Biomedical Engineering Reference
In-Depth Information
Figure 7
. Three-Body Problem. The analytical solution to this problem is universally ir-
resolvable (not "integrable"). In this example the mutual interaction between three cell types
(neurocytes, endothelial, and myocytes) cannot be predicted/understood in terms of reduced
sets of interactions, further confounded by the "surrounding" environment (mechano- and
chemomodulation). This form of autopoiesis suggests a mutual coevolution in function. The
joint interaction is figuratively localized at the intersection of the virtual dynamic "orbits"
(arrows). This is a well-known problem of celestial mechanics that remains unsolvable unless
the interaction is confined to a single plane.
As regards the relations among levels in the vast hierarchy-heterarchy of
living order, researchers have expressed interest in simulating biological sys-
tems, i.e., bottom-up, commencing with single genes and protein molecules, or
top-down, starting with large-scale physiological behavior (devoid of gene and
protein-protein interactions). Notable modelers (see chapter 3.2 by Winslow,
Part III, this volume) advocate a compromise, working in both directions from
the middle (middle-out approach) because of the two levels of data-rich simula-
tion available using this approach (15). A limitation of mathematical and New-
tonian paradigms implies that living systems are in fact state-determined, i.e.,
explicit values can be specified that relate state variables to rates at all levels of
organization.
