Michaelis-Menten Calculator
Calculate enzyme reaction velocity using Michaelis-Menten kinetics: v = Vmax[S] / (Km + [S]). Find reaction rate at any substrate concentration with enzyme saturation percentage.
🧪 Enzymology📐 v = Vmax[S] / (Km + [S])🧬 Biology
Substrate concentration [S] (uM)
Michaelis constant Km (uM)
Maximum velocity Vmax (uM/s)
Please enter valid values.
Formula & Reference
| Variable | Symbol | Formula | Units |
|---|---|---|---|
| Michaelis-Menten Calculator | — | v = Vmax[S] / (Km + [S]) | uM/s |
Step-by-Step Examples
Example 1
Half-Maximum Velocity
When [S] = Km, what is the velocity? (Vmax=10, Km=50, [S]=50)
- v = 10 x 50 / (50 + 50)
- v = 500 / 100 = 5 uM/s
- This is exactly Vmax/2 - that's the definition of Km!
✓ v = 5 uM/s = Vmax/2
Example 2
High Substrate
Hexokinase: Km=0.1 mM glucose, Vmax=500 uM/s. At [S]=10 mM:
- [S] >> Km so enzyme is nearly saturated
- v = 500 x 10 / (0.1 + 10) = 495 uM/s
- 99% saturation
✓ v = 495 uM/s (99% of Vmax)
Example 3
Low Substrate
Same enzyme at [S]=0.01 mM (below Km):
- v = 500 x 0.01 / (0.1 + 0.01) = 45.5 uM/s
- Only 9% saturation
- Linear range: v proportional to [S]
✓ v = 45.5 uM/s (9% saturation)
Real-World Applications
Drug Development
Km and Vmax reveal how drugs compete with substrates or alter enzyme behavior.
Medical Diagnosis
Abnormal enzyme kinetics in blood indicate organ damage (ALT, AST in liver disease).
Industrial Enzymes
Optimize bioreactor substrate concentrations using Michaelis-Menten kinetics.
Metabolic Modeling
Systems biology uses MM kinetics to model metabolic flux in cells.
Common Mistakes to Avoid
⚠️
Using wrong units for [S]
Km and [S] must be in the same units. If Km is mM and [S] is uM, convert first.
⚠️
Confusing Km with Kd
Km is not the dissociation constant Kd; it's the substrate concentration at half-Vmax. For simple cases they're related but not identical.
⚠️
Ignoring substrate depletion
MM kinetics assume [S] is constant (initial rate). In closed systems, [S] falls over time, so use initial rate conditions only.
Frequently Asked Questions
What does Km tell you? ▾
Km is the substrate concentration at half-maximum velocity. Low Km means high affinity (enzyme saturates at low [S]). High Km means low affinity.
What does Vmax depend on? ▾
Vmax = kcat x [E]total. It depends on enzyme concentration. If you add more enzyme, Vmax increases but Km stays the same.
How is Km determined experimentally? ▾
Measure initial velocity v at multiple [S] values, plot v vs [S], fit to MM equation. Or use Lineweaver-Burk double-reciprocal plot for linear analysis.
What is kcat? ▾
kcat (turnover number) = Vmax / [E]total. Units: s-1. Tells how many substrate molecules one enzyme molecule converts per second at saturation.
When does MM kinetics break down? ▾
At very high [S] (substrate inhibition), with allosteric enzymes (use Hill equation), or when product inhibition is significant.