Drybench Assay.
Km and Vmax from initial rates (Michaelis–Menten)
Fit Km and Vmax to initial rates by least squares, with 95 percent profile intervals, the fit diagnostics, and kcat from an active-site concentration.
Km and Vmax from initial rates you measured at several substrate concentrations, by least squares on the rates, with the diagnostics that say whether the data support them: convergence inside the search bounds, the Km–Vmax correlation and whether Km lies within the tested range, and a 95 percent profile interval on each of Km and Vmax.
Enzyme kinetics: initial rates
Paste initial rates measured at several substrate concentrations. Km and Vmax are fitted to v = Vmax·S/(Km + S) by ordinary least squares on the rates, with the diagnostics you need to judge whether the data support them.
Rates
Columns: substrate, rate. One measured initial rate per row; replicate rates are separate rows, each an observation. CSV or tab-separated text. For a two-substrate model add a column substrate b (the second substrate; substrate is A, the one that binds first if binding is ordered).
Progress curves
Synthetic demonstration data: duplicate rates from Vmax 10 µM/min and Km 2 µM with a fixed noise vector; not experimental evidence.
Units and conditions
You choose the model. Substrate inhibition needs rates at six or more substrate concentrations, two of them beyond the fitted optimum. The Hill equation needs six or more, two below and two above S0.5. The two-substrate models need a substrate b column.
Leave empty for no kcat. kcat = Vmax / [E] needs the active-site concentration, not the total protein.
Assay conditions
Recorded with the result as you type them; a condition left empty is reported as not stated.
Ordinary least squares with constant rate variance, a stated assumption; each rate is an observation. Km is not a dissociation constant.
Rates
Enter a reason, then choose a rate. The raw value is retained; changing a decision clears the current result.
| Source row | Substrate (µM) | Rate (µM/min) | Fitted rate | Residual | Decision |
|---|---|---|---|---|---|
| 2 | 0.25 | 1.1377777777777778 | – | – | |
| 3 | 0.25 | 1.0711111111111111 | – | – | |
| 4 | 0.5 | 2.036 | – | – | |
| 5 | 0.5 | 1.976 | – | – | |
| 6 | 1 | 3.4333333333333336 | – | – | |
| 7 | 1 | 3.2600000000000002 | – | – | |
| 8 | 2 | 5.04 | – | – | |
| 9 | 2 | 4.87 | – | – | |
| 10 | 4 | 6.8933333333333335 | – | – | |
| 11 | 4 | 6.5600000000000005 | – | – | |
| 12 | 8 | 8.096 | – | – | |
| 13 | 8 | 7.776 | – | – | |
| 14 | 16 | 9.066666666666666 | – | – | |
| 15 | 16 | 8.8 | – | – |
What this analysis does not do
- From progress curves it takes the slope over the one window you choose, for every well; it never picks a window itself, does not fit the integrated rate equation and does not subtract a no-enzyme background slope.
- Percent conversion counts the product formed inside the window only, from the extinction coefficient and path length as you declare them; above 10 percent the initial-rate assumption is flagged as strained, not refused.
- It does not weight the rates or fit inhibitor models; the inhibition analysis does. Substrate inhibition is fitted only when you choose it, without an interval or kcat, and is not tested against other causes of a decline.
- It reports individual, not simultaneous, intervals on Km and Vmax; kcat's is the Vmax interval divided by the enzyme concentration, and none is reported for Vmax/Km.
- It does not draw or fit a Lineweaver–Burk plot, and does not read Km as a binding constant.
- The Hill equation describes the shape of a sigmoidal rate curve. h measures steepness: it is not the number of binding sites, and values other than 1 can arise from cooperativity, a mixture of enzyme forms, hysteresis or an assay artefact such as coupling lag or substrate depletion.
- Two-substrate fits assume initial rates measured with no product present and constant-variance errors. The rate law does not distinguish ordered from random binding, and the better-fitting model is not proof of a mechanism.
Method
Km and Vmax were estimated by ordinary least squares on the initial rates (constant rate variance assumed) with a bounded Levenberg–Marquardt search in log parameters from three starts, keeping the lowest residual sum of squares. Fewer than four distinct positive substrate concentrations are refused; a fit at the search bound or one that did not converge is withheld. Each of Km and Vmax has a 95 percent profile extra-sum-of-squares interval, one parameter at a time: the parameter is held at trial values and the other refitted until the residual sum of squares reaches RSS_min × (1 + F(0.95; 1, n − 2)/(n − 2)). The search steps outward on the log scale inside the same bounds; a side that meets a bound first is reported as not resolved. kcat's interval is the Vmax interval divided by the enzyme concentration. In 2,000 simulated data sets (seven substrate levels in duplicate from 0.125 to 8 × Km, rate noise 2 percent of Vmax) the intervals contained the true Km in 95.3 percent and the true Vmax in 95.0 percent of cases; with four single levels, 94.3 and 94.6 percent.
1.2.0
Open in the appThe app carries no data in its link; paste your own export there.
Worked example
- The synthetic duplicate rates loaded below (14 rates at 7 substrate concentrations, generated from Vmax 10 µM/min and Km 2 µM with a fixed noise vector) give Km = 2.009 µM (95 percent profile interval 1.865 to 2.164 µM) and Vmax = 10.02 µM/min (9.784 to 10.26 µM/min). Computed when this page is built by the same engine the app uses, and checked against SciPy on the published fixtures.
- Three substrate levels are refused, rates that never saturate are withheld at the search bound, and a Km beyond the highest substrate is kept and flagged: the fixture holds each case.
Method
- Initial-rate Michaelis–Menten. src/lib/kinetics/michaelis-menten.ts 1.2.0Checked against SciPy curve_fit (trf, log parameters, three starts) on 5 estimated cases including noiseless rates matching the hand values, an unsaturated series flagged for range support, bound contact and two refusals: Km and Vmax within 1e-5 relative, the residual sum of squares within 1e-6 relative, kcat within 1e-5 (10 October 2026); R not run. Failed convergence is unit-tested, not in the fixture.
- Profile extra-sum-of-squares interval on Km and Vmax. src/lib/fit/profile.ts 1.1.0Checked against a SciPy direct profile on 9 cases: bounds within 1e-3 ln units, side states exact. Simulated coverage: Km 95.3, Vmax 95.0 percent (7 levels × 2). Also checked against a direct profile computed in R 4.4.3 from its own nls fit on the 7 cases with an interval: resolved bounds within 1e-3 ln units, the threshold within 1e-8 relative (12 October 2026).
Limits
- For research and education only, and not medical advice: a C50 estimated here describes this assay under these conditions and is not a binding constant.