Substrate for a Target Fraction of Vmax (Michaelis-Menten Inverse)
The assay-design inverse of Michaelis-Menten: enter Km and the fraction of Vmax you want, get the substrate concentration to use. [S] = Km x f/(1 - f). Half of Vmax takes exactly one Km (the definition of Km), but 90% takes 9 x Km and 99% takes 99 x Km -- the runaway excess that shows why an enzyme approaches Vmax but never reaches it. Feeds straight back into the forward tile. Steady state, substrate in excess of enzyme; the assay conditions govern.
Formula and source
[S] = Km x f/(1 - f) with f = target_velocity/Vmax; at f = 0.5, [S] = Km; fold_km = f/(1 - f).
The Michaelis-Menten equation inverted for the substrate concentration at a target fraction of Vmax, by name.
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