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Nonlinear least squares regression
applied to Michaelis & Menten kinetics

Also in a smartphonecompact version, suitable for small screens (smartphones). Disponible también en español.

You may additional help texts.
  1. Experimental data points:
    Choose a format and enter your data in the text box, using one line per point. For each one, first type the independent variable (substrate concentration), followed by a comma and the dependent variable (velocity of reaction). If your data come from another software, like a spreadsheet, you can copy from there and paste here in the textbox (they may come tab-delimited, but this will be automatically fixed).
    Format of the data:
    If your data use comma for decimal position, check this:
    (then they must use semicolon or tab as separator)
    1, 4.1
    3, 6.3
    5, 11.2
    1, 4.0, 4.2, 3.9
    3, 5.9, 6.1, 6.2
    5, 11.0, 10.8, 11.1
    1, 4.1, 0.2
    3, 6.3, 0.15
    5, 11.2, 0.25
    Type (or paste) your [S], ѵ data :

    State the units you are using for your data:
    [S] in mM µM
    ѵ in µM/min µM/s
  2. Either accept these initial estimated values or enter others (These are initial values that will later be improved with regression)
    Advice: The initial value for ѵmax must be higher than ѵ of all experimental data. The value of Km must be in between [S] of the first data. If the calculation leads to negative values, infinity or NaN this means the calculation has failed; please try with different initial values.
    (p1) ѵmax = ( ) Improvement:
    (p2) Km = ( ) Improvement:
    The result displayed is: calculated value ± standard error, p= level of significance
  3. ѵ
    Press to copy the graph:
    Press this button to perform a single iteration, and check how the parameters change in the boxes above. Check too the graph on the right and the RMS error and detailed results below.

    RMS error =
    Weighted standard error for the estimate: average dispersion of the points with respect to the fitted curve, relative to the estimated error for the points themselves. Values >>1 indicate the curve is not fitting well to the points within their intrinsic errors.
  4. If the new values of the parameters look reasonable, press the calculate button again, and keep pressing repeatedly until the parameters converge (i.e., their values do not change significantly, the RMS does not change, the ‘improvement’ values displayed approach zero).
    Note that the results displayed are based on the parameter values at the end of the previous iteration; therefore, you should always run an additional calculation or iteration once convergence has been reached.
  5. To keep the results, select all the contents of the results box and copy it. Then paste into a spreadsheet, word processor or text editor.
  6. If any of the parameters diverges, try with other reasonable values for the initial estimates and press the calculate button again.
    If it becomes difficult to achieve convergence, you may try a fractional adjustment factor here: and repeat the iterations. Values <1 will make convergence slower but more stable.


(*) these are measurements of the quality of fit