Unit of v0 in the Michaelis-Menten Equation
The unit of v0 in the equation v0 = Vmax × [S] / ([S] + Km) is the same as the unit of Vmax, representing a reaction rate expressed as concentration per time or enzyme activity units.
Why Units of v0 Match Vmax
The equation contains a ratio [S] / ([S] + Km) where both [S] (substrate concentration) and Km (Michaelis constant) are concentrations. Since they have identical units, this ratio is dimensionless.
Multiplying the dimensionless ratio by Vmax preserves the units of Vmax. Thus, the initial velocity v0 shares the same units as Vmax.
Typical Units for Reaction Velocity
- Concentration per time: Most commonly, reaction rates are expressed in molarity per second (M/s) or micromolar per minute (μM/min).
- Enzyme activity units: Alternative units include U (one micromole of product formed per minute) and katal (one mole of product per second).
These units quantify how fast the enzyme converts substrate to product over time.
Constants and Variables in the Equation
| Parameter | Description | Units |
|---|---|---|
| Vmax | Maximum reaction velocity for given enzyme concentration | Concentration/time (e.g., M/s, μmol/min) |
| Km | Substrate concentration at half Vmax | Concentration (e.g., M) |
| [S] | Substrate concentration | Concentration (e.g., M) |
| v0 | Initial reaction velocity | Same as Vmax |
Summary of Key Points
- v0 units match those of Vmax due to dimensionless substrate concentration term.
- Reaction rates typically use concentration/time units (e.g., M/s).
- Common enzyme activity units include micromoles per minute (U) and moles per second (katal).
- Km and [S] share the same units, cancelling out in the ratio.
- Units reflect how fast substrate converts to product under enzyme catalysis.
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