Enzyme Kinetics Calculator (Michaelis-Menten Km & Vmax Fitting)
Analyze enzyme velocity data to calculate Michaelis constant (Km), maximum velocity (Vmax), turnover number (kcat), and catalytic efficiency (kcat/Km). Visualize hyperbolic saturation curves and Lineweaver-Burk double reciprocal plots.
Michaelis-Menten & Lineweaver-Burk Kinetics
| [S] (mM) | Velocity (µM/min) | |
|---|---|---|
Enzyme Kinetics Calculator Equations: Michaelis-Menten & Lineweaver-Burk
1. Michaelis-Menten Velocity Equation
Describes initial reaction velocity (v) as a function of substrate concentration ([S]):
Where Vmax is the limiting reaction rate at infinite substrate saturation, and Km (the Michaelis constant) equals the substrate concentration at which the velocity is exactly half of Vmax.
2. Lineweaver-Burk Double Reciprocal Transformation
Taking the reciprocal of both sides yields the classical linear form:
3. Turnover Number (kcat) and Catalytic Perfection
Enzymes with kcat / Km approaching 10⁸ to 10⁹ M⁻¹s⁻¹ (such as catalase, acetylcholinesterase, and carbonic anhydrase) have reached kinetic perfection, where catalysis is limited only by the diffusion rate of substrate entering the active site.
Enzyme Kinetics Modes of Inhibition: Competitive, Uncompetitive & Non-Competitive
Competitive Inhibition
Inhibitor binds active site. Vmax remains unchanged, while apparent Km increases. On Lineweaver-Burk, lines intersect at the Y-axis (1/Vmax).
Non-Competitive (Allosteric) Inhibition
Inhibitor binds with equal affinity to free enzyme and enzyme-substrate complex. Vmax decreases, while Km remains unchanged. Lines intersect on the X-axis (-1/Km).
Uncompetitive Inhibition
Inhibitor binds exclusively to the enzyme-substrate complex. Both Vmax and Km decrease by the same factor. Lineweaver-Burk plots yield distinct parallel lines.
Frequently Asked Questions
What does the Michaelis constant (Km) physically represent?
Km is the substrate concentration at which reaction velocity reaches half of Vmax in the Michaelis–Menten model. A lower Km means half-maximal velocity is reached at a lower substrate concentration; Km is not always a direct binding-affinity constant.
Why is non-linear regression preferred over Lineweaver-Burk linearization for calculating Km and Vmax?
The Lineweaver-Burk double-reciprocal transformation distorts experimental error structures. Reciprocals of small velocities at low substrate concentrations have disproportionately large influence on linear regression slopes. Non-linear least-squares fitting of the hyperbolic Michaelis-Menten curve is statistically much more robust.
What is catalytic efficiency (kcat / Km) and what is the diffusion limit?
kcat / Km measures an enzyme's ability to convert substrate into product at low substrate concentrations. The upper physical ceiling for catalytic efficiency is approximately 10⁸ to 10⁹ M⁻¹s⁻¹, defined by the rate at which substrate can diffuse into the enzyme active site.
How can I distinguish competitive, non-competitive, and uncompetitive inhibition?
On Lineweaver-Burk plots: Competitive inhibition maintains unchanged Vmax (identical 1/Vmax Y-intercept) with increased apparent Km. Non-competitive inhibition lowers Vmax while keeping Km constant (identical -1/Km X-intercept). Uncompetitive inhibition reduces both Vmax and Km proportionally, generating parallel lines.
Share This Page
Recommend Tools
Codon Usage Frequency Calculator
BioinformaticsCount codons from DNA/RNA/FASTA input and compare codon frequency, GC3, and rare codons against expression hosts
IC50 & EC50 Calculator (Dose-Response)
BioinformaticsFit dose-response assay curves with 4-parameter logistic (4PL) Hill equations, calculate IC50, EC50, Hill slope, and convert to Ki using Cheng-Prusoff
Hardy-Weinberg Equilibrium & Chi-Square Calculator
BioinformaticsCalculate allele frequencies (p, q), expected genotype counts, Chi-square goodness-of-fit (df=1), and autosomal recessive carrier risks
Explore All Lab Calculators →