10.4 Enzymes

Classification and catalytic function

Enzymes are 12% of Chemistry. The official plan is short: classification and function; kinetics and regulation. That brevity is a trap. Item writers still expect the six EC classes, a working Michaelis-Menten model, Lineweaver-Burk intercepts, the competitive/noncompetitive pair, and the regulatory menu (allosteric, phosphorylation, induction) already used on PFK-1, ACC, and CPS-I.

Quick Answer: Enzymes are protein (sometimes RNA) catalysts that lower activation energy without changing ΔG. Six classes. Km is [S] at ½ Vmax. Competitive inhibitors raise Km, same Vmax, y-axis intersect. Noncompetitive inhibitors lower Vmax, same Km, x-axis intersect. Allostery is conformational; phosphorylation is covalent; induction is more enzyme molecules.

An enzyme binds substrate in an active site (lock-and-key is the historical picture; induced fit is the better one). It stabilizes the transition state, lowering activation energy (Ea). Equilibrium (ΔG, Keq) does not change; both forward and reverse rates increase. Cofactors: metal ions (Zn2+ in carboxypeptidase, Mg2+ with ATP, Fe in cytochromes), coenzymes (often vitamin-derived, loosely bound: NAD+, CoA), and prosthetic groups (tightly bound: FAD on succinate dehydrogenase, biotin on carboxylases, heme on catalase). Holoenzyme = apoenzyme + cofactor.

Isozymes are different gene products catalyzing the same reaction (hexokinase versus glucokinase; LDH H and M subunits; CK-MM, CK-MB, CK-BB). They can differ in Km, regulation, and tissue of origin — the point of a serum CK-MB item is isozyme geography, not a cardiology rotation.

Naming traps. A kinase is a transferase (phosphoryl from ATP). A phosphorylase uses Pi to split a bond (glycogen phosphorylase) — also a transferase in EC logic, not a hydrolase. A phosphatase is a hydrolase. A synthetase is a ligase (ATP); a synthase need not hydrolyze NTP (citrate synthase). Lyases add across double bonds or remove groups leaving double bonds; they are not hydrolases.

Zymogens (pepsinogen, trypsinogen, clotting factors) are inactive precursors; proteolytic cut is an irreversible on-switch. That is regulation by limited proteolysis, distinct from reversible phosphorylation.

Many enzymes use acid-base catalysis (His in chymotrypsin), covalent catalysis (serine acyl-enzyme), or metal-ion catalysis. Chymotrypsin’s catalytic triad (Ser-His-Asp) is the serine-hydrolase prototype; organophosphate insecticides phosphorylate that serine in acetylcholinesterase — irreversible inhibition, not Michaelis-Menten competitive.

Michaelis-Menten kinetics

For a simple enzyme that follows E + S ⇌ ES → E + P, the initial velocity is

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

Vmax is the velocity when enzyme is saturated: Vmax = kcat [E]t. kcat (turnover number) is product molecules per enzyme molecule per time at saturation. Km is the substrate concentration at which v = ½ Vmax. When kcat is small compared with the off-rate, Km approximates the dissociation constant Kd and is an inverse affinity measure: low Km = high affinity. Hexokinase’s low Km versus glucokinase’s high Km is that sentence in tissue form.

At [S] << Km, v ≈ (Vmax/Km)[S] — first order, the slope Vmax/Km is the specificity constant (actually kcat/Km when written per enzyme). At [S] >> Km, v ≈ Vmax — zero order. Alcohol dehydrogenase and phenytoin at therapeutic levels are physiologic zero-order examples; they are not excuses to forget the hyperbolic shape of a typical MM enzyme.

Catalytic efficiency is kcat/Km, the apparent second-order rate constant at low [S]. Diffusion-limited enzymes approach ~10^8–10^9 M−1 s−1 (triose phosphate isomerase is the textbook “perfect” enzyme).

Assumptions: initial rate (no product), free [S] ≈ total [S] (so [S] >> [E]), steady-state d[ES]/dt ≈ 0 (Briggs-Haldane), one substrate, no allostery. PFK-1 does not obey this hyperbola for fructose-6-phosphate; it is sigmoidal (Hill coefficient > 1). Do not force an MM Km onto a cooperative enzyme; report K0.5.

Lineweaver-Burk (double reciprocal) linearizes MM:

1/v = (Km/Vmax)(1/[S]) + 1/Vmax

• Y-intercept = 1/Vmax
• X-intercept = −1/Km
• Slope = Km/Vmax

The plot exaggerates error at low [S], but Part I loves the intercept pattern for inhibitors. Eadie-Hofstee (v versus v/[S]) is less commonly tested.

Worked number. If Vmax is 40 μmol/min and Km is 2 mM, v at 2 mM substrate is 20 μmol/min. At 18 mM (9 × Km) v is 36 μmol/min — 90% of Vmax, not “almost zero remaining capacity.” Saturation is asymptotic.

Inhibitors: competitive, noncompetitive, uncompetitive, irreversible

Reversible competitive inhibition. Inhibitor binds the active site of free E, competing with substrate. Enough substrate displaces it, so Vmax is unchanged. Apparent Km increases (more [S] needed to reach ½ Vmax). Lineweaver-Burk: lines intersect on the y-axis. Classic pairs: malonate versus succinate on succinate dehydrogenase; statins versus HMG-CoA on HMG-CoA reductase; methotrexate versus dihydrofolate on DHFR; ethanol versus methanol on alcohol dehydrogenase (the therapeutic competitive substrate). Sulfanilamide versus PABA on bacterial folate synthesis is the same logic.

Reversible noncompetitive inhibition (pure textbook case). Inhibitor binds a site available on E and ES equally, so it does not change substrate affinity: Km unchanged, Vmax decreased (a fraction of enzyme is always inactive). Lineweaver-Burk: lines intersect on the x-axis. Mixed inhibition (unequal binding to E versus ES) is more common in reality and moves both parameters; if an item shows a shared x-intercept, they mean the pure noncompetitive cartoon.

Uncompetitive inhibition. Inhibitor binds only ES. Both apparent Km and Vmax fall (parallel Lineweaver-Burk lines). Rare in simple metabolic enzymes; still a discriminator if the stem says parallel lines.

Irreversible inhibition. Covalent inactivation. Aspirin acetylates Ser530 of COX. Organophosphates phosphorylate AChE serine (pralidoxime can rescue before aging). Penicillin acylates bacterial transpeptidase. Allopurinol is a suicide substrate of xanthine oxidase (oxypurinol binds tightly). Vmax in the surviving enzyme pool is what you measure; adding substrate does not recover dead enzyme.

IC50 is an empirical [I] that cuts activity in half under one set of [S]; it is not Km. Ki is the inhibitor dissociation constant. You do not need a numeric Ki on Part I; you need the Km/Vmax direction.

Regulation: allosteric, covalent, induction

Metabolic enzymes are not left at a fixed kcat. Three time scales:

1. Allosteric (milliseconds). A modulator binds away from the active site and shifts T (tense, low affinity) ⇌ R (relaxed, high affinity) in a multimeric protein. Homotropic effectors are the substrate (cooperativity, sigmoid curve, Hill coefficient). Heterotropic effectors are other metabolites. PFK-1 is the chapter mascot: F6P is homotropic; AMP and F-2,6-BP are positive heterotropic; ATP and citrate are negative heterotropic. CPS-I needs N-acetylglutamate. ACC polymerizes with citrate. Aspartate transcarbamoylase (ATCase) is the historical example (CTP inhibits, ATP activates) even though pyrimidine synthesis is the next chapter.

Sigmoidal kinetics mean a small change in [S] or in an effector near K0.5 produces a large change in rate — a switch, not a dimmer. MM hyperbolas do not switch.

2. Covalent modification (seconds to minutes). Phosphorylation by kinases (ATP) and dephosphorylation by phosphatases. Direction is enzyme-specific: glycogen phosphorylase is activated by phosphorylation; glycogen synthase and ACC and liver pyruvate kinase are inactivated by phosphorylation. The same glucagon/PKA wave therefore breaks glycogen, stops liver glycolysis, and stops fat synthesis together. AMPK phosphorylates ACC and HMG-CoA reductase when energy is low. Other covalent marks exist (acetylation, adenylylation in bacteria); phosphorylation is the human high-yield mark.

3. Induction and repression (hours). Insulin induces glucokinase, PFK-1, pyruvate kinase, ACC, FAS. Glucagon/cortisol induce PEPCK, FBPase-1, G6Pase. That is more enzyme protein, not a faster existing molecule. CYP induction by ethanol or barbiturates is the same regulatory class applied to xenobiotics.

Compartmentation is regulation too: FA oxidation in mitochondria, FA synthesis in cytosol, urea CPS-I in mitochondria, CPS-II in cytosol. Substrate cycling (PFK-1 versus FBPase-1) is wasteful if both are on; F-2,6-BP prevents that, which is why the carbohydrate chapter and this chapter are one exam.

pH and temperature. Each enzyme has a pH optimum (pepsin ~2, alkaline phosphatase ~9, most metabolic enzymes ~7.4) because catalytic residues must be in the correct protonation state. Fever raises rates modestly; denaturation kills them. These are not the first-line regulation items, but they explain why a pepsin item mentions gastric acid and why a pancreatectomy item mentions bicarbonate.

Worked regulation stack on one enzyme. Hepatic PFK-1: allosteric ATP/citrate off, AMP/F-2,6-BP on; F-2,6-BP amount set by PKA phosphorylation of PFK-2 (covalent, seconds); PFK-1 protein amount induced by insulin (hours). An item that says “minutes after a glucagon surge” is F-2,6-BP, not a transcriptional event.

Clinical enzyme measurements. Serum ALT/AST, CK, amylase/lipase, alkaline phosphatase are activity assays, usually zero-order (saturating substrate) so the rate reports [E] that leaked from damaged cells. That is pathology using this section’s Vmax idea.

/practice/nbce-part1Practice questions with detailed explanations