5. Enzyme Catalysis & Mechanisms

What Are Enzymes?

Enzymes are biological catalysts that accelerate chemical reactions without being consumed in the process. The vast majority of enzymes are proteins, although a small but important class of catalytic RNA molecules (called ribozymes) also exist. Enzymes are remarkable for their extraordinary catalytic power, high specificity, and capacity for regulation.

Crucially, enzymes lower the activation energy ($\Delta G^\ddagger$) of a reaction without altering the overall free energy change ($\Delta G$) or the equilibrium constant ($K_\text{eq}$). They accelerate both the forward and reverse reactions equally, reaching equilibrium faster but not shifting it.

Transition State Theory

The rate of a chemical reaction depends on the energy barrier separating reactants from products. The transition state (denoted $\ddagger$) represents the highest-energy species along the reaction coordinate. Enzymes work by preferentially stabilizing this transition state, thereby lowering the activation energy.

The Arrhenius Equation

The empirical relationship between rate constant and temperature:

where $A$ is the pre-exponential (frequency) factor, $E_a$ is the activation energy,$R$ is the gas constant, and $T$ is absolute temperature.

The Eyring Equation

Transition state theory provides a more fundamental description. The Eyring equation relates the rate constant to the free energy of activation:

where $k_B$ is the Boltzmann constant and $h$ is Planck's constant. The activation free energy decomposes into enthalpic and entropic contributions:

Catalytic Mechanisms

Enzymes employ several fundamental chemical strategies to accelerate reactions. Most enzymes use a combination of these mechanisms simultaneously.

1. Acid-Base Catalysis

In general acid-base catalysis, amino acid side chains donate or accept protons during the reaction. This is distinct from specific acid-base catalysis, which involves only $\text{H}^+$ or $\text{OH}^-$ from water. Common residues involved include His (p$K_a \approx 6$), Glu/Asp, Lys, and Cys. The rate depends on the concentration of the proton-donor or -acceptor amino acid side chain:

2. Covalent Catalysis

The enzyme forms a transient covalent bond with the substrate. A nucleophilic group on the enzyme (typically Ser-OH, Cys-SH, His-imidazole, or Lys-$\varepsilon$-NH$_2$) attacks an electrophilic center on the substrate, forming a covalent intermediate that is subsequently hydrolyzed. This lowers $\Delta G^\ddagger$ by breaking the reaction into two steps, each with a lower activation barrier than the single uncatalyzed step.

3. Metal Ion Catalysis

Metal ions ($\text{Zn}^{2+}$, $\text{Mg}^{2+}$, $\text{Fe}^{2+}/\text{Fe}^{3+}$, $\text{Mn}^{2+}$) contribute to catalysis in several ways:

• Electrostatic stabilization of negative charges in the transition state
• Generation of nucleophilic hydroxide ions from water at neutral pH
• Redox chemistry via reversible changes in oxidation state (e.g., cytochrome P450)
• Orientation of substrates for optimal orbital overlap

4. Proximity and Orientation Effects

The Active Site

The active site is a three-dimensional cleft or pocket on the enzyme surface where substrate binding and catalysis occur. Although the active site typically comprises only a small fraction of the total enzyme volume (often just 10-20 amino acid residues), it is responsible for the enzyme's catalytic power and specificity.

Lock-and-Key vs. Induced Fit

Emil Fischer (1894) proposed the lock-and-key model: the enzyme active site has a rigid, pre-formed shape perfectly complementary to the substrate. While this explains specificity, it fails to account for many experimental observations.

Daniel Koshland (1958) proposed the induced fit model: substrate binding induces conformational changes in the enzyme that optimize the active site geometry for catalysis. This model explains why some substrates that structurally resemble the true substrate are not catalyzed -- they cannot induce the correct conformational change.

Serine Proteases: A Case Study

The serine proteases are among the best-characterized enzyme families and serve as a paradigm for understanding enzyme catalysis. The family includes chymotrypsin (cleaves after large hydrophobic residues), trypsin (cleaves after Arg and Lys), and elastase (cleaves after small residues like Ala, Gly, Ser). Despite their different specificities, they share an identical catalytic mechanism.

The Catalytic Triad

Catalytic Mechanism (Step by Step)

Cofactors and Coenzymes

Many enzymes require additional non-protein chemical groups for activity. These are broadly classified as cofactors (inorganic metal ions) and coenzymes (organic molecules, often derived from vitamins). A holoenzyme is the complete catalytically active form (apoenzyme + cofactor/coenzyme), while the apoenzyme is the protein portion alone.

Metal Ion Cofactors

Approximately one-third of all enzymes require metal ions. Tightly bound metals are called metalloenzymes; loosely associated metals are metal-activated enzymes.

Organic Coenzymes

Coenzymes act as transient carriers of specific functional groups. They may be tightly bound (prosthetic groups) or loosely associated (cosubstrates). Most water-soluble vitamins serve as coenzyme precursors.

Key Concepts