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Michaelis-Menten and Lineweaver-Burk calculator

Solve the Michaelis-Menten equation for v, Km, Vmax or [S], or paste a table of [S] and v to fit a Lineweaver-Burk plot. Every step is shown.

Km and [S] in the same unit

    How Michaelis-Menten works

    v = Vmax [S] / (Km + [S])

    Km is the substrate concentration where the enzyme reaches half of Vmax. When [S] equals Km, v is exactly Vmax / 2. When [S] is ten times Km, v is about 91 percent of Vmax, and the enzyme is close to saturated.

    Taking the reciprocal of both sides gives a straight line, the Lineweaver-Burk plot:

    1/v = (Km / Vmax)(1/[S]) + 1/Vmax

    The y-intercept is 1/Vmax, the slope is Km/Vmax, and the x-intercept is -1/Km. One caution: the double-reciprocal plot over-weights the points at low [S], so a small error there moves the whole line.

    Mistakes that cost points

    Reading Km straight off the x-interceptThat intercept is -1/Km. Flip it and drop the minus sign, or use Km = slope x Vmax.
    Using the slope as KmThe slope is Km / Vmax, so multiply it by Vmax.
    Taking the highest measured v as VmaxThe enzyme only approaches Vmax. Get it from the intercept: Vmax = 1 / intercept.

    Practice problems

    Vmax is 100 uM/min and Km is 2 mM. What is v at [S] = 2 mM?
    v = 50 uM/min. [S] equals Km, so v is half of Vmax.
    Same enzyme at [S] = 20 mM. What is v?
    v = 100 x 20 / 22 = 90.9 uM/min. At ten times Km the enzyme is close to saturated.
    Vmax is 120 uM/min. At [S] = 3 mM you measure v = 90 uM/min. What is Km?
    Km = [S] x (Vmax - v) / v = 3 x 30 / 90 = 1.0 mM.
    Km is 2 mM. At [S] = 8 mM you measure v = 80 uM/min. What is Vmax?
    Vmax = v x (Km + [S]) / [S] = 80 x 10 / 8 = 100 uM/min.
    Vmax is 100 uM/min and Km is 2 mM. What [S] gives v = 90 uM/min?
    [S] = Km x v / (Vmax - v) = 2 x 90 / 10 = 18 mM. Going from half speed to 90 percent takes nine times Km.
    Fit this table: [S] (mM) 0.5, 1, 2, 4, 8 and v (uM/min) 20, 33.33, 50, 66.67, 80.
    The Lineweaver-Burk fit gives Vmax = 100 uM/min and Km = 2.0 mM. Paste it into the Fit a table tab to see every step.

    Practice it until it sticks

    Novis turns problems like these into a spaced-repetition deck, checks your own written work one step at a time, and tells you which step went wrong. Novis opens October 20.

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