◄ WORLD V · SONNY 5DART 586 · a helldive into the living

THE MICHAELIS-MENTEN how fast an enzyme works

The founding equation of enzyme kinetics: reaction velocity v = Vmax[S] / (Km + [S]). At low substrate the enzyme races linearly; as substrate floods in, every active site fills and the rate saturates at Vmax. The constant Km is the substrate level at which the enzyme runs at half speed — a measure of its grip. Published in 1913 by Leonor Michaelis and Maud Menten, one of the first women to earn a medical doctorate in Canada.

THE TECHNIQUE v = Vmax[S]/(Km+[S])

The demo runs the velocity curve and shows v = Vmax/2 exactly at [S]=Km: live demo







  
HISTORY & CREDIT Michaelis & Menten · 1913

  
“Km is how tightly the enzyme binds.” — Km is the half-maximal-velocity substrate concentration; it approximates affinity only under conditions, not always. cited

  
the race · at low [S], velocity climbs nearly linearly.
saturation · sites fill; v → Vmax; and v = Vmax/2 exactly at [S]=Km.
1913 · Leonor Michaelis & Maud Menten — the bedrock of enzymology.

  
A hyperbola that governs every enzyme. kinetics






  
RECOMMEND FOR I-13 half-max, on the compiler

  
On i-13, with Vmax=100, Km=10, v is 50 at [S]=Km and saturates toward 100:

  
$ i13 run lf_michaelis-menten.i13
RUN OK · 55 step(s)
v_at_km = 50    -- Vmax/2 when [S]=Km
v_high = 99.0   half_max_at_km = 1  saturates = 1

  
Recommend as a NULL — a kinetic law (B39). The velocity is a pinned function of [S], Vmax, Km; every correct evaluation agrees. NULL — how fast an enzyme works.