All examples · Example 24 of 34
Enzyme Kinetics: Michaelis–Menten
Initial reaction velocity against substrate concentration (triplicates) with the fitted Michaelis–Menten curve.
Key findings
- Velocity rises monotonically with substrate (Spearman ρ = 0.992, p = 2.3 × 10⁻²⁶), while Pearson r = 0.74 is lower because the relationship saturates.
Replicate velocities at each substrate concentration
Location, spread and shape for every group — the first thing to read before choosing a test. Skewness near 0 and excess kurtosis near 0 are what a normal distribution looks like.
| Group | n | Mean | SD | SEM | Median | Q1 – Q3 | Min – Max | Skewness | Excess kurtosis |
|---|---|---|---|---|---|---|---|---|---|
| 0.5 µM | 3 | 3.557 | 0.0611 | 0.03528 | 3.57 | 3.53 – 3.59 | 3.49 – 3.61 | -0.935 | — |
| 1.0 µM | 3 | 7.06 | 0.3132 | 0.1808 | 7.21 | 6.955 – 7.24 | 6.7 – 7.27 | -1.66 | — |
| 2.0 µM | 3 | 13.02 | 0.5773 | 0.3333 | 12.84 | 12.7 – 13.25 | 12.56 – 13.67 | 1.29 | — |
| 4.0 µM | 3 | 23.07 | 1.086 | 0.6269 | 23.25 | 22.58 – 23.66 | 21.91 – 24.06 | -0.713 | — |
| 8.0 µM | 3 | 36.66 | 2.212 | 1.277 | 37.18 | 35.7 – 37.87 | 34.23 – 38.56 | -1.01 | — |
| 15.0 µM | 3 | 51.88 | 1.797 | 1.037 | 51.64 | 50.92 – 52.71 | 50.21 – 53.78 | 0.582 | — |
| 30.0 µM | 3 | 69.5 | 1.084 | 0.6258 | 69.7 | 69.02 – 70.09 | 68.33 – 70.47 | -0.802 | — |
| 60.0 µM | 3 | 78.32 | 1.202 | 0.6942 | 78.64 | 77.81 – 78.98 | 76.99 – 79.33 | -1.11 | — |
| 120.0 µM | 3 | 84.48 | 2.746 | 1.585 | 84.87 | 83.22 – 85.94 | 81.56 – 87.01 | -0.626 | — |
| 240.0 µM | 3 | 85.59 | 1.628 | 0.9401 | 85.91 | 84.87 – 86.47 | 83.83 – 87.04 | -0.842 | — |
LabTools call
stats.describelabtools stats describe --groups @groups.json
The same method is available as an MCP tool (stats_describe) and from the desktop app's statistics panel.
Is velocity monotonic in substrate?
Michaelis–Menten kinetics are saturating, not linear, so the rank-based coefficients (Spearman, Kendall) are the right test of a monotonic rise; Pearson understates it because the curve bends.
| Coefficient | Estimate | r² | n | p |
|---|---|---|---|---|
| Pearson r (linear) | 0.7396 | 0.5469 | 30 | 3.0 × 10⁻⁶ |
| Spearman ρ (monotonic, rank) | 0.9915 | — | 30 | 2.3 × 10⁻²⁶ |
| Kendall τ (rank, tie-robust; normal-approximation p) | 0.9172 | — | 30 | 1.1 × 10⁻¹² |
LabTools calls (3)
stats.correlationlabtools stats correlation --a @Substrate.json --b @Velocity.json --method pearson
stats.correlationlabtools stats correlation --a @Substrate.json --b @Velocity.json --method spearman
stats.correlationlabtools stats correlation --a @Substrate.json --b @Velocity.json --method kendall
The same method is available as an MCP tool (stats_correlation) and from the desktop app's statistics panel.
LabTools notes
- Pearson's r measures LINEAR association only, and is sensitive to outliers. A scatter plot (plot.create kind='scatter') is worth a look before reporting it; use method='spearman' if the relationship is monotonic but curved.
Methods paragraph
Written to go straight into a manuscript.
A Michaelis–Menten model fitted by nonlinear least squares gave Vmax = 92.1 ± 0.8 nmol/min/mg and Km = 11.5 ± 0.4 µM (R² = 0.997).
Every number on this page was computed by the LabTools statistics engine (version 0.14.3) from the example's CSV on 2026-09-23. Where a value was derived before the data reached LabTools (replicate means, paired differences, log odds ratios), the text says so. The data are simulated from a fixed random seed.
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