Question

the 1/v axis of a reciprocal plot is labeled v^-1 x 10^2. The 1/[S] axis is labeled [S]^-1 x 10^-4. The plot intersects the two aces at "2" and "-4" respectively. What are Vmax and Km?

The answers are
-Vmax = (1)/(0.02 = 50, and
-Km = (1)/(4x10^4) = 0.25x10^-4 M, AND 2.5x10^-5 M

How do you get to those answers?

Answer 1

Recall that this plot is used for Michaelis –Menten equation. It helps to calculate the constants much easier (via graph)

From Michaelis–Menten equation.

V = Vmax*[S] / (Km + [S])

Where

Vmax = max rate velocity (M/s)

[S] = substrate concentration (M)

Km = Michaelis–Menten constant [M]

V = reaction rate [M/s]

Now… mathematical manipulation

Inverse:

1 / [ V = Vmax*[S] / (Km + [S]) ]

1/V = (Km + [S]) / (Vmax*[S])

Separate species

1/V = (Km) / (Vmax*[S])  + [S] / (Vmax*[S])

1/V = Km / Vmax*[S]  + 1/ Vmax

Now, note that:

1/V = Km / Vmax*[S]  + 1/ Vmax

1/V = y-axis

Km/Vmax = slope

1/[S] = x-axis

1/Vmax = y-intercept

-1/Km = x-intecept ( when y = 0 )

for... y-intercept:

note that it is 10^2 , so the value 2, must have 2*10^-2

1/Km = x-intercept

nbote that x is 10^-4 so choose 10^4

Km = 1/(x-intercept) = 1/(4*10^4)

now..

for Km

Km = 2.5*10^-5