
Linear systems 57
normalised mode l, α is a quantity proportional to the probability of internal-
isation of unbound rece ptors, β is a quantity proportional to the probability
of interna lisation of captured ligand by receptors be fore dissociatio n of the
ligand from the receptors, and γ repre sents the level o f sensitivity o f the re-
ceptors to the external signals [9]. By assuming that the number of receptors
is much larger than the number of ligands, i.e. dR/dt ≈ 0 (R ≈ R
T
), the
following simplified ligand and ligand–complex kinetics are obtained:
d
dt
∗
C
∗
L
∗
=
−(1 + β) 1
γ −γ
C
∗
L
∗
+
0
1
u (2.51)
where β and γ are given by
β =
k
e
k
off
, γ =
K
a
R
T
N
av
V
c
,