Biology Reference
In-Depth Information
They further postulated that the hierarchical branching networks provided the
following constraints:
1. Networks service all local biologically active regions in both mature and grow-
ing biological systems. Such networks are called space filling.
2. The networks' terminal units are invariant within a class or taxon.
3. Organisms evolve toward an optimal state in which the energy required for
resource distribution is minimized.
It is interesting to note that the concept of networks employed by West and his
coworkers (e.g., animal circulatory systems, plant vascular systems) focuses on the
static spatial and geometric aspect of bionetworks, which may be viewed as
belonging to the class of the equilibrium structures of Prigogine (Sect. 3.1.5 ) .
Since living systems are dynamic and better described in terms of dissipative
structures (Prigogine 1977, 1980, Ji 1985a, b), and since living processes are almost
always mediated by enzymes whose behaviors can be best characterized in terms of
“temporal networks” in contrast to “spatial networks” as pointed out in Sect. 7.2.3 ,
it may be reasonable to formulate an alternative theory of allometric scaling based
on the notion of dissipative network , which are at least 4-dimensional in the sense
that it takes four coordinates to characterize them, namely, x, y, x, and t.
Therefore, a simple explanation for the quarter-power scaling laws may be
derived on the basis of the following assumptions:
1. The body mass (x) of an organism is not a geometric object (i.e., equilibrium
structure ) but a 4-dimensional entity, because it can be viewed as an organized
system of cells and processes catalyzed by enzymes (acting as coincidence
detectors) (see Fig. 7.8 in Sect. 7.2.3 ).
2. The number of cells (n) of an organism can be viewed as the projection of
organisms on to the 3-dimensional Euclidean space (i.e., devoid of the time
dimension).
3. The metabolic rate (y) of an organism is directly proportional to the number of cells
constituting that organism (whose Euclidean volume is v), the proportionality
constant increasing with both body temperature (T) and cell density, d ¼ n/v,
defined as the number of cells per unit body volume. (For simplicity, it will be
assumed that the mitochondrial contents, or better the average respiratory
activities, of cells are invariant among individual organisms and across species.)
Based on Assumptions (1) and (2), we can write:
x 3 = 4
ax 3 = 4
n
)
n
¼
(15.10)
Based on Assumption (3), we can write:
y
n
(15.11)
Combining Eqs. (15.10) and (15.11) leads to:
a i x i 3 = 4
y i ¼
(15.12)
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