The Transport of Insulin-Like Growth Factor through Cartilage - Porous Media: Applications in Biological Systems and Biotechnology - page 436

11.5.2.1 IGF-I Transport and Interaction with IGFBPs and

Receptors

It is reasonable to assume that IGF-I may bind to IGFBPs, or cell surface
receptors (R1). Binding of IGF-I to receptors forms the IGF-I/R1 complex
(R1I) and initiates an intracellular signaling cascade, ultimately leading to the
production of cartilage ECM constituents (e.g., aggrecan). IGF-I is may be
internalized during this initiation process [27], and a new, unoccupied receptor
is returned to the cell's surface [81]. The reversible reaction involving IGF-I,
receptors and IGFBPs can be described by

IGF-I + IGFBP k +1 Complex (11.66)

←→
k − 1

IGF-I + R1 k +2 R1I k 0

↔ R1

(11.67)

←→
k − 2

Equations (11.66) and (11.67) can be included in the reactive-transport
equations for IGF-I and IGFBPs as follows:

c I + v f c I

dc I
dt

k +1 c I c BP + k − 1 c I − k +2 c I c R 1 + k − 2 c R 1 I

(11.68)

= −∇ • − D I ∇ −

−∇ • v s c I + k +1 c I c BP −

dc I
dt

k − 1 c I = (11.69)

dc BP
dt

k +1 c I c BP + k − 1 c I = − (11.70)

dc R 1
dt

k +2 c I c R 1 +( k − 2 + k 0 ) c R 1 I = − (11.71)

dc R 1 I
dt

= k +2 c I c R 1 − ( k − 2 + k 0 ) c R 1 I (11.72)

where c I , c BP , c I , c R 1 , and c R 1 I are volume-based IGF-I, IGFBP, IGF-
I/IGFBP complex, receptor, and IGF-I/receptor complex concentrations,
respectively. k +1 , k − 1 , k +2 , k − 2 , and k 0 are the respective reaction rate con-
stants.
In unconfined compression, equations (11.68)-(11.72) can be written in
radial coordinate as

∂ 2 c I
∂r 2

+ φ f v r −

∂c I
∂r

φ f ∂c I

∂c I
∂r

+ 1
r

κ ∂p
∂r

φ f D I

∂t −

−k +1 φ f 1 − φ f c I c BP + k − 1 1 − φ f c I − k +2 φ f 1 − φ f c I c R 1

=

+ k − 2 1 φ f c R 1 I

− (11.73)