Lineweaver-Burk Plot: Intercepts & Inhibition Patterns

A Lineweaver-Burk plot (double-reciprocal plot) graphs 1/V₀ on the y-axis against 1/[S] on the x-axis, turning the curved Michaelis-Menten hyperbola into a straight line. Its y-intercept is 1/Vmax, its x-intercept is −1/Km and its slope is Km/Vmax. Inhibitors are identified by what the lines share: competitive lines meet on the y-axis (Km ↑, Vmax unchanged), pure noncompetitive lines meet on the x-axis (Vmax ↓, Km unchanged), uncompetitive lines run parallel (both fall by the same factor) and mixed lines cross left of the y-axis, off both axes. Only competitive inhibition can be overcome by adding more substrate.

Lineweaver-Burk plot at a glance

Michaelis-Menten first: the curve behind the plot

For a simple, non-cooperative enzyme, initial velocity follows the Michaelis-Menten equation:

V₀ = Vmax × [S] / (Km + [S])

It assumes initial velocity (little substrate used up), substrate in large excess over enzyme, and a steady-state enzyme-substrate complex (ES).

Three facts that keep coming back:

• Km and affinity. A lower Km means half-maximal speed at less substrate, the "higher affinity" reading exams expect. Strictly, Km = (koff + kcat)/kon, which approaches the true dissociation constant only when substrate falls off much faster than it is converted.
• First order vs zero order. When [S] ≪ Km, V₀ ≈ (Vmax/Km) × [S]: rate rises in proportion to substrate. When [S] ≫ Km, V₀ ≈ Vmax and rate no longer depends on [S]. The same saturation explains zero-order drug elimination; the fomepizole label, for example, says its elimination after acute doses is best characterized by Michaelis-Menten kinetics.
• Km separates look-alike enzymes. Liver glucokinase has a much higher Km for glucose than hexokinase, which is also inhibited by its own product, glucose-6-phosphate. Plotted together, the glucokinase line crosses the x-axis closer to the origin.

The hyperbola only approaches Vmax, so reading Vmax and Km off the curve is imprecise. Taking reciprocals straightens it so both constants can be read from the intercepts.

Lineweaver-Burk plot explained: the double-reciprocal equation

Invert both sides of the Michaelis-Menten equation and split the fraction:

1/V₀ = (Km/Vmax) × (1/[S]) + 1/Vmax

This is y = mx + b, with y = 1/V₀, x = 1/[S], slope m = Km/Vmax and intercept b = 1/Vmax. Both intercepts fall straight out:

• y-intercept: infinite substrate means 1/[S] = 0, so 1/V₀ = 1/Vmax.
• x-intercept: setting 1/V₀ = 0 gives 1/[S] = −1/Km. No experiment has a negative substrate concentration, so this point is always found by extending the line.

What the graph looks like: the measured points sit right of the y-axis and form a straight line rising to the right; the points nearest the y-axis come from the highest [S]. Extended to the left, the line crosses the y-axis at 1/Vmax and then the negative x-axis at −1/Km.

Lineweaver-Burk plot example: calculating Km and Vmax

Units here: V₀ in µmol/min and [S] in mM, so 1/V₀ is in min/µmol and 1/[S] in mM⁻¹.

Example 1: read the constants. A line crosses the y-axis at 0.020 min/µmol and the x-axis at −0.25 mM⁻¹.

• Vmax = 1/0.020 = 50 µmol/min.
• Km = 1/0.25 = 4 mM. Drop the minus sign: Km is always positive.
• Slope = Km/Vmax = 4/50 = 0.08 mM·min/µmol. Shortcut: slope = y-intercept ÷ |x-intercept|.

Example 2: build the line from two measurements. V₀ is 20 µmol/min at 2 mM substrate and 40 µmol/min at 8 mM.

• Reciprocal points (1/[S], 1/V₀): (0.50, 0.050) and (0.125, 0.025).
• Slope = (0.050 − 0.025)/(0.50 − 0.125) ≈ 0.0667 mM·min/µmol.
• y-intercept = 0.025 − (0.0667 × 0.125) ≈ 0.0167 min/µmol, so Vmax ≈ 60 µmol/min.
• Km = slope × Vmax ≈ 0.0667 × 60 = 4 mM. Check: 60 × 2/(4 + 2) = 20, as measured.

Example 3: add an inhibitor and name it. Start from Example 1 (Vmax 50 µmol/min, Km 4 mM, slope 0.08):

Example 4: find Ki for a competitive inhibitor. In the first row, 10 µM inhibitor raised the apparent Km from 4 to 10 mM. Apparent Km = Km × (1 + [I]/Ki), so 1 + [I]/Ki = 2.5, [I]/Ki = 1.5 and Ki ≈ 6.7 µM.

Lineweaver-Burk plot inhibitors: the master table

The general model of reversible inhibition uses two dissociation constants: Ki for the inhibitor binding free enzyme (E), which steepens the slope, and Ki′ for the inhibitor binding the ES complex, which raises the y-intercept (texts also write them Kis and Kii, or Kc and Ku). The lower the constant, the tighter the binding. With α = 1 + [I]/Ki and α′ = 1 + [I]/Ki′, the general (mixed) equation is:

1/V₀ = (α × Km/Vmax) × (1/[S]) + α′/Vmax

Competitive inhibition is the case α′ = 1, uncompetitive is α = 1, and pure noncompetitive is α = α′.

Each plot in words (inhibited line compared with the control line):

For a hand-drawn walkthrough of the two most-tested patterns, see competitive vs noncompetitive inhibition.

Lineweaver-Burk plot for competitive inhibition

The enzyme can bind substrate or inhibitor but never both, so a high enough [S] wins the competition: Vmax is unchanged and apparent Km rises by the factor 1 + [I]/Ki. The inhibited line pivots upward around the same y-intercept, and its x-intercept slides toward the origin. More inhibitor gives a fan of steeper lines pinned to one point on the y-axis.

Pure noncompetitive inhibition

The inhibitor binds away from the active site with equal affinity for E and ES. Substrate binds normally (Km unchanged), but inhibitor-bound enzyme cannot turn over, so Vmax falls as if there were less enzyme, and extra substrate cannot rescue it. The lines share the x-intercept; the inhibited line starts higher on the y-axis and is steeper.

Uncompetitive inhibition

The inhibitor binds only the ES complex. Tying up ES pulls E + S ⇌ ES to the right, so half-maximal velocity comes at a lower [S] (apparent Km ↓), while the trapped complex makes no product (Vmax ↓). Both fall by the same factor, so the slope is unchanged and the lines are parallel. More substrate only makes more ES for the inhibitor to bind.

Lineweaver-Burk plot for mixed inhibition

A mixed inhibitor binds both E and ES but prefers one of them; Vmax always falls. Solving the two line equations gives the crossing point, the same for every inhibitor concentration:

x = −(Ki/Ki′) × (1/Km) and y = (1/Vmax) × (1 − Ki/Ki′)

• Prefers free enzyme (Ki < Ki′): the lines cross left of the y-axis and above the x-axis; apparent Km rises. In Example 3, the mixed lines meet near (−0.083 mM⁻¹, 0.013 min/µmol).
• Equal affinity (Ki = Ki′): they cross on the x-axis, so pure noncompetitive inhibition is the special case.
• Prefers ES (Ki > Ki′): they cross below the x-axis; apparent Km falls.

Irreversible inhibitors

An irreversible inhibitor dissociates very slowly, often because it bonds covalently, so it effectively removes working enzyme. Because Vmax = kcat × [E]total, Vmax falls, while the enzyme molecules that escape keep a normal Km. The plot therefore mimics pure noncompetitive inhibition even when the inhibitor attacks the active site; the Assay Guidance Manual on the NCBI Bookshelf says irreversible inhibitors "display a noncompetitive phenotype" regardless of their true binding mode. Activity comes back only slowly, as the inhibitor dissociates or, once the bond is permanent, as new enzyme is made. Suicide (mechanism-based) inhibitors are processed by the enzyme's own catalytic mechanism into the form that inactivates it.

• Aspirin: acetylates a serine residue of COX-1, a covalent change that irreversibly inactivates the enzyme, so platelets stay inhibited for their lifespan of about 7–10 days. Compare aspirin vs clopidogrel.
• Organophosphates: can bind cholinesterase irreversibly; DIPF, the textbook example, modifies a reactive active-site serine of acetylcholinesterase. Carbamates inhibit the same enzyme but are cleared spontaneously within about 48 hours.
• Penicillin: covalently modifies bacterial transpeptidase, so cell-wall synthesis stops.

Drug examples: what each source actually says

Labels and textbooks don't always use exam vocabulary, so check what each one actually states.

Going deeper: HMG-CoA reductase, the antibiotic mechanisms chart for sulfonamides and penicillin, and HIV antiretroviral drugs for NNRTIs.

The pharmacology twin: dose-response curves

Receptor pharmacology runs on the same logic. Potency is where a dose-response curve sits along the dose axis; efficacy is the greatest response the drug can produce.

A competitive antagonist is surmountable: enough agonist restores the full response, just at higher doses. A noncompetitive antagonist lowers the maximal effect without changing the ED50 (the dose giving half of that maximum), so more agonist cannot restore it: the receptor twin of pure noncompetitive inhibition (Vmax ↓, Km unchanged). Watch the direction: a dose-response curve shifting right (lower potency) matches a Lineweaver-Burk x-intercept moving right, toward zero (higher Km). More on dose-response curves.

Limitations of the Lineweaver-Burk plot and better alternatives

The plot is excellent for recognizing inhibition patterns and poor for measuring constants:

• It magnifies the worst data. Low-[S] points, with the largest 1/[S] and 1/V₀ values, get undue weight, yet they are the least precise because the least product has formed.
• It bunches the rest. Concentrations of 1, 2, 5, 10 and 20 mM become 1/[S] values of 1, 0.5, 0.2, 0.1 and 0.05 mM⁻¹: the three highest concentrations crowd near the y-axis, while the single 1 mM point far to the right has the most leverage on the slope.
• It breaks regression assumptions. Ordinary linear regression assumes every plotted point carries the same error; even when the V₀ measurements do, their reciprocals do not. Use a weighted fit or, better, fit V₀ against [S] directly to the hyperbola by nonlinear regression, using linear-plot values only as starting estimates.

How USMLE tests it: exam traps

• Only the x-intercept is negative. It equals −1/Km, so an x-intercept of −0.5 mM⁻¹ means Km = 2 mM, not 0.5 or −2.
• Reciprocals flip direction. A higher y-intercept means a lower Vmax; an x-intercept closer to zero means a higher Km.
• The right side of the x-axis is low substrate. The points nearest the y-axis are the highest concentrations.
• Units. 1/[S] is in inverse concentration (mM⁻¹ or µM⁻¹) and 1/V₀ in time per amount (min/µmol). Mixing mM and µM puts Km off by a factor of 1,000.
• "Noncompetitive" vs "mixed." On USMLE-style questions, "noncompetitive" means the pure form (Vmax ↓, Km unchanged, lines meeting on the x-axis), which matches how Berg, Tymoczko and Stryer's Biochemistry (free on the NCBI Bookshelf) defines it. Jakubowski and Flatt call that pure form quite rare and name the general case mixed; drug labels (efavirenz) say "noncompetitive" without specifying a plot. If Vmax falls, Km changes and the lines are not parallel, the answer is mixed.
• "Binds an allosteric site" is not a plot. It tells you where an inhibitor binds, not which pattern it gives; read the intercepts.
• Competitive does not mean harmless. At any real [S] the reaction is slower; only the ceiling is spared.
• Cooperative enzymes break the model. Cooperative allosteric enzymes give sigmoidal rather than hyperbolic V₀-vs-[S] curves, so these straight-line rules do not apply; see allosteric regulation.

Worked vignettes

Vignette 1. Researchers test compound X on purified HMG-CoA reductase. Without X, the Lineweaver-Burk line crosses the y-axis at 0.02 min/µmol and the x-axis at −0.5 µM⁻¹. With X, the y-intercept is unchanged, but the line is steeper and crosses the x-axis at −0.25 µM⁻¹. What kind of inhibitor is X?

Answer: Competitive. Vmax stays 1/0.02 = 50 µmol/min, apparent Km doubles from 2 to 4 µM, and high substrate overcomes it, matching the "competitive inhibitor" wording of the atorvastatin label.

Vignette 2. A man who drank methanol is treated with fomepizole. How does the drug change alcohol dehydrogenase kinetics for methanol, and why does that help?

Answer: Apparent Km for methanol rises while Vmax is unchanged, so the lines meet on the y-axis. At the methanol concentrations present, the enzyme converts less methanol, so less formic acid, the metabolite behind the acidosis and visual disturbances, is made.

Vignette 3. An enzyme is incubated with compound Y, and unbound Y is then removed by dialysis. The Lineweaver-Burk y-intercept has doubled, the x-intercept is unchanged, and activity does not recover. What best explains this?

Answer: Irreversible inactivation of half the enzyme molecules, as organophosphates do to acetylcholinesterase. Vmax halves (y-intercept doubles) and the surviving enzyme keeps its Km (same x-intercept). A pure noncompetitive inhibitor gives the same plot, but because reversible inhibitors dissociate rapidly, removing it would restore activity.

Key takeaways

• Lineweaver-Burk plots 1/V₀ against 1/[S]: y-intercept 1/Vmax, x-intercept −1/Km, slope Km/Vmax.
• Competitive: same y-intercept; Km ↑, Vmax unchanged; overcome by substrate (statins, fomepizole, methotrexate, sulfonamides).
• Pure noncompetitive: same x-intercept; Vmax ↓, Km unchanged; not overcome by substrate.
• Uncompetitive: parallel lines; Km and Vmax both ↓ by the same factor.
• Mixed: lines cross left of the y-axis, above the x-axis if the inhibitor prefers free enzyme and below if it prefers ES; Vmax ↓, Km ↑ or ↓.
• Irreversible inhibitors (aspirin, organophosphates, penicillin) lower Vmax with Km unchanged, mimicking noncompetitive inhibition.
• For real data, fit the hyperbola by nonlinear regression; use the double-reciprocal plot to recognize patterns.

Sources

• Biochemistry, 5th ed., Section 8.5: Enzymes Can Be Inhibited by Specific Molecules — Berg, Tymoczko and Stryer, NCBI Bookshelf (2002)
• 6.3: Kinetics with Enzymes — Jakubowski and Flatt, Fundamentals of Biochemistry, LibreTexts (2026)
• 6.4: Enzyme Inhibition — Jakubowski and Flatt, Fundamentals of Biochemistry, LibreTexts (2026)
• Mechanism of Action Assays for Enzymes — Strelow et al., Assay Guidance Manual, NCBI Bookshelf (2012)
• The effect of substrate concentration on enzyme activity — University College London teaching page (undated)
• Programmed Problem Set on Agents Affecting the Autonomic Nervous System — Volicer, Boston University School of Medicine (undated)
• Dose-Response Relationships — Merck Manual Professional Edition (2026)
• Sulfonamides — Merck Manual Professional Edition (2024)
• Organophosphate Poisoning and Carbamate Poisoning — Merck Manual Professional Edition (2025)
• LIPITOR (atorvastatin calcium) tablets: prescribing information — DailyMed (2024)
• Fomepizole injection: prescribing information — DailyMed, American Regent (2020)
• Allopurinol tablets: prescribing information — DailyMed, Accord Healthcare (2023)
• Efavirenz tablets: prescribing information — DailyMed, Camber Pharmaceuticals (2023)
• DURLAZA (aspirin) extended-release capsules: prescribing information — DailyMed (2015)