Enzyme Catalysis and Action Mechanisms

Enzymes are biological catalysts, mostly proteins, that speed up reactions by lowering the activation energy through binding the substrate at the active site; their kinetics are described by the Michaelis–Menten equation, v = V_max[S] / (K_m + [S]). In brief: an enzyme with V_max = 100 µmol/min and K_m = 2.0 mM works at half its maximum rate at a substrate concentration of 2.0 mM, and at 83 µmol/min when [S] is 10 mM.

Almost every reaction in a cell is catalyzed by an enzyme. Without them, reactions such as the hydrolysis of proteins would take years at body temperature, and with them they take milliseconds. Enzymes are specific, efficient and regulated. This article explains how enzymes work (active site, induced fit and catalytic mechanisms), presents the Michaelis–Menten kinetics with a worked example, covers inhibition and cofactors, classifies enzymes in a table and gives a short history of enzyme research.

How do enzymes speed up reactions?

A catalyst provides a reaction pathway with a lower activation energy. An enzyme binds the substrate (S) to form an enzyme–substrate complex (ES), converts it into the product (P) and releases it, unchanged: E + S ⇌ ES → E + P. The enzyme does not change the equilibrium of the reaction (ΔG and K stay the same), only the rate. The rate enhancement is huge: carbonic anhydrase speeds up the hydration of CO₂ by a factor of about 10⁷, and orotidine monophosphate decarboxylase by 10¹⁷, which would take 78 million years without the enzyme. A single catalase molecule can break down about 4 × 10⁷ molecules of hydrogen peroxide per second.

What is the active site?

The active site is a pocket or cleft in the enzyme, formed by a small number of amino acids, which binds the substrate, and carries the groups that catalyze the reaction. The specificity of an enzyme is based on the shape, charge and polarity of the site. Emil Fischer proposed the lock-and-key model in 1894, with a rigid active site that fits the substrate like a key in a lock. Daniel Koshland suggested in 1958 the induced-fit model, in which the binding of the substrate changes the shape of the enzyme, so that the groups are brought into the optimal position, like a glove that adjusts to a hand. The induced fit is now the accepted view. Enzymes may also be specific for one enantiomer: proteases act only on L-amino acid peptides.

What are the catalytic mechanisms?

• Proximity and orientation: the enzyme holds the reactants close together in the right orientation, which increases the effective concentration by a large factor.
• Transition-state stabilization: the active site is complementary to the transition state more than to the substrate, and binds it most tightly, which lowers the energy barrier. This is considered the main source of catalysis.
• Acid–base catalysis: amino acid side chains (such as histidine) donate or accept protons.
• Covalent catalysis: a temporary covalent bond between the enzyme and the substrate. In the protease chymotrypsin, the serine-195 hydroxyl attacks the peptide bond, helped by histidine-57 and aspartate-102 (the catalytic triad), forming an acyl-enzyme intermediate that is then hydrolyzed.
• Metal ion catalysis: ions such as Zn²⁺ (carbonic anhydrase) or Mg²⁺ polarize bonds and stabilize negative charges.

What is Michaelis–Menten kinetics?

At a low concentration of substrate the rate is proportional to [S], and at a high concentration the enzyme is saturated and the rate reaches a maximum V_max. The relationship (Leonor Michaelis and Maud Menten, 1913) is:

v = Vmax [S] / (Km + [S])

• V_max = k_cat[E]_t: the maximum rate, when all of the enzyme (total concentration [E]_t) is in the ES complex.
• K_m: the substrate concentration at which v = ½V_max. A low K_m means high affinity for the substrate (but it is only an approximate measure of affinity).
• k_cat (turnover number): the number of substrate molecules converted per enzyme molecule per second when it is saturated.
• k_cat/K_m: the catalytic efficiency. The upper limit is the rate of diffusion, about 10⁸–10⁹ M⁻¹s⁻¹, which is reached by enzymes such as catalase, carbonic anhydrase and triose phosphate isomerase.

A plot of 1/v against 1/[S] (Lineweaver–Burk plot, 1934) is a straight line with an intercept of 1/V_max and a slope of K_m/V_max.

How do inhibitors work?

Competitive inhibition can be overcome by a high concentration of the substrate. Irreversible inhibitors form a covalent bond with the enzyme: aspirin acetylates a serine in cyclooxygenase, penicillin blocks the bacterial transpeptidase and nerve agents inhibit acetylcholinesterase. Allosteric regulation: a molecule binds at a site other than the active site, and activates or inhibits the enzyme, often by changing its quaternary structure. Many pathways are controlled by feedback inhibition, in which the end product inhibits the first enzyme of its own pathway.

Cofactors: many enzymes need non-protein helpers. Metal ions (Zn²⁺, Mg²⁺, Fe²⁺) and organic coenzymes (NAD⁺, FAD, coenzyme A) are derived from vitamins. The enzyme without its cofactor is the apoenzyme, and with it the holoenzyme.

Classes of enzymes

Worked examples

Example 1: the rate at different substrate concentrations

V_max = 100 µmol/min and K_m = 2.0 mM.

• [S] = 0.5 mM: v = 100 × 0.5 / (2.0 + 0.5) = 20 µmol/min.
• [S] = 2.0 mM: v = 100 × 2.0 / 4.0 = 50 µmol/min (half of V_max).
• [S] = 10 mM: v = 100 × 10 / 12 = 83.3 µmol/min.
• [S] = 100 mM: v = 100 × 100 / 102 = 98 µmol/min (almost saturated).

Example 2: the turnover number

An enzyme solution contains 1.0 nM of enzyme, and the maximum rate is 10 µM/s. k_cat = V_max / [E]_t = 1.0 × 10⁻⁵ M/s / 1.0 × 10⁻⁹ M = 1.0 × 10⁴ s⁻¹. If K_m = 0.50 mM, the catalytic efficiency is k_cat/K_m = 1.0 × 10⁴ / 5.0 × 10⁻⁴ = 2 × 10⁷ M⁻¹s⁻¹.

Example 3: the effect of a competitive inhibitor

With a competitive inhibitor, the apparent K_m becomes K_m(1 + [I]/K_i). For K_m = 2.0 mM, [I] = 1.0 mM and K_i = 0.50 mM, the apparent K_m = 2.0 × (1 + 2) = 6.0 mM. At [S] = 6.0 mM, the rate is now ½V_max, instead of the 75 % V_max that it would be without the inhibitor, and V_max is unchanged.

Example 4: the lowering of the activation energy

An enzyme increases the rate of a reaction by a factor of 10⁸ at 37 °C (310 K). If the pre-exponential factor is unchanged, the activation energy is reduced by ΔE_a = RT ln(10⁸) = 8.314 × 310 × 18.42 = 47.5 kJ/mol.

Example 5: a time comparison

A reaction that takes 1 second with the enzyme and is accelerated by a factor of 10¹² would take 10¹² s = about 32,000 years without it.

How were enzymes discovered?

Anselme Payen and Jean-François Persoz isolated the first enzyme, diastase (amylase), from malt in 1833. Wilhelm Kühne proposed the name “enzyme” (Greek, “in yeast”) in 1877. Eduard Buchner showed in 1897 that a yeast extract without cells can ferment sugar, and received the Nobel Prize in Chemistry in 1907. James Sumner crystallized the first enzyme, urease, in 1926 and showed that it is a protein, a conclusion that was long disputed, and he shared the Nobel Prize in 1946 with John Northrop and Wendell Stanley. Ribozymes, RNA molecules with catalytic activity, were discovered by Thomas Cech and Sidney Altman in the early 1980s (Nobel Prize in 1989).

Which mistakes are common?

• Saying that enzymes are used up: they are regenerated.
• Believing that enzymes change the equilibrium: they only speed up the approach to it.
• Mixing up K_m and V_max: K_m is a concentration, V_max is a rate.
• Thinking that a high K_m means high affinity: a low K_m does.
• Assuming that all enzymes are proteins: some RNAs are catalytic.