Biomedical Engineering Reference
In-Depth Information
the art. But understanding the transformations of these data into
linear correlations, as well as plots of these transformations, is
necessary for critical reading of papers, on the one hand, and for
testing results of computer programs, on the other.
The main plots used in enzyme kinetics and receptor binding
studies are the Scatchard plot, the Lineweaver-Burk plot, and
the linearization for estimation of the Hill coefficient. This chapter
gives a short survey of these transformations of enzyme kinetics or
receptor binding data.
The interaction of reversibly binding ligand L (enzyme sub-
strate) with its receptor R (enzyme) follows the law of mass action:
[
] · [
]
k
1
k
2
R
L
=
=
K
D
[
RL
]
with K
D
, dissociation constant; [R], concentration of receptor; [L],
concentration of ligand; and [RL], concentration of the receptor-
ligand complex.
If a distinct amount of receptor is incubated with its ligand,
a part of the ligand will be bound to the receptor in a proportion
given by the equilibrium ratio. The concentration of the bound
portion B of the total ligand concentration L is equal to the con-
centration of the receptor-ligand complex:
=
=
[RL]
[B]
[L] − [F]
[F] gives the concentration of free, unbound ligand.
Merging both equations and transformation of the result gives
the Scatchard graph, characterized by plotting [B]/[F] on or-
dinate and 1/K
D
on abscissa. The constant B
max
represents that
concentration of L needed for complete saturation of all binding
sites at the receptor and the maximal number of binding sites,
respectively.
K
D
·
[B] + B
max
[B]
[F]
1
=
An example for binding experiment is given in Protocol 5.3.2.2.
The Hill coefficient n gives an impression of the number of
binding sites for a ligand per single receptor molecule, i.e., if n
=
1,
the receptor has one binding site for the specified ligand. Using
a further transformation, the slope of the straight line is the Hill
coefficient:
lg
[B]
B
max
=
n
·
lg[F] − lgK
D
The association constant k
1
is calculated either by use of the inde-
pendent determined maximal number of binding sites B
max
(v
max
in enzyme kinetics) from the equation
