Biology Reference
In-Depth Information
multi-stable behavior that enables adaptation to external changes and
disturbances.
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Taking all of these effects into account presents a grand
challenge to simulation models not only because many of the hypotheti-
cal regulatory mechanisms are still unknown or poorly characterized.
2.3. Geometric Complexity
Biological systems are mostly characterized by irregular and often mov-
ing or deforming geometries. Processes on curved surfaces may be cou-
pled to processes in enclosed spaces; and surfaces frequently change their
topology, such as in fusion or fission of intracellular compartments.
Examples of such complex geometries are found on all length scales and
include the prefractal structures of taxonomic and phylogenetic trees,
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regions of stable population growth in ecosystems,
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pneumonal and
arterial trees,
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the shapes of neurons,
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the cytoplasmic space,
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clusters
of intracellular vesicles,
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electric currents through ion channels in cell
membranes,
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protein chain conformations,
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and protein structures.
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Complex geometries are not only difficult to resolve and represent in the
computer, but the boundary conditions imposed by them on dynamic
spatiotemporal processes may also qualitatively alter the macroscopically
observed dynamics. Diffusion in complex-shaped compartments such as
the endoplasmic reticulum (ER; Fig. 1) may appear anomalous, even if
the underlying molecular diffusion is normal.
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2.4. Nonlinearity
Common biological phenomena such as interference, cooperation, and
competition lead to nonlinear dynamic behavior. Many processes, from
repressor interactions in gene networks over predator-prey interactions
in ecosystems to calcium waves in cells, are not appropriately described
by linear systems theory as predominantly used and taught in physics and
engineering. Depending on the number of degrees of freedom, nonlin-
ear systems exhibit phenomena not observed in linear systems. These
phenomena include bifurcations, nonlinear oscillations, and chaos and
fractals. Nonlinear models are intrinsically hard to solve. Most of them are
impossible to solve analytically; and computer simulations are hampered
