Biology Reference
In-Depth Information
physical, discrete vs. continuous, and deterministic vs. stochastic. We
summarized for each of these model classes some of the available numer-
ical simulation methods with pointers to specialized literature. We then
motivated the use of point-based particle methods that do not require
any connectivity-based discretization and allow simulating both discrete
and continuous systems. While their application to discrete systems is
standard, the use of continuum particle methods is less widespread. We
have reviewed continuum particle methods in more detail and demon-
strated their application to diffusion and reaction-diffusion problems.
This was intended as an easy-to-follow introduction. Applications to
other phenomena such as flows and waves are well documented in the
literature.
Notwithstanding the inherent complexity of biological systems, a
wealth of methods and tools are available that enable highly accurate and
predictive spatiotemporal simulations. At the same time, biology can
serve as an important technology driver to stimulate the development of
new methods and further advances in numerical analysis, computational
science, and high-performance computing. Numerical methods that effi-
ciently handle multi-scale systems
27-31
and topological changes in com-
plex geometries are at the forefront of research in computational science.
In parallel, computer algorithms have to be efficient enough to deal with
the vast number of degrees of freedom, and software platforms must be
available to effectively and robustly implement these algorithms on
multi-processor supercomputers.
32
Just as fluid dynamics — in particular,
the nonlinear, multi-scale problem of turbulence — has driven the devel-
opment of numerical methods in the past, the major scientific goal of
modeling an entire cell
138
might continue to do so in the future.
References
1.
Turing AM. (1952) The chemical basis of morphogenesis.
Phil Trans R Soc
Lond B
237
: 37-72.
2.
Marée AFM. (2000)
From Pattern Formation to Morphogenesis
. PhD thesis.
University of Utrecht, Utrecht, The Netherlands.
3.
Harrison LG, Wehner S, Holloway DM. (2001) Complex morphogenesis of
surfaces: theory and experiment on coupling of reaction-diffusion patterning
to growth.
Faraday Discuss
120
: 277-94.
