Michaelis–Menten: K_m from Lineweaver–Burk
Unknown enzyme. Measure initial rate v at several [S] and recover K_m from a Lineweaver–Burk fit of 1/v versus 1/[S].
Goal
Determine K_m from v = V_max [S] / (K_m + [S]). On 1/v versus 1/[S] the intercept is 1/V_max and the slope is K_m/V_max, so K_m = slope / intercept.
Equipment
- Unknown enzyme
- Substrate stock
- Initial-rate assay
Experiment
Theory
Lineweaver–Burk linearizes Michaelis–Menten. The bench hides K_m, V_max and any ready-made double-reciprocal line. You only change [S]. An assay reports v after you record. This lab grades K_m (the characteristic substrate scale), not V_max.
Procedure
- The enzyme is unknown. You only change substrate concentration [S].
- Record. The assay logs initial rate v with small noise. There is no live v, K_m or Lineweaver–Burk overlay.
- The notebook computes 1/[S] and 1/v. Use points on both sides of the expected K_m scale (about 0.5–20).
- Repeat for at least 6 concentrations.
- Fit 1/v versus 1/[S]; K_m = slope / intercept. Compare with the reference.
Conclusion
The fitted K_m agrees with the hidden enzyme constant. Main uncertainties: assay noise and the Lineweaver–Burk weighting of low-v points.