Biology Reference
In-Depth Information
method. One often hears that this is because biological systems are
“complex”.
Biochemical networks, ecosystems, biological waves, heart cell syn-
chronization, and life in general are located in the high-dimensional,
nonlinear regime of the map of dynamical systems,
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together with quan-
tum field theory, nonlinear optics, and turbulent flows. None of these
topics are completely explored. They are at the limit of our current
understanding and will remain challenging for many years to come. Why
is this so, and what do we mean by “complex”?
Biological systems exhibit a number of characteristics that render them
difficult. These properties frequently include one or several of the following:
•
high-dimensional (or infinite-dimensional in the continuum limit);
•
regulated;
•
delineated by complex shapes;
•
nonlinear;
•
coupled across scales and subsystems;
•
plastic over time (time-varying dynamics); and/or
•
nonequilibrium.
Due to these properties, biological systems challenge existing meth-
ods in modeling and simulation. They are thus particularly well suited to
drive the development of new methods and theories. The challenges pre-
sented by spatiotemporal biological systems have to be addressed on sev-
eral fronts simultaneously: numerical simulation methods, computational
algorithms, and software engineering.
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Numerical methods are needed
that can deal with multi-scale systems
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and topological changes in
complex geometries. Computer algorithms have to be efficient enough
to deal with the vast number of degrees of freedom, and software plat-
forms must be available to effectively and robustly implement these
algorithms on multiprocessor computers.
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2.1. Dimensionality and Degrees of Freedom
The large number of dimensions (degrees of freedom) is due to the fact that
biological systems typically contain more compartments, components, and
