Michaelis–Menten Kinetics

How fast does an enzyme work at a given substrate concentration? Solve for the reaction rate, the maximum rate V_max, the Michaelis constant K_m or the substrate concentration.

BiochemistryEnzymesKinetics

Inputs

Input examples

Click Solve next to the quantity you want to find: it moves into the result below. Then fill in the other three. v and V_max share the rate unit; K_m and [S] can each have their own concentration unit.

Rate unit (for v and V_max)

Substrate concentration [S]

Michaelis constant K_m

Maximum rate V_max

µmol/min

Reaction rate v

µmol/min

What is Michaelis–Menten Kinetics?

An enzyme E binds its substrate S, converts it and releases the product. At low [S] most enzymes are idle, so the rate rises almost in proportion to [S]. At high [S] every enzyme is busy and the rate levels off at V_max: the enzyme is saturated.

The Michaelis constant K_m is the substrate concentration at which the rate is exactly half of V_max. A low K_m means the enzyme reaches high speed already at little substrate — a high affinity.

[S] = K_mv = ½ V_max

[S] « K_mv ≈ (V_max/K_m)[S]

[S] » K_mv → V_max

low K_mhigh affinity

Live Graph

Result

Enter the values above

Typical K_m Values

approximate

Enzyme	Substrate	K_m
Hexokinase	glucose	0.1 mM
β-Galactosidase	lactose	4 mM
Chymotrypsin	peptide substrates	~5 mM
Carbonic anhydrase	CO₂	8 mM
Catalase	H₂O₂	~25 mM

Key Relations

Fraction of Maximum Speed

Depends only on the ratio [S]/K_m: at [S] = K_m it is 50%, at 4K_m 80%, at 9K_m 90%.

Example:

Lineweaver–Burk Plot

Plotting 1/v against 1/[S] gives a straight line: the y-intercept is 1/V_max and the x-intercept is −1/K_m. Handy for reading K_m and V_max from lab data.

Example: competitive inhibitors change the slope, not the y-intercept.

Turnover Number

How many substrate molecules one enzyme converts per second at saturation. k_cat/K_m measures overall catalytic efficiency.

Example: carbonic anhydrase: k_cat ≈ 10⁶ s⁻¹.

Sources & Verification

References

J. M. Berg, J. L. Tymoczko, G. J. Gatto & L. Stryer, Biochemistry, 9th ed., W. H. Freeman, 2019 — Ch. 8 (Enzymes: Basic Concepts and Kinetics).
L. Michaelis & M. L. Menten, “Die Kinetik der Invertinwirkung”, Biochemische Zeitschrift 49, 333–369 (1913).
K. A. Johnson & R. S. Goody, “The original Michaelis constant: translation of the 1913 Michaelis–Menten paper”, Biochemistry 50(39), 8264–8269 (2011).