Biomedical Engineering Reference
In-Depth Information
(see Figure 2) (6,15,42). By taking the square root of the number of elements in
a network, one can approximate the number of attractors. Therefore, Boolean
networks obey a power law. Kauffman used these networks to show how the
size of an organism's genome is related to the number of cell types it generates
(42). For example, a sponge has approximately 10,000 genes and about 12 cell
types. Humans have about 30,000 to 40,000 genes and over 250 cell types. A
Boolean network with 100,000 elements, with each element linked to two oth-
ers, has the potential of 10
30,000
states. In fact, only 370 states are realized. Each
of these states is an attractor; likewise, each cell type in a human body is a state-
cycle attractor of the genome. A state-cycle attractor is defined by certain
boundary conditions. In the cell, it has been proposed that these boundary condi-
tions are defined by the ribonucleic acid (RNA)-protein complex termed the
nuclear matrix (15,43). The nuclear matrix, therefore, may define the boundary
conditions of a cell. Perturbation of a steady-state attractor through mutation
may upset the genetic stability and cause the cell to enter the carcinogenic cas-
cade (a new state,
E
). This state
E
is fundamentally unstable and results in a new
set of attractors, i.e., cell types. These cell types are manifested as tumor cell
heterogeneity. Cancer, then, is the result of multiple perturbations (i.e., muta-
tions) to a cell that result in a redefinition, or perhaps even loss, of its boundary
conditions. For a further discussion of modeling tumors as complex biosystems,
see chapter 6.3, by Mansury and Deisboeck (Part III, this volume).
