Calculate the substrate concentration when the initial velocity is 1/8th of Vmax. The km for its substrate is 10 mM.

Answer 1

v = Vm [S] / Km + [S] ... Michaelis Menten equation

v = initial velocity

[S] = concentration of substrate

Km = Michaelis constant

Vm = maximal velocity

Vm / 8 = Vm [S] / Km + [S]

VmKm + Vm[S] = 8Vm[S]

VmKm = 7Vm[S]

[S] = 1/7 Km = 1.4 mM

To demonstrate this process, look at when v = 1/2 Vm (not 1/8 Vm):

v = Vm[S] / Km + [S]

Vm/2 = Vm[S] / Km + [S]

VmKm + Vm[S] = 2Vm[S]

VmKm = Vm[S]

Km = [S] which is exactly what Km is supposed to be when you have 1/2 maximal velocity. Km is the concentration of substrate when the velocity is 1/2 maximal velocity.