Michaelis-Menten enzyme kinetics formula: reaction velocity v, Km & kcat

Hyperbolic saturation kinetics: why Km equals the substrate concentration at 0.5 × Vmax!

For an enzyme following a simple Michaelis-Menten mechanism under steady-state initial-rate conditions, v=Vmax*[S]/(Km+[S]). Use matching concentration units for Km and substrate. This model does not describe every enzyme, receptor or growth process; cooperativity and inhibition may require different equations.

For Vmax=120 µM/min and Km=40 µM, substrate concentrations 10, 40 and 360 µM give rates 24, 60 and 108 µM/min. The ratios v/Vmax are 0.2, 0.5 and 0.9. Interpret these as relative rates; a binding occupancy interpretation needs the corresponding mechanism, and Km is not generally a binding dissociation constant.

With compatible units, Vmax divided by active enzyme concentration gives kcat. Specify the active-site/enzyme concentration convention for multimeric enzymes. Changing reaction conditions can change the parameters.

Initial velocity and fraction of Vmax

Ensure Km (B2) and Substrate [S] (C2) use the same molar unit (both µM or both mM).

=IF(OR(COUNT(A2:C2)<>3,A2<0,B2<=0,C2<0),"Invalid inputs",ROUND(A2*C2/(B2+C2),2))

Relative rate v/Vmax

Dividing Vmax (µM/min) by total enzyme [Et] (µM, D2) yields kcat in min⁻¹ (catalytic events per enzyme molecule per minute).

=IF(OR(COUNT(A2:C2)<>3,A2<0,B2<=0,C2<0),"Invalid inputs",ROUND(C2/(B2+C2),4))

Turnover number kcat

For Vmax in µM/min and active enzyme in µM, the result is in min⁻¹. Divide by 60 for s⁻¹.

=IF(OR(NOT(ISNUMBER(A2)),NOT(ISNUMBER(D2)),A2<0,D2<=0),"Invalid inputs",ROUND(A2/D2,1))

Further reading

• Microsoft Support — ROUND function
• Assay Guidance Manual — Basics of enzymatic assays