Biology Reference
In-Depth Information
Fig. 10.
(a) Evolution of the total mass of
a
and
b
(solid lines) for
M
= 10 mole-
cules per unit mass. See text for problem description. The location of the wave front
is shown by the dashed curve. The reaction front moves into the region of
b
until all
of
b
is consumed. (b) Dependence of the front speed
s
on the reaction parameter
c
.
In dimensionless representation, the two curves for
D
= 0.1 (open circles) and
D
= 1.0 (filled triangles) collapse to one. The theoretical scaling
136,137
is indicated by
the dashed line.
important tools in modern biology. “Virtual experiments”
in silico
enable
control over all variables and influence factors, allowing us to dissect bio-
logical systems, formulate physical models for their constituents, and dis-
entangle coupled processes that are not separable in classical experiments.
Moreover, spatiotemporal modeling makes accessible time and length
scales unreachable by experiments. This allows studying systems as small
as the atoms in an individual protein or as large as complete ecosystems.
The characteristic properties of biological systems frequently compli-
cate the formulation and simulation of spatiotemporal models.
Regulation mechanisms, geometric shape complexity, nonlinearity, and
couplings across scales increase model complexity, and require powerful
and flexible numerical methods as well as efficient high-performance
software implementations on supercomputers.
26,32
We have surveyed some of the most common modeling techniques
and categorized them along the dimensions of phenomenological vs.
