Biomedical Engineering Reference
In-Depth Information
corresponds to the "breakpoint" in the gene expression profile of Tenascin C and
PCNA. At t = 335, a "bulging" structure at the NE tip starts to emerge, pointing
toward the peak of the second nutrient source. Finally, the bulge becomes a
prominent structural feature of the NE quadrant at t = 371, just before the first
tumor cell successfully invades the peak of the second nutrient source. At the
molecular level, we found that this emergence of a structural asymmetry in the
rim of the growing tumor is accompanied by a positive correlation between tu-
mor diameter and the gene expression of Tenascin C, and at the same time a
negative one between the former and PCNA expression. To determine the domi-
nant phenotype responsible for this micro-macro link, we next examine the gene
expression profiles separately for proliferating, migrating, and quiescent cells.
We found that Tenascin C expression is always higher among the migratory
phenotype than among their proliferating peers, while the converse is true for
the expression of PCNA, i.e., it is always upregulated among the proliferative
cells. Intriguingly, detrended fluctuation analysis (DFA) analyses indicate that
the time series of gene expression of the combined tumor cells (i.e., including all
phenotypes), the long-range autocorrelation indicates non-random-walk predict-
ability as represented by B = 1.32 for gTenascin and B = 1.06 for gPCNA . How-
ever, when DFA is applied separately to migrating and to proliferating cells, the
resulting values of B reveal the time-series properties of random walk behavior
(i.e., with B = 0.5).
DISCUSSION , CONCLUSIONS , AND FUTURE WORK
7.
The underlying hypothesis of our work is that malignant tumors behave as
complex dynamic self-organizing and adaptive biosystems . In this chapter, we
have presented a numerical agent-based model of malignant brain tumor cells in
which both time and space are discrete yet environmental variables are treated
realistically as continuous. Simulations of this model allow us to infer the statis-
tical properties of the model and to establish the cause-effect relationships that
emerge from various interactions among and between the cells and their envi-
ronments. The key findings of our works can be briefly summarized as follows.
In (6), we showed the nonlinear dynamical behavior of a virtual tumor sys-
tem in the form of phase transitions and self-organization . The phase transitions
indicate that if global search is dominant, then lowering r S (i.e., higher mobility)
can actually result in slower overall velocity of the tumor system, while self-
organization in the form of smaller clusters can contribute to a longer lifetime of
the tumor system. Subsequently, in (7), we demonstrated that tumor systems can
achieve maximum velocity at less than 100% search precision. This finding
challenges the conventional wisdom that an error-free search procedure would
maximize the velocity of a tumor system dependent on receptor-based mobility.
In a follow-up paper examining the structure-function relationship, (8) used
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