Biology Reference
In-Depth Information
epidemic spread of a disease. In all of these examples, and many others,
the spatial distributions of some quantities play an essential role. Models
and simulations of such systems should thus account for and resolve these
distributions. When determining the location of an epileptic site in the
brain, it is, for instance, of little value to know the total electric current
density in the whole brain — we need to know precisely where the source
is. These examples extend across all scales of biological systems, from the
above-mentioned predator-prey interactions in ecosystems over mor-
phogenesis
1-5
and intracellular processes to single molecules. Think,
for example, of conformational changes in proteins. Examples at
the intracellular level include virus entry
6,7
and transport,
8-10
intracellular
signaling,
11,12
the diffusion of proteins in the various cellular compart-
ments,
13-15
or the fact that such compartments exist in the first place.
Spatial organization is important, as the same protein can have dif-
ferent effects depending on the intracellular compartment in which it is
located. The most prominent example is probably cytochrome C, which
is an essential part of the cell respiration chain in the mitochondria, but
triggers programmed cell death (apoptosis) when released into the cyto-
plasm.
16
Another example is found in the role of transmembrane signal-
ing during morphogenesis. Differences in protein diffusion constants are
not large enough to produce Turing patterns,
1
and the slow transport
across intercompartment membranes is essential.
17
Examples of spatiotem-
poral processes at the multi-cellular level include tumor growth
18-20
and
cell-cell signaling,
21
including phenomena such as bacterial quorum sens-
ing, the microscopic mechanism underlying the macroscopic phenome-
non of bioluminescence in certain squid.
22
Given the widespread importance of spatiotemporal processes, it is
not surprising that a number of large software projects for spatiotempo-
ral simulations in biology have been initiated. Examples in computational
cell biology
23,24
include E-Cell, MCell, and the Virtual Cell.
2. Properties of Biological Systems
Simulating spatially resolved processes in biological systems, such as
geographically structured populations, multicellular organs, or cell
organelles, provides a unique set of challenges to any mathematical
