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Enzyme kinetics — Michaelis-Menten Km, Vmax, kcat (turnover), and kcat/Km (catalytic efficiency / specificity constant) from substrate-velocity data, plus inhibition-mechanism analysis (competitive / uncompetitive / non-competitive, Ki). Fits the MM equation by nonlinear regression (and reports Lineweaver-Burk for reference).
Passed 19 of 21 test cases with the skill, and 17 of 21 without it.
and 2 more in the full report
3 fixed17 passed either way1 still failing1 broke
Tokens, turns and time describe resource use, not a dollar price.
One of 3 test cases the skill fixed. Same model, same prompt, with and without the skill.
Construct the tool execution payload for ToolUniverse to perform a non-linear Michaelis-Menten fit on substrate concentrations [0.2, 0.5, 1.0, 2.5, 5.0, 10.0] mM and initial velocities [12, 25, 40, 62, 75, 82] umol/min/mg.
| Checked | Without skill | With skill |
|---|---|---|
| Specify operation as michaelis_menten in the command parameters. | Missed | Passed |
| Pass the array of substrate concentrations using the parameter key substrate_concs. | Missed | Passed |
The instructions your model reads when the skill loads.
Turn substrate concentration vs initial velocity data into Km, Vmax, kcat, and catalytic efficiency — and classify an inhibitor's mechanism.
The Michaelis-Menten model: v = Vmax·[S] / (Km + [S]).
For published kinetic constants (someone else's Km/kcat), use the BRENDA tools instead — this skill is for analyzing your own measured data.
| Issue | What to do |
|---|---|
| Initial velocities, not endpoints | v must be the initial rate (linear phase, <10% substrate consumed). Endpoint or plateaued rates give a wrong Km/Vmax. |
| Substrate range must span Km | Include [S] both well below and well above Km (ideally ~0.2×Km to ~5×Km). Points only above Km can't define Km; only below can't define Vmax. |
| Units — be consistent | One [S] unit (mM, µM) → Km comes back in that unit. One velocity unit. Keep them fixed. |
| For kcat you need [E] | kcat = Vmax / [E]total. The tool's "catalytic_efficiency" is Vmax/Km on the velocity scale; to get true kcat (per-second turnover) and kcat/Km, divide Vmax by the molar enzyme concentration yourself. |
| ≥5–7 points | Few points → unstable fit. Spread them across the range, not clustered. |
tu run EnzymeKinetics_calculate '{"operation":"michaelis_menten",
"substrate_concs":[0.1,0.25,0.5,1,2,5,10],
"velocities":[8.5,18,32,52,72,90,98]}'
Returns a nonlinear_fit block (Vmax, Km, R2, SSE) — use these as the answer, a lineweaver_burk block (for reference only), catalytic_efficiency (Vmax/Km), and predicted_velocities + residuals.
Prefer the nonlinear fit, not Lineweaver-Burk. The double-reciprocal (Lineweaver-Burk) linearization distorts error (it over-weights low-
[S]points) and is only for visualization/sanity — never report its Km/Vmax as the final values. The tool gives both; citenonlinear_fit.
scripts/fit_michaelis_menten.py does the same nonlinear fit from a CSV and converts Vmax→kcat→kcat/Km when you supply the enzyme concentration.
test cases passed, vs 17 / 21 without
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