Fitting the Michaelis–Menten Equation in SciDAVis

Enzyme kinetics lives on one curve: reaction rate v versus substrate concentration [S], rising steeply and flattening toward a maximum. The Michaelis–Menten model describes it:

v = V_max · [S] / (K_m + [S])

where V_max is the maximum rate and K_m (the Michaelis constant) is the substrate concentration at half-maximum rate. SciDAVis has no built-in Michaelis–Menten model, but its Fit Wizard accepts any custom formula — so you can fit this classic properly, with real parameter errors, instead of eyeballing it or linearizing it away. Back to all tutorials.

Step 1 — Prepare and plot your data

1. Put substrate concentrations in one table column (X) and measured initial rates in another (Y).
2. Select both columns and create a Scatter plot from the Plot menu. Check the shape first: you should see a rising curve that levels off. If the highest [S] points are still climbing steeply, your data may not reach saturation — K_m will be poorly determined, and no software can fix that.
3. Click the curve in the graph so it is selected — the Fit Wizard operates on the active curve.

Step 2 — Enter the custom formula in the Fit Wizard

1. Open Analysis → Fit Wizard (or press Ctrl+Y).
2. Under the model category, choose User-defined.
3. Type the formula in muParser syntax — the same expression language SciDAVis uses for column formulas. The independent variable is x; declare your two fit parameters as names:

Vm*x/(Km+x)

4. In the parameter list, enter Vm, Km — every name in the formula must be declared as a parameter to fit.
5. Set sensible units in your head now: if your rates are in µmol/min and [S] in mM, then Vm comes out in µmol/min and Km in mM. SciDAVis doesn’t track units — you do.

Step 3 — Give good initial guesses (this is where fits fail)

Nonlinear fitting is iterative: the algorithm refines your guesses, and bad guesses converge to nonsense. This exact failure — fitting Michaelis–Menten and getting garbage — is a real, documented user struggle on the SciDAVis forums. The fix is always the same: read the starting values off the plot.

Parameter	What it means on your plot	How to guess it
Vm (Vmax)	The plateau height — the rate your data levels off toward	Read the Y-value where the curve flattens. If no clear plateau, guess slightly above your highest point.
Km	The [S] at which the rate is half of Vmax	Halve your Vm guess, find that Y on the curve, and read the corresponding X. That’s your Km guess.

Step 4 — Run the fit and read the results

1. Click Fit in the wizard. SciDAVis draws the fitted curve on your graph in red.
2. Open the Results Log (log window): you’ll see Vm and Km each with a standard error, plus chi-square and R².
3. Judge the fit with your eyes first: zoom in and check that the red curve passes through the data with residuals scattering randomly around it. A systematic S-shaped miss means the simple model is wrong (cooperativity, substrate inhibition — beyond this tutorial).

Sanity checks before you trust the numbers:

• Parameter errors vs. values: if the Km error is larger than Km itself, your data doesn’t pin down Km — you need more points in the low-[S] rising region.
• Does Km sit inside your data range? A fitted Km far above your highest [S] is an extrapolation, not a measurement. Say so in your report.
• Reproducibility: save the project (.sciprj) — it stores the formula, parameters, and results together.

Should you linearize instead (Lineweaver–Burk)?

The old textbook trick — plot 1/v vs 1/[S] and fit a straight line — exists because scientists in the 1930s had no computers. It distorts your error structure: small measurement errors at low [S] become enormous errors in 1/[S], and the linear fit weights them wrongly. Direct nonlinear fitting of the Michaelis–Menten equation, as above, is the statistically correct modern practice. Linearization is fine for a quick classroom illustration; it is not how you report K_m in a thesis.

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