (from pantothenic acid/B5), and pyridoxal phosphate (PLP, from B6).
• Holoenzyme = apoenzyme (protein) + cofactor/coenzyme (complete, active form).

The Michaelis-Menten equation describes the rate of enzyme-catalyzed reactions as a function of substrate concentration:

Where:

• v — Reaction velocity (rate)
• V_max — Maximum velocity achieved when all enzyme molecules are saturated with substrate
• [S] — Substrate concentration
• K_m (Michaelis constant) — The substrate concentration at which the reaction rate is half of V_max. K_m is a measure of the enzyme's affinity for its substrate: low K_m = high affinity (the enzyme needs very little substrate to reach half-maximal velocity).

The Michaelis-Menten Curve

When you plot v vs. [S], you get a rectangular hyperbola:

• At low [S]: The reaction rate increases almost linearly (first-order kinetics — rate depends on [S]).
• At high [S]: The curve plateaus at V_max as all enzyme active sites are occupied (zero-order kinetics — rate is independent of [S]).
• At [S] = K_m: v = V_max/2 by definition.

Lineweaver-Burk (Double Reciprocal) Plot

Taking the reciprocal of both sides of the Michaelis-Menten equation yields a straight line when plotting 1/v vs. 1/[S]:

• Y-intercept = 1/V_max
• X-intercept = −1/K_m
• Slope = K_m/V_max

This plot is particularly useful for distinguishing between types of enzyme inhibition, as each type produces a characteristic pattern of line changes.

Enzyme inhibitors reduce the rate of enzyme-catalyzed reactions. Understanding inhibition types is essential for pharmacology, as many drugs work as enzyme inhibitors.

Reversible Inhibition

1. Competitive Inhibition

• The inhibitor resembles the substrate and binds to the active site, competing with the substrate.
• Effect on kinetics: K_m increases (apparent lower affinity); V_max unchanged (can be overcome by adding more substrate).
• On Lineweaver-Burk plot: Lines intersect at the same y-intercept (same 1/V_max) but the slope increases.
• Clinical example: Methotrexate competitively inhibits dihydrofolate reductase (DHFR), blocking folate synthesis. Used in cancer chemotherapy and autoimmune diseases. Statins (e.g., atorvastatin) competitively inhibit HMG-CoA reductase, the rate-limiting enzyme of cholesterol synthesis.

2. Noncompetitive Inhibition

• The inhibitor binds to a site other than the active site (an allosteric site), reducing catalytic activity without affecting substrate binding.
• Effect on kinetics: V_max decreases; K_m unchanged.
• On Lineweaver-Burk plot: Lines intersect at the same x-intercept (same −1/K_m) but the y-intercept increases.
• Cannot be overcome by adding more substrate.

3. Uncompetitive Inhibition

• The inhibitor binds only to the enzyme-substrate complex, not to the free enzyme.
• Effect on kinetics: Both V_max and K_m decrease proportionally.
• On Lineweaver-Burk plot: Parallel lines (same slope, different intercepts).

Irreversible Inhibition

The inhibitor forms a covalent bond with the enzyme, permanently inactivating it. The enzyme must be degraded and resynthesized.

• Aspirin — Irreversibly acetylates cyclooxygenase (COX-1), inhibiting prostaglandin and thromboxane synthesis. Because platelets lack nuclei and cannot synthesize new COX, the effect lasts the lifetime of the platelet (~7-10 days).
• Organophosphates (nerve agents, some pesticides) — Irreversibly inhibit acetylcholinesterase, causing accumulation of acetylcholine at synapses. Treated with atropine and pralidoxime.