Enzyme Kinetics & Inhibitor Plots
Read Km and Vmax off the graph and predict what each inhibitor does
Michaelis–Menten Kinetics
The saturation curve. For a simple enzyme, velocity V = Vmax[S]/(Km + [S]). Plotted against substrate concentration, velocity rises steeply and then flattens toward Vmax as active sites fill, tracing a hyperbola. Far below Km, velocity is proportional to [S] (first-order); far above Km, the enzyme is saturated and velocity is constant (zero-order). Saturable metabolism is why ethanol, phenytoin, and high-dose aspirin are eliminated at a constant amount per unit time.
Vmax. The maximal rate when every enzyme molecule is occupied. It is proportional to enzyme amount, so doubling the enzyme doubles Vmax without changing Km.
Km. The substrate concentration that gives half-maximal velocity. It is inversely related to affinity: a low Km means the enzyme works well at low substrate levels. Km belongs to the enzyme–substrate pair and does not depend on how much enzyme is present.
| Feature | Hexokinase | Glucokinase |
|---|---|---|
| Location | Most tissues (brain, RBCs, muscle) | Liver, pancreatic β cells |
| Km for glucose | Low (high affinity) | High (low affinity) |
| Vmax | Low | High |
| Regulation | Inhibited by glucose-6-phosphate | Inhibited by fructose-6-phosphate via its regulatory protein; induced by insulin |
| Role | Traps glucose even when it is scarce | Glucose sensor; handles large post-meal loads |
Cooperative and allosteric enzymes. Multisubunit enzymes in which substrate binding at one site raises affinity at the others give a sigmoid velocity curve, like hemoglobin's oxygen curve, and do not obey Michaelis–Menten kinetics. Allosteric effectors bind away from the active site: activators shift the curve left, inhibitors shift it right. Phosphofructokinase-1, the rate-limiting enzyme of glycolysis, is the classic example: activated by AMP and fructose-2,6-bisphosphate, inhibited by ATP and citrate.
The Lineweaver–Burk Plot
Taking reciprocals linearizes the equation: 1/V = (Km/Vmax)(1/[S]) + 1/Vmax. Plotting 1/V against 1/[S] gives a straight line from which the constants are read directly.
- y-intercept = 1/Vmax. A higher y-intercept means a lower Vmax.
- x-intercept = −1/Km. An x-intercept closer to zero means a higher Km (lower apparent affinity).
- Slope = Km/Vmax. A steeper line means a larger Km, a smaller Vmax, or both.
The y-axis (1/[S] = 0) corresponds to infinitely high substrate, so any inhibitor that substrate can outcompete leaves the y-intercept untouched.
Reversible Inhibition
Competitive. The inhibitor resembles the substrate and binds the active site. Enough substrate outcompetes it, so Vmax is unchanged while apparent Km rises; Lineweaver–Burk lines intersect on the y-axis.
Noncompetitive. The inhibitor binds an allosteric site on free enzyme or the enzyme–substrate complex, disabling a fraction of enzyme that extra substrate cannot rescue. Vmax falls, Km is unchanged, and the lines intersect on the x-axis.
Uncompetitive. The inhibitor binds only the enzyme–substrate complex, lowering Vmax and apparent Km by the same factor, so the slope is unchanged and the lines run parallel. Mixed inhibitors bind free enzyme and the complex with different affinities: Vmax falls, Km rises or falls, and the lines intersect off the axes.
| Feature | Competitive | Noncompetitive | Uncompetitive |
|---|---|---|---|
| Binds | Active site (free enzyme) | Allosteric site (E or ES) | ES complex only |
| Overcome by ↑[S] | Yes | No | No |
| Km | ↑ | Unchanged | ↓ |
| Vmax | Unchanged | ↓ | ↓ |
| Lineweaver–Burk | Lines cross on y-axis | Lines cross on x-axis | Parallel lines |
Competitive inhibitors in the clinic. Methotrexate (human dihydrofolate reductase) and trimethoprim (bacterial DHFR); statins (HMG-CoA reductase, the rate-limiting step of cholesterol synthesis); sulfonamides (dihydropteroate synthase, as PABA analogs); and fomepizole (alcohol dehydrogenase) for methanol or ethylene glycol poisoning. Ethanol serves the same purpose as a competing substrate, slowing formation of formic acid and oxalate.
Receptors follow the same logic: a competitive antagonist shifts the dose-response curve right (↓potency, same maximal effect), whereas a noncompetitive antagonist lowers the maximal effect (↓efficacy).
Irreversible Inhibition
Covalent inactivation. Irreversible inhibitors bond covalently to the enzyme and remove it from the working pool. The remaining enzyme behaves normally, so kinetically they mimic noncompetitive inhibition (↓Vmax, unchanged Km), and extra substrate cannot overcome them. Activity returns only as new enzyme is synthesized, so the effect outlasts the drug's plasma half-life.
- Aspirin acetylates a serine in cyclooxygenase. Anucleate platelets cannot make new COX-1, so thromboxane A2 stays suppressed for their 7–10-day lifespan, whereas nucleated endothelial cells resynthesize COX and restore prostacyclin. (Clopidogrel's week-long effect has the same logic but targets a receptor, irreversibly blocking platelet P2Y12.)
- Organophosphates (insecticides, nerve agents) phosphorylate the active-site serine of acetylcholinesterase. Pralidoxime regenerates the enzyme only before "aging" (loss of an alkyl group) makes the bond permanent.
- Omeprazole and other proton pump inhibitors are acid-activated prodrugs that form disulfide bonds with the H+/K+-ATPase; acid suppression lasts beyond 24 hours despite a plasma half-life of about an hour.
- Others: disulfiram (aldehyde dehydrogenase), phenelzine and tranylcypromine (monoamine oxidase), and clavulanate (a "suicide" inhibitor of β-lactamase).
Reversible NSAIDs such as ibuprofen occupy the same COX-1 channel; taken before aspirin, they can blunt its antiplatelet effect.