Michaelis Menten Equation Calculator

The Michaelis-Menten equation describes the rectangular hyperbola relating initial reaction velocity to substrate concentration for an enzyme that binds a single substrate. Its form follows from assuming the enzyme-substrate complex reaches a steady state: velocity rises almost linearly when substrate concentration is far below Km, because free enzyme is abundant, and flattens toward Vmax once essentially every active site is occupied. Km is the substrate concentration giving half of Vmax and carries units of concentration. It approximates a dissociation constant only when catalysis is slow relative to substrate release. Reported values span a wide range, from roughly 0.05 mM for hexokinase with glucose to about 26 mM for carbonic anhydrase with carbon dioxide, and the specificity constant kcat divided by Km reaches the diffusion limit near 10^8 to 10^9 per molar per second for catalytically perfect enzymes such as triose phosphate isomerase. Reversible inhibitors perturb the two parameters in diagnostic ways. A competitive inhibitor raises apparent Km by the factor 1 plus the inhibitor concentration divided by Ki, and leaves Vmax alone, since saturating substrate outcompetes it. An uncompetitive inhibitor binds only the enzyme-substrate complex and divides both Km and Vmax by that same factor. A pure non-competitive inhibitor lowers Vmax while leaving Km unchanged. The model assumes initial-rate conditions with negligible product accumulation, substrate in large excess over enzyme, and no cooperativity. Allosteric enzymes give sigmoidal curves requiring the Hill equation instead, and substrate inhibition at high concentrations produces a downturn that a hyperbola cannot represent.

Victor Henri laid the groundwork in his 1903 doctoral thesis in Paris, deriving from invertase data a rate equation with the hyperbolic form and proposing that the enzyme first forms a complex with its substrate. His work was undervalued partly because the pH scale did not yet exist and reaction conditions could not be properly controlled. That gap closed after Soren Sorensen introduced pH and buffering in 1909, when Leonor Michaelis and Maud Menten repeated the invertase experiments under controlled acidity and temperature and published Die Kinetik der Invertinwirkung in Biochemische Zeitschrift in 1913. Menten, a Canadian physician and one of the first women in Canada to earn a medical doctorate, later spent much of her career in pathology in Pittsburgh. George Briggs and John Burdon Sanderson Haldane replaced the original rapid-equilibrium assumption with a steady-state treatment in a short 1925 paper in the Biochemical Journal. That is the derivation taught today, and it redefined Km as a composite of rate constants rather than a simple dissociation constant. Hans Lineweaver and Dean Burk published the double-reciprocal plot in 1934, giving a straight-line method for extracting Km and Vmax that dominated the literature for decades despite distorting the weighting of low-concentration points, and the Eadie-Hofstee and Hanes-Woolf transformations followed. Since inexpensive computing became available, direct non-linear regression on the untransformed data has become the accepted way to fit the parameters.