21.1 Enzymes: Kinetics & Regulation

Enzyme Structure and the Active Site

Enzymes are biological catalysts — almost always proteins — that accelerate chemical reactions by lowering activation energy without being consumed. With the exception of ribozymes (catalytic RNA), every enzyme in human metabolism is a polypeptide whose three-dimensional fold creates an active site: a solvent-excluded pocket of residues whose geometry and charge complement a specific substrate. The active site accounts for enzyme specificity through two models. The lock-and-key model (Fischer) posits a rigid, pre-formed complementary pocket; the more accurate induced-fit model (Koshland) describes the active site as flexible, reshaping around the substrate upon binding. Catalytic residues within the site stabilize the transition state — the highest-energy intermediate — through acid-base chemistry, covalent catalysis, metal-ion coordination, or electrostatic stabilization. Because enzymes stabilize the transition state rather than the substrate, they can accelerate reactions by factors of 10^6 to 10^12.

Many enzymes require non-protein helpers. Cofactors are inorganic ions (Mg2+, Zn2+, Fe2+) that participate directly in catalysis; coenzymes are organic molecules derived from vitamins — NAD+/NADH (niacin), FAD/FADH2 (riboflavin), coenzyme A (pantothenate), thiamine pyrophosphate (thiamine), pyridoxal phosphate (B6). An enzyme without its required cofactor is called an apoenzyme; the complete, catalytically active complex is the holoenzyme. The PA-CAT Bulletin of Information, rev. 20240815, lists cofactors and coenzymes within the Biochemistry blueprint under Enzymes.

Michaelis-Menten Kinetics

For a simple single-substrate reaction, the enzyme E binds substrate S to form an ES complex, which yields product P and free enzyme: E + S ⇌ ES → E + P. The Michaelis-Menten equation relates initial velocity v to substrate concentration [S]:

v = (Vmax · [S]) / (Km + [S])

Vmax is the maximum velocity achieved when all enzyme active sites are saturated. Km, the Michaelis constant, is the substrate concentration at which v = ½ Vmax. Km is an inverse affinity indicator: a low Km means high affinity (the enzyme reaches half-maximal velocity at low [S]), while a high Km means low affinity. Two practical rules: when [S] ≪ Km, v is approximately first-order in [S]; when [S] ≫ Km, v approaches Vmax (zero-order, independent of [S]).

Lineweaver-Burk Plot

Taking the reciprocal of the Michaelis-Menten equation gives the Lineweaver-Burk (double-reciprocal) form: 1/v = (Km/Vmax)·(1/[S]) + 1/Vmax. Plotting 1/v versus 1/[S] yields a straight line with y-intercept 1/Vmax, x-intercept −1/Km, and slope Km/Vmax. This linearization makes it straightforward to extract Vmax and Km from experimental data and, crucially, to distinguish inhibition types by how the lines shift.

Enzyme Inhibition

Competitive inhibitors resemble the substrate and bind the active site reversibly, competing with S. They raise the apparent Km (more substrate needed to reach ½ Vmax) but leave Vmax unchanged because saturating [S] outcompetes the inhibitor. On a Lineweaver-Burk plot the lines intersect at the y-axis. Example: methotrexate competitively inhibits dihydrofolate reductase.

Noncompetitive inhibitors bind an allosteric site (not the active site) and reduce Vmax without changing Km, because substrate can still bind but the catalytic step is impaired. Lines intersect at the x-axis on a Lineweaver-Burk plot.

Uncompetitive inhibitors bind only the ES complex, lowering both Km and Vmax by the same factor; the Lineweaver-Burk lines are parallel. Irreversible inhibitors form covalent or very tight bonds with the enzyme (e.g., aspirin acetylating cyclooxygenase, organophosphates inhibiting acetylcholinesterase), effectively removing enzyme from the pool and lowering Vmax proportionally.

Allosteric Regulation and Regulatory Strategies

Allosteric enzymes do not follow Michaelis-Menten kinetics. They are typically oligomeric, with multiple active sites, and display sigmoidal (S-shaped) v versus [S] curves reflecting cooperative substrate binding. An allosteric effector binds a regulatory site distinct from the active site and shifts the enzyme between a high-affinity R (relaxed) and low-affinity T (tense) state. Homotropic effectors are the substrate itself (cooperativity); heterotropic effectors are other molecules — activators or inhibitors. Aspartate transcarbamoylase (ATCase) is the textbook example: CTP is a heterotropic inhibitor, ATP a heterotropic activator.

Beyond allostery, cells regulate enzyme activity by: (1) covalent modification — phosphorylation by kinases / dephosphorylation by phosphatases is the dominant signaling switch (e.g., glycogen phosphorylase activated by phosphorylation); (2) proteolytic activation — zymogens are secreted inactive and cleaved to active forms (e.g., trypsinogen → trypsin, prothrombin → thrombin); (3) induction/repression — changes in gene expression that alter enzyme concentration over hours; and (4) compartmentation — separating opposing pathways (e.g., fatty acid synthesis in cytosol, β-oxidation in mitochondria). Understanding these regulatory modes is essential for the PA-CAT Biochemistry (5%) content, which groups Enzymes, Metabolism, and Proteins per the Bulletin of Information, rev. 20240815.