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Encyclopedia of Physical Science and Technology EN016J-783 August 1, 2001 10:58

826 Tissue Engineering

FIGURE 6 Simplified model for the binding and fate of a ligand (growth factor) binding to its receptor on the cell
surface. After binding, the ligand–receptor complexes are internalized into an endosomal compartment. Its contents
can then be recycled to the cell surface or fuse with a lysosome and undergo degradation. The k parameters shown
represent first-order rate constants for each process shown.

intracellular changes occur in the time scale of seconds to nalization is to immobilize the growth factor to the surface
minutes, and a steady state is reached within one hour. In of the substrate to which the cells are attached. This has
many cases, it can be assumed that the cellular response is been shown to work in the case of EGF and fibroblasts;
proportional to the total number of receptor-bound growth however, in other systems, the activity of the growth factor
factor molecules. Since in most cases growth factor levels may be partially or completely lost. The EGF–EGF recep-
also do not change very quickly in the environment, one tor model can be further refined by taking into account the
can assume a pseudo steady state and obtain the following removal of growth factor from the extracellular medium,
results for the number of EGF–EGF receptor complexes: the effect of receptor clustering, several pathways oper-
ating at different rates, etc. Cells that produce their own
K ss L V s k eC k f

C s = , K ss = growth factors as part of an autocrine loop can also be
1 + K ss L k eC k eR (k rec + k eC ) modeled in a similar fashion by adding appropriate terms
(1) for growth factor release and diffusion around the cells.
Such a model may be useful to predict the effect of cell
k eC
C i = C s (2) density on growth rate as well as other density-dependent
k deg
functions.
(3)
C T = C s + C i A difficult problem which remains in this area is to re-
late, on a theoretical basis, the receptor–ligand binding
C s
R s = (k r + k eC ) (4) phenomena on the cell surface to the observed cellular
k f L
response. The intracellular signaling pathways typically
Using accepted parameter values for this system, one function as a cascade of events leading to the sequential
can notice that the proportion of complexes that are activation of intracellular signaling molecules, often by
intracellular increases with EGF concentration (Fig. 7). phosphorylation of specific amino acid residues on the
Furthermore, the total number of bound receptors in the signaling proteins. One of the final targets of this cas-
cell as well as on the cell surface reaches a maximum cor- cade may be one or several transcription factors, special-
responding to about 25% of the total number of receptors. ized proteins that have the ability to migrate into the cell
The process of receptor-mediated endocytosis thus limits nucleus and trigger the synthesis of new proteins or al-
the number of receptors available for binding at any time, terations in cell behavior, such as cell division. A large
which is a well-known mechanism of downregulation of number of growth factors trigger the mitogen-activated
growth factor responses. Several studies have shown that a protein (MAP) kinase cascade (Fig. 8), and there is evi-
more sensitive response to a particular growth factor may dence that similar cascades exist for other mediators. Ki-
be obtained using modified growth factors or cells with al- netic modeling of each step as a reaction, using param-
tered receptors which reduce the rate of internalization of eters determined through analyses in cellular extracts of
the complexes. Another strategy to reduce the rate of inter- the intracellular concentrations and kinetic properties of