Biomedical Engineering Reference
In-Depth Information
1
ln
B
max
·
(L
T
−B)
=
k
1
(L
T
−B
max
)
·
t
·
L
T
·
(B
max
−B)
or, if the dissociation constant k
2
is known, from the plot of the
functions
B
e
B
e
−B
=
ln
k
obs
·
t
and
=
k
.
1
L
T
k
obs
−k
2
B
e
: concentration of the bound ligand at equilibrium; B
0
:concentra-
tion of the specifically bound ligand at time t
=
0; B: concentration
of the specifically bound ligand at time t; L
T
: total ligand concen-
tration; k
obs
: experimentally determined rate constant; t: time
The dissociation constant k
2
is determined by off-kinetics ex-
periments. It is the slope of the function
B
B
0
=
ln
k
2
·
t
The dose-dependent saturation of a constant amount of receptor is
described by sigmoid or hyperbolic curve shape. If the measuring
signal is plotted against ligand concentration, the curves show
a minimal signal (blank, lower plateau) and an upper plateau (B
max
).
The equation for the hyperbola is
B
max
x
K
D
+x
=
·
B
max
[L
total
]
K
D
+[L
total
]
·
=
=
y
[bound]-[blank]
or in the case of two binding sites with different binding characteris-
tics (different dissociation constants K
D
and Michaelis-Menten
constant K
M
, respectively)
B
max1
·
x
K
D1
+x
B
max2
·
x
K
D2
+x
=
y
+
In these equations the abscissa value y represents the concentration
of bound ligand, whereas x is the total concentration of ligand.
A sigmoid shape is described by the equation
B
max
−blank
1+10
(lg(EC
50
)−x)
·
n
=
y
blank +
EC
50
: concentration halfway between blank and B
max
;n:Hillcoef-
ficient; x: logarithm of ligand concentration and substrate concen-
tration; y: amount of bound ligand: (“bound”-“blank”)
