STOCHASTIC AND STATE SPACE MODELS OF CARCINOGENESIS: SOME NEW MODELING APPROACHES - Quantitative Medical Data Analysis Using Mathematical Tools and Statistical Techniques - page 65

Evading apoptosis. (4) Unlimited replicative potential (immortalization).
(5) Sustained angiogenesis, and (6) Tissue invasion and metastasis. The
rst 4 capabilities are required to establish uncontrollable growth of stem
cells (avacular carcinogenesis) whereas the last two are for the development
of cancer spread and metastasis of cancer cells (vascular carcinogenesis).
Each of the above capabilities involves at least one or many genetic and/or
epigenetic changes although in some cases some genetic changes may invoke
more than one capabilities. To understand carcinogenesis, in what follows
we further discuss some important items in carcinogenesis.
2.1. The Multi-Staging and Sequential Nature of
Carcinogenesis
The discussion above and studies in cancer biology 41 also indicate that
for a normal stem cell to develop into a malignant cancer tumor cell, it
must accumulate many gene mutations or genetic changes. Because gene
mutations and genetic changes are rare events and can occur only during cell
division, it is a statistical near-impossibility that all mutation and genetic
changes can occur simultaneously during a single cell division. It follows
that dierent gene mutations or genetic changes must occur in dierent
cell division at dierent times. This also leads to the observation that all
steps in the carcinogenesis process must occur in sequence. Furthermore,
while any genetic changes can take place at any time, only certain sequence
or order of genetic changes can lead to a successful completion of the cascade
of carcinogenesis to generate cancer tumors. For example, in FAP (Familial
Adenomatous Polys) and in most sporadic human colon cancer, the rst
event leading to the cancer phenotype is the mutation or loss of the APC
gene at 5q, followed by loss or inactivation or mutation of the Smad4 gene
in chromosome 18q and p53 in chromosome 17p (see [29, 31, 35, 47, 53,
10, 18]). The mutation or activation of the oncogenes ras and src, and
the mutation or inactivation of the suppressor p53 appear to be relatively
late. In human lung cancer, as reported by Fong and Sekido 20 , Osada and
Takahashi 44 , and Wistuba et al. 67 , the loss of the suppressor genes (i.e.
FHIT and VHL) in 3p through Loss of Heterozygosity (LOH) are the early
event, followed by the loss of the gene p16 INK4 in 9p through LOH, the
loss of p53 in 17p through LOH and the mutation of the oncogene ras.