Enzyme kinetics

In short

Enzyme kinetics is the quantitative study of how fast enzymes convert substrate into product and how that rate changes with substrate concentration, enzyme concentration, pH, temperature, inhibitors and activators. It gives the two numbers that define a catalyst — Km (substrate concentration at half-maximal velocity, a measure of apparent affinity) and Vmax (saturation velocity, from which kcat is derived) — and it is the physical basis of a large share of modern drugs — roughly a quarter to a third of marketed drug targets are enzymes, acted on by inhibitors. It is a guaranteed scoring section in B.Sc/M.Sc Biochemistry papers, CSIR-UGC NET Life Sciences, GAT-B/DBT-JRF, ICMR-JRF, GATE Biotechnology (BT) and Life Sciences (XL) papers. In jobs, it is tested in interviews for analytical and QC roles in Indian pharma and enzyme companies (Biocon, Sun Pharma, Dr Reddy's, Advanced Enzyme Technologies, Novozymes South Asia), in clinical biochemistry labs (NABL-accredited, running ALT, AST, ALP, CK, LDH assays) and in biofuel, detergent and food-enzyme process development.

Explained

Basic concepts and rate measurement

• An enzyme lowers the activation energy (ΔG‡) of a reaction; it does not change ΔG°, Keq or the position of equilibrium — it accelerates attainment of equilibrium in both directions.
• Initial velocity (v₀) is measured over the early linear phase (usually <10% substrate consumed) so that reverse reaction, product inhibition and enzyme inactivation are negligible. All classical kinetics is initial-velocity kinetics.
• Measured as change in product or substrate per unit time: typically absorbance per minute (spectrophotometric, e.g. NADH at 340 nm, ε = 6,220 M⁻¹cm⁻¹; p-nitrophenol at 405 nm), or by fluorescence, pH-stat, oxygen electrode, HPLC or radiolabel.
• Units of activity: 1 IU (enzyme unit) = 1 µmol substrate converted per minute under defined conditions. SI unit is the katal (kat) = 1 mol s⁻¹; 1 IU = 16.67 nkat.
• Specific activity = IU per mg total protein — rises during purification and is the index of purity. Molar (molecular) activity = IU per µmol enzyme = turnover per minute.
• At fixed, saturating [S], v₀ is directly proportional to [E]ₜ — the basis of all diagnostic enzyme assays.

Michaelis–Menten model and its derivation

• Scheme: E + S ⇌ ES → E + P, with rate constants k₁ (forward binding), k₋₁ (dissociation) and k₂ (= kcat, catalysis).
• Assumptions: (i) initial velocity, so [P] ≈ 0 and the reverse step is ignored; (ii) [S] ≫ [E]ₜ so free [S] ≈ total [S]; (iii) steady state (Briggs–Haldane): d[ES]/dt = 0; (iv) a single substrate, single ES intermediate, no cooperativity or inhibition.
• Derivation outline (steady state): formation of ES = k₁[E][S]; breakdown = (k₋₁ + k₂)[ES]. Setting them equal with [E] = [E]ₜ − [ES] gives [ES] = [E]ₜ[S]/(Km + [S]) where Km = (k₋₁ + k₂)/k₁. Since v₀ = k₂[ES] and Vmax = k₂[E]ₜ, v₀ = Vmax[S]/(Km + [S]).
• The plot of v₀ versus [S] is a rectangular hyperbola: first-order in [S] when [S] ≪ Km (v₀ ≈ (Vmax/Km)[S]), mixed order near Km, and zero order (saturated, v₀ = Vmax) when [S] ≫ Km.
• Michaelis' original (rapid-equilibrium) assumption takes k₂ ≪ k₋₁, so Km = k₋₁/k₁ = Ks, the true dissociation constant. Km equals the true binding constant only in this limiting case; otherwise Km ≥ Ks.
• Meaning of Km: [S] at which v₀ = Vmax/2. Low Km = high apparent affinity. It is independent of [E], expressed in molar units (often mM or µM), and characteristic of an enzyme–substrate pair at a given pH and temperature.
• kcat (turnover number): molecules of substrate converted per active site per second = Vmax/[E]ₜ (divide by number of active sites for an oligomer). Range: ~0.5 s⁻¹ (lysozyme) to ~10⁷ s⁻¹ (catalase).
• Catalytic efficiency / specificity constant kcat/Km (M⁻¹s⁻¹) governs rate at low, physiological [S]. Its upper limit is the diffusion-controlled encounter rate, 10⁸–10⁹ M⁻¹s⁻¹ — enzymes at that limit (catalase, carbonic anhydrase, triose phosphate isomerase, superoxide dismutase) are called catalytically perfect.
• Deviations from Michaelis–Menten: allosteric (sigmoidal) enzymes, multi-substrate enzymes, substrate inhibition at high [S] (v falls after a peak), and enzymes where [E] is comparable to [S] (tight-binding).

Linearised plots and parameter estimation

• Lineweaver–Burk is the plot examiners demand for identifying inhibition types, but it distorts error: low [S] values (large 1/v) dominate the fit. Hanes–Woolf spreads error better; non-linear least-squares regression on the untransformed hyperbola is the method of choice in practice (GraphPad Prism, R, Origin, SigmaPlot).
• Good practice: span [S] from about 0.2 Km to 5 Km, at least 6–8 concentrations in duplicate.

Inhibition: types, equations and diagnosis

• Reversible inhibitors bind non-covalently and can be removed by dialysis or gel filtration; irreversible inhibitors form covalent or extremely tight bonds and progressively destroy activity (kinetics are time-dependent).
• Define α = 1 + [I]/Ki (binding to free E) and α′ = 1 + [I]/Ki′ (binding to ES). General equation: v = Vmax[S]/(αKm + α′[S]).
• Competitive: inhibitor resembles the substrate and binds the free active site. Km apparent increases (αKm), Vmax unchanged; relieved by raising [S]. Lineweaver–Burk lines meet on the y-axis. Example: methotrexate on dihydrofolate reductase; statins on HMG-CoA reductase; ethanol therapy for methanol poisoning (both on alcohol dehydrogenase).
• Uncompetitive: inhibitor binds only the ES complex. Both Km apparent and Vmax fall by the same factor α′, so Km/Vmax (slope) is unchanged — lines are parallel. Example: lithium on inositol monophosphatase.
• Non-competitive (pure mixed with Ki = Ki′): inhibitor binds E and ES equally at a site other than the active site. Vmax falls, Km unchanged; lines meet on the x-axis. Not relieved by more substrate.
• Mixed inhibition (Ki ≠ Ki′): both Vmax and Km change; lines intersect to the left of the y-axis — in the second quadrant when Ki < Ki′ (apparent Km raised) and in the third quadrant, below the x-axis, when Ki > Ki′.
• Substrate (high-substrate) inhibition: a second substrate molecule binds unproductively; v rises, peaks, then falls — Lineweaver–Burk curves upward at low 1/[S].
• Product inhibition and feedback inhibition: the end product of a pathway inhibits the first, committed, usually allosteric enzyme (CTP on aspartate transcarbamoylase, whose inhibition ATP relieves; ATP on phosphofructokinase-1).
• IC₅₀ is the inhibitor concentration giving 50% inhibition under the assay conditions; it depends on [S]. For a competitive inhibitor, Cheng–Prusoff: Ki = IC₅₀/(1 + [S]/Km).
• Irreversible / mechanism-based examples: aspirin acetylating COX-1/COX-2; penicillin on transpeptidase; DIPF and organophosphate pesticides on acetylcholinesterase; allopurinol metabolite oxypurinol on xanthine oxidase (suicide inhibitor); 5-fluorouracil (as FdUMP) on thymidylate synthase.

Allosteric and cooperative kinetics

• Allosteric enzymes are usually oligomeric, with regulatory sites distinct from catalytic sites; they give sigmoidal v versus [S] curves and do not obey Michaelis–Menten kinetics. [S]₀.₅ (or K₀.₅) replaces Km.
• Hill equation: v = Vmax[S]ⁿ/(K₀.₅ⁿ + [S]ⁿ). The Hill coefficient n > 1 indicates positive cooperativity, n = 1 none (hyperbolic), n < 1 negative cooperativity. Hill plot: log(v/(Vmax − v)) versus log[S], slope = n.
• Models: MWC (concerted, symmetry) model — all subunits switch together between T (low-affinity) and R (high-affinity) states; explains positive cooperativity only. KNF (sequential, induced-fit) model — subunits change one at a time; can explain negative cooperativity too.
• K-type (K-system) modulators change K₀.₅ with Vmax constant; V-type change Vmax with K₀.₅ constant.
• Covalent regulation (phosphorylation by kinases/dephosphorylation by phosphatases, as in glycogen phosphorylase a/b) and proteolytic activation of zymogens (trypsinogen → trypsin, pepsinogen → pepsin) are regulation mechanisms that alter kinetic parameters but are not themselves equilibrium-binding effects.
• Isozymes (LDH1–LDH5, hexokinase I–III versus glucokinase/hexokinase IV) have different Km and Vmax values, letting tissues tune flux: glucokinase has a high Km (~10 mM) and is not inhibited by glucose-6-phosphate, so the liver takes up glucose only after a meal.

Multi-substrate reactions and bisubstrate kinetics

• Sequential (single-displacement): all substrates bind before any product leaves, forming a ternary complex.
  • Ordered sequential: fixed order of binding — most NAD⁺-dependent dehydrogenases (NAD⁺ first).
  • Random sequential: either substrate may bind first — creatine kinase, many kinases.
  • Lineweaver–Burk plots at varying fixed second substrate give intersecting lines.
• Ping-pong (double-displacement): the first product leaves before the second substrate binds; a substituted enzyme intermediate forms — transaminases (ALT/AST via pyridoxamine-enzyme), chymotrypsin (acyl-enzyme), nucleoside diphosphate kinase. Plots give parallel lines.
• Diagnosis uses primary plots (1/v versus 1/[A] at several fixed [B]), secondary plots of slopes and intercepts, product inhibition patterns and isotope exchange.

Effect of pH, temperature and other factors

• pH: bell-shaped activity curve; ionisation of catalytic and substrate-binding groups (His ~6.0, Cys ~8.3, Asp/Glu ~4, Lys ~10.5) and of the substrate itself. pH optima: pepsin ~1.5–2, salivary amylase ~6.8, trypsin ~8, alkaline phosphatase ~9–10. Extreme pH also denatures the protein (irreversible).
• Temperature: rate first rises (Arrhenius; Q₁₀ ≈ 1.5–2 per 10 °C) then falls steeply as thermal denaturation takes over. The peak is the "temperature optimum" — an operational value depending on incubation time, not a thermodynamic constant. Human enzymes ~37 °C; *Taq* polymerase ~72 °C.
• Arrhenius plot: ln k versus 1/T, slope = −Ea/R. A break in slope suggests a change in rate-limiting step or in conformation.
• Cofactors, metal ions and activators: Mg²⁺ for kinases, Zn²⁺ for carbonic anhydrase and carboxypeptidase; Cl⁻ activates α-amylase; coenzymes NAD⁺/NADP⁺, FAD, TPP, PLP, biotin, CoA.
• Enzyme stability: ionic strength, substrate protection, carrier protein (BSA), reducing agents and glycerol; immobilised enzymes show altered apparent Km because of diffusion limitation in the support.
• Pre-steady-state (transient) kinetics: stopped-flow and rapid-quench methods on the millisecond scale resolve individual steps; a burst phase of product formation (as in chymotrypsin with p-nitrophenyl acetate) proves a covalent acyl-enzyme intermediate — steady-state kinetics alone cannot do this.
• Indian practice and standards: clinical enzyme assays in NABL-accredited labs (ISO 15189) follow IFCC reference methods at 37 °C with results in IU/L; drugs and enzyme preparations follow Indian Pharmacopoeia (IP) monographs under the Drugs and Cosmetics Act, 1940 and Rules, 1945 and the New Drugs and Clinical Trials Rules, 2019 (CDSCO); food enzymes are permitted under the FSS Act, 2006 and FSSAI regulations; GLP compliance is monitored by the National GLP Compliance Monitoring Authority (DST). Enzyme assay specifics in IP/IS monographs change between editions — check the current edition rather than relying on a remembered value.

Key points

• v₀ - initial velocity, measured in the linear phase with <10% substrate used, so reverse reaction and product inhibition are negligible.
• Michaelis–Menten equation - v₀ = Vmax[S]/(Km + [S]); a rectangular hyperbola derived under the steady-state assumption.
• Km - [S] giving half of Vmax; units of concentration; independent of [E]; equals (k₋₁ + k₂)/k₁; low Km means high apparent affinity.
• Vmax - velocity at saturating substrate; directly proportional to [E]ₜ, so it is not a constant of the enzyme alone.
• kcat - turnover number = Vmax/[E]ₜ (per active site), units s⁻¹; a true constant of the enzyme.
• kcat/Km - catalytic efficiency, M⁻¹s⁻¹; diffusion limit 10⁸–10⁹; best criterion for comparing substrates.
• Lineweaver–Burk - 1/v versus 1/[S]; slope Km/Vmax, y-intercept 1/Vmax, x-intercept −1/Km; distorts error at low [S].
• Competitive inhibition - Km apparent up, Vmax same, lines meet on the y-axis, reversed by excess substrate.
• Non-competitive inhibition - Vmax down, Km same, lines meet on the x-axis, not reversed by substrate.
• Uncompetitive inhibition - binds ES only; Vmax and Km both fall equally; parallel Lineweaver–Burk lines.
• Mixed inhibition - both Vmax and Km change; Ki ≠ Ki′; lines intersect in the second quadrant.
• Cheng–Prusoff - Ki = IC₅₀/(1 + [S]/Km) for competitive inhibitors; IC₅₀ alone is assay-dependent.
• Allosteric enzymes - sigmoidal kinetics, Hill coefficient n > 1, described by MWC (concerted) or KNF (sequential) models, not by Km.
• Sequential versus ping-pong - ternary complex gives intersecting plots; substituted-enzyme (ping-pong) gives parallel plots.
• Enzyme unit - 1 IU = 1 µmol/min; 1 katal = 1 mol/s; 1 IU = 16.67 nkat; specific activity = IU/mg protein.
• pH and temperature optima - bell-shaped curves; the temperature optimum is operational, set by the balance of rate increase and denaturation.
• Pre-steady-state burst - stopped-flow evidence of a covalent intermediate; invisible to steady-state kinetics.

Formulas and examples

Example 1 — Km and Vmax from the Michaelis–Menten equation. An enzyme has Vmax = 60 µmol min⁻¹ mg⁻¹ and Km = 2.0 mM. Find v₀ at [S] = 0.5, 2.0 and 20 mM, and the [S] needed for 90% of Vmax.

• [S] = 0.5 mM: v₀ = 60 × 0.5/(2.0 + 0.5) = 30/2.5 = 12 µmol min⁻¹ mg⁻¹ (20% of Vmax).
• [S] = 2.0 mM: v₀ = 60 × 2/(2 + 2) = 120/4 = 30 (exactly Vmax/2, confirming [S] = Km).
• [S] = 20 mM: v₀ = 60 × 20/(2 + 20) = 1,200/22 = 54.5 (90.9% of Vmax).
• For v₀ = 0.9 Vmax: rearranging, [S] = Km × (v/Vmax)/(1 − v/Vmax) = 2.0 × 0.9/0.1 = 18 mM = 9 Km. (General rule: 9 Km gives 90%, 99 Km gives 99% — saturation is approached very slowly.)

Example 2 — kcat and catalytic efficiency. A purified enzyme of molecular mass 50,000 g/mol (one active site) is assayed at 0.20 µg per 1.0 mL reaction; Vmax = 0.015 µmol min⁻¹ per mL and Km = 0.40 mM.

• Enzyme in the assay = 0.20 µg = 0.20 × 10⁻⁶ g; moles = 0.20 × 10⁻⁶/50,000 = 4.0 × 10⁻¹² mol in 1.0 mL → [E]ₜ = 4.0 × 10⁻⁹ M = 4.0 nM.
• Vmax in molar terms = 0.015 µmol min⁻¹ per 1 mL = 1.5 × 10⁻⁸ mol per mL per min = 1.5 × 10⁻⁵ M min⁻¹ = 2.5 × 10⁻⁷ M s⁻¹.
• kcat = 2.5 × 10⁻⁷/4.0 × 10⁻⁹ = 62.5 s⁻¹.
• kcat/Km = 62.5/(4.0 × 10⁻⁴ M) = 1.56 × 10⁵ M⁻¹s⁻¹ — about 10³–10⁴-fold below the diffusion limit, so not catalytically perfect.
• Specific activity = 0.015 µmol min⁻¹ / 0.0002 mg = 75 IU/mg.

Example 3 — identifying the inhibition type from data. With Km = 5 mM and Vmax = 100 units, adding 1 mM of an inhibitor gives apparent Km = 20 mM and apparent Vmax = 100 units.

• Vmax unchanged, Km raised 4-fold → competitive inhibition, α = 4.
• α = 1 + [I]/Ki → 4 = 1 + 1/Ki → Ki = 1/3 = 0.33 mM.
• At [S] = 5 mM, uninhibited v₀ = 100 × 5/(5 + 5) = 50; inhibited v₀ = 100 × 5/(20 + 5) = 20 → inhibition = (1 − 20/50) × 100 = 60%.
• Raise [S] to 100 mM: inhibited v₀ = 100 × 100/(20 + 100) = 83.3 versus uninhibited 100 × 100/105 = 95.2 → only 12.5% inhibition, confirming reversal by excess substrate.
• If instead the data had shown Vmax falling to 25 with Km staying at 5 mM, it would be non-competitive, with α = α′ = 4 and Ki = Ki′ = 0.33 mM (α′ = 4 alone, with α = 1, would instead be uncompetitive, which also lowers apparent Km).

Example 4 — clinical assay: activity in IU/L from absorbance. An ALT (SGPT) assay follows NADH oxidation at 340 nm (ε = 6,220 M⁻¹cm⁻¹, l = 1 cm). Total reaction volume 1.0 mL contains 0.100 mL serum; ΔA/min = −0.040.

• Rate of NADH loss = 0.040/6,220 = 6.43 × 10⁻⁶ mol L⁻¹ min⁻¹ = 6.43 µmol L⁻¹ min⁻¹ in the cuvette.
• µmol/min in the cuvette = 6.43 × 10⁻⁶ mol L⁻¹min⁻¹ × 1.0 × 10⁻³ L = 6.43 × 10⁻⁹ mol = 6.43 × 10⁻³ µmol min⁻¹ = 6.43 mIU.
• Serum used = 0.100 mL = 1.0 × 10⁻⁴ L → activity = 6.43 × 10⁻³ µmol min⁻¹ / 1.0 × 10⁻⁴ L = 64.3 IU/L.
• Shortcut: IU/L = (ΔA/min × 10⁶ × V_total)/(ε × l × V_sample) = (0.040 × 10⁶ × 1.0)/(6,220 × 1 × 0.100) = 40,000/622 = 64.3 IU/L. Typical adult reference interval is roughly up to 35–45 IU/L (laboratory- and method-specific), so this value is mildly raised.

Example 5 — Lineweaver–Burk from experimental points. Data: [S] = 0.2 mM, v = 20; [S] = 1.0 mM, v = 60 (arbitrary units).

• Reciprocals: (1/[S], 1/v) = (5.0, 0.0500) and (1.0, 0.01667).
• Slope = (0.0500 − 0.01667)/(5.0 − 1.0) = 0.03333/4 = 8.333 × 10⁻³.
• Intercept = 0.01667 − 8.333 × 10⁻³ × 1.0 = 8.333 × 10⁻³ → Vmax = 1/8.333 × 10⁻³ = 120 units.
• Km = slope × Vmax = 8.333 × 10⁻³ × 120 = 1.0 mM. Check: v at 1.0 mM = 120 × 1/(1 + 1) = 60 ✓; v at 0.2 mM = 120 × 0.2/1.2 = 20 ✓.

Where it is used

• Pharmaceutical discovery and development: screening and Ki/IC₅₀ determination for enzyme-target drugs (statins, ACE inhibitors, protease inhibitors, DPP-4 inhibitors) at Sun Pharma, Dr Reddy's, Cipla, Zydus, Biocon, Syngene and Aurigene; enzyme-inhibition kinetics also underlies drug–drug interaction studies on cytochrome P450 in DMPK labs (CDSCO/ICH-aligned).
• Clinical biochemistry and diagnostics: ALT, AST, ALP, GGT, CK-MB, LDH, amylase, lipase and troponin-linked panels reported in IU/L by NABL-accredited (ISO 15189) labs — Dr Lal PathLabs, SRL, Metropolis, Thyrocare; kit development at Transasia/Erba and Agappe uses kinetic linearity and reagent Km optimisation.
• Industrial enzyme production and application: Advanced Enzyme Technologies (Thane), Novozymes South Asia, Maps Enzymes — amylases, cellulases, proteases, phytase and lipases for detergents, textiles, leather, baking, brewing, animal feed and 2G ethanol; process design uses Km, thermal stability and immobilised-enzyme kinetics.
• Biotech process development and bioreactors: feeding strategies and reactor sizing use Michaelis–Menten and the analogous Monod model; immobilised-enzyme reactors (CSTR, packed bed) use the effectiveness factor and apparent Km.
• Job roles: QC/QA analyst, R&D associate (enzymology), assay development scientist, clinical biochemist, bioprocess engineer, medical/scientific writer; entry assessments typically test units of activity, Km/Vmax calculations and inhibition plots.
• Academic and agri-environment research: CSIR labs (CDRI, IICT, NCL, IMTech), ICAR institutes (soil enzyme assays for dehydrogenase and phosphatase as soil-health indices), and CPCB/SPCB-linked work on enzyme biosensors and pesticide (acetylcholinesterase-inhibition) detection.

Interview questions

• Q: What exactly does Km tell you, and when is it a true affinity constant? A: Km is the substrate concentration at half-maximal velocity, equal to (k₋₁ + k₂)/k₁; it equals the true dissociation constant Ks only when catalysis is much slower than substrate dissociation (k₂ ≪ k₋₁).
• Q: Why is kcat/Km a better measure of catalytic performance than Vmax? A: Vmax depends on how much enzyme you added, while kcat/Km is a second-order rate constant describing the enzyme at the low substrate concentrations found in cells and therefore ranks substrates and enzymes fairly; its ceiling is the diffusion limit.
• Q: How do you tell competitive from non-competitive inhibition experimentally? A: Measure v₀ at a range of [S] with and without inhibitor and plot 1/v versus 1/[S] — lines meeting on the y-axis (Vmax unchanged, Km raised) indicate competitive, lines meeting on the x-axis (Vmax lowered, Km unchanged) indicate non-competitive.
• Q: Why is initial velocity used instead of the rate at any convenient time? A: Only at the start is substrate essentially unconsumed and product absent, so the reverse reaction, product inhibition and enzyme inactivation do not distort the measured rate.
• Q: An inhibitor gives parallel Lineweaver–Burk lines. What is it and what does that mean mechanistically? A: Uncompetitive — it binds only the ES complex, lowering both Km apparent and Vmax by the same factor, so the slope Km/Vmax is unchanged; raising substrate makes the inhibition worse, not better.
• Q: Why does a sigmoidal v versus [S] curve rule out simple Michaelis–Menten analysis? A: Sigmoidicity means cooperative substrate binding among subunits, so the derivation's single-site, independent-binding assumption fails; the data are fitted with the Hill equation and reported as K₀.₅ and n.
• Q: Does an enzyme change the equilibrium constant of its reaction? A: No — it lowers the activation energy of both forward and reverse reactions equally and only accelerates the approach to the same equilibrium.
• Q: What is the difference between IC₅₀ and Ki? A: IC₅₀ is an empirical, assay-dependent concentration giving 50% inhibition; Ki is a true equilibrium dissociation constant for the enzyme–inhibitor complex, obtained from IC₅₀ by Cheng–Prusoff correction for the substrate concentration used.
• Q: How would you distinguish a reversible from an irreversible inhibitor in the lab? A: Dilute or dialyse (or gel-filter) the inhibited enzyme — a reversible inhibitor dissociates and activity returns, an irreversible one does not; irreversible inhibition also shows time-dependent loss of activity.
• Q: Why is a reported "temperature optimum" of an enzyme not a true constant? A: It is the balance between rising reaction rate and progressive thermal denaturation, so it shifts with incubation time, protein concentration and buffer — longer assays give a lower apparent optimum.
• Q: Why do liver glucokinase and muscle hexokinase differ, and what does kinetics have to do with it? A: Hexokinase has a low Km (~0.05 mM) and is product-inhibited by glucose-6-phosphate, so muscle takes up glucose even when blood glucose is low; glucokinase has a high Km (~10 mM) and no such inhibition, so the liver stores glucose only after a meal.
• Q: You measure a Vmax that falls over the assay while Km stays the same. Diagnosis? A: Progressive loss of active enzyme — thermal or pH inactivation, proteolysis, adsorption to the cuvette, or an irreversible inhibitor — not a change in substrate binding; verify by measuring activity of the same enzyme stock over time.

Common mistakes

• Saying Km is "the affinity of the enzyme for substrate" without qualification, or quoting it as a dimensionless number — it is a concentration and only approximates 1/affinity when k₂ ≪ k₋₁.
• Confusing Vmax (depends on [E]ₜ, units of velocity) with kcat (per-active-site constant, units s⁻¹), or forgetting to divide by the number of active sites for oligomeric enzymes.
• Reading the x-intercept of a Lineweaver–Burk plot as Km when it is −1/Km (so Km = −1/x-intercept), or reporting the slope as Km instead of Km/Vmax.
• Mislabelling uncompetitive as non-competitive (many textbooks in the market blur them) — uncompetitive lines are parallel, non-competitive lines meet on the x-axis.
• Unit errors in activity calculations: forgetting the 10⁶ factor when ε is in M⁻¹cm⁻¹ but the answer is wanted in µmol, using the cuvette volume where the sample volume belongs, or reporting IU instead of IU/L or IU/mg.
• Measuring "velocity" after substrate is heavily depleted or a non-linear part of the progress curve, then fitting Michaelis–Menten to it.
• Applying Michaelis–Menten to allosteric enzymes, or claiming an enzyme "shifts the equilibrium" or "is used up" in the reaction.

Related topics

Biochemistry: biomolecules and enzymes · Bioenergetics and oxidative phosphorylation · Enzyme mechanisms and catalytic strategies · Protein purification and assay techniques · Metabolic regulation and glycolysis · Pharmacology of enzyme-inhibitor drugs