Cellular Engineering - Principles of Biomedical Engineering - page 262

reactions, and other drug-related effects. In enzyme-catalyzed reactions, (7.7) is
rewritten as

SV .

max

V =

(7.8)

KS +

M

where V is the reaction velocity, S is the substrate concentration, V max is the maxi-
mum reaction velocity, and K M is the Michaelis-Menten constant (defined as the
concentration at which the rate of the enzyme reaction is half of V max ).
A common approach used to determine the rate constants is linearizing (7.7)
and plotting the coordinates. There are a variety of algebraically equivalent ways
to linearize (7.7) and plot, including the Lineweaver-Burk (or the double recipro-
cal equation), Eadie-Hofstee, Wolff, and Scatchard-Rosenthal plots. With perfect
data, all yield identical answers, yet each is affected more by different types of
experimental error. A commonly used method in receptor-ligand interactions is the
Scatchard plot (Figure 7.3), where (7.7) is linearized as

B ⎛ 1 ⎞ B

=− B +

max

⎜ ⎟

L ⎝ K ⎠ K

0 D D

Then the X -axis is specific binding ( B ) and the Y -axis is the ratio of specific bind-
ing divided by free-to-bind ligand concentration ( B / L 0 ). From the plot, K D is the
negative reciprocal of the slope and B max is the X intercept. The Lineweaver-Burk
plot and the Eadie-Hofstee plot are more common enzyme-catalyzed reactions.

EXAMPLE 7.1

A bioengineering group is interested in generating a novel estrogen receptor similar to the
native form of the estrogen receptor-alpha (ER- α ). They successfully construct a mutant
and produce a mutated ER- α . They perform experiments using surface plasmon resonance
biosensors to determine the affinity for the estrogen, and the data is given below. Calculate
K D and determine whether the mutant is as good as the native ER- α or if there is a need
for a new design.

Bound estrogen (nM) 1 0.8 0.6 0.4 0.2 0.05
Free estrogen in the native ER- α mixture (nM) 5.2 1.38 0.67 0.27 0.1 0.025
Free estrogen (nM) in the mutant ER- α mixture (nM) 15.35 4.12 1.8 0.85 0.39 0.08
Solution: Using the given data, calculate the ratio of bound-to-free ligand and plot the
Scatchard plots.