Biomedical Engineering Reference
In-Depth Information
lifetime of the very same tumor, making it more difficult to rank the
fitness
of
the tumor system itself. Another parameter that we chose to examine in (6) is the
rate of
nutrient depletion r
G
(see Eq. [6]), because the metabolic uptake of tumor
cells is an important parameter of interest from the experimental standpoint. We
found that
self-organizing
behavior emerges as we simultaneously vary both
r
S
and the rate of nutrient depletion,
r
G
. Specifically, we show that at slower me-
tabolism rates,
r
G
<
r
G
*, raising
r
S
(i.e., encouraging more local search) results in
self-organization of tumor cells into increasingly smaller clusters. The formation
of smaller cluster sizes, however, disappears as
r
G
is increased even further. That
is, when nutrients are rapidly depleting due to the high metabolism rates
r
G
>
r
G
*, tumor cells reorganize into clusters that are insensitive to variations in
r
S
.
Perhaps most interestingly, it turns out that this self-organization behavior at a
high cellular metabolism rate leads to improved performance of the entire tumor
system by way of both accelerating its average velocity and also longer lifetime.
Although a faster average velocity is to be expected since tumor cells are
"forced" to migrate as nutrient levels experience a rapid depletion, from a bio-
logical perspective it is intriguing that such aggressive virtual tumor cells actu-
ally survive longer under these rather adverse microenvironmental conditions.
6.2. Search Precision
In (7), we vary the search precision parameter,
4
[0,1], to study the im-
pact of cellular signal sensitivity on the performance of the tumor system. As
defined in Eq. [9], higher
4
represents the proportion of time in which tumor
cells correctly assess the attractiveness of a location. We found that, unexpect-
edly, the maximum average velocity of the tumor systems always occurs at
less
than 100% search precision. At the outset, one would expect that a strictly non-
random search procedure (with
4
= 1) should optimize the average velocity of
the tumor system. In fact, we found that, although initially it is true that decreas-
ing randomness results in increasing average velocity, there is a threshold level
beyond which the velocity starts to decline if randomness is reduced further.
Such a
phase transition
corresponding to a 70% search precision (i.e., 30%
chance of committing an error in signal reception or processing) actually ele-
vates average velocity to its maximum, and hence yields optimal performance of
the tumor. We also experimented with varying both the extent of search preci-
sion
4
and
k
prolif
, the parameter controlling the probability to proliferate (see Eq.
[1]). Recall that higher values of
k
prolif
implies lower proliferation rates as it ren-
ders tumor cells less likely to produce offsprings. As expected, spatial velocity
increases even more at higher values of
k
prolif
due to the dichotomy assumption
between proliferation and invasion as supported experimentally (11). What is
not expected is that increasing
k
prolif
is also accompanied by a shift toward higher
search precision in order to reach maximum velocity; this is an
emergent
behav-
