pattern formation in interacting cell systems
with cellular automata
Technische Universitaet Dresden, Germany
of interacting cell systems are life cycles of bacteria or social amoebae,
embryonic tissue formation, wound healing or tumour growth and metastasis.
Mathematical models of spatio-temporal pattern formation can offer insight
into the principles of cooperativity in interacting cell systems which can
not be explained at the single cell level.
Typical modelling attempts focus on a macroscopic perspective, i.e. the models
describe the spatio-temporal dynamics of cell concentrations. A modelling
alternative are cell-based models in which the fate of each individual cell
can be tracked. Cellular automata are discrete dynamical systems and can be
used as cell-based models. Here, we analyze pattern formation in cellular
automaton models of actively moving and interacting discrete cells. Model
applications are in particular bacterial pattern formation and avascular tumour
Chick Limb Development
Indiana University, USA
Mark Alber, George Hentschel, Stuart Newman, Gabor Forgacs and Jesus Izaguirre
discuss a variety of approaches to modelling early stage development of mesenchymal
condensation and chondrogenesis in the chick limb. Methods to be discussed
incluse classical reaction diffusion modelling, cellular automaton modeling
and the Extended (or Cellular) Potts Model.
models of growth and reproduction for individual
University of California, Santa Barbara, USA
Masami Fujiwara and Bruce E Kendal
important feature of individual-based population models is the ability to
take account of variability in the growth, reproduction and survival probability
of individual organisms. Formulating stochastic models of organismal growth
involves confronting the issue that for many animals, length increases monotonically,
while weight may increase or decrease in response to changes in energy acquisition
from food and expenditure for growth maintenance and reproduction. Modelling
this situation requires dynamic energy budget (DEB) models that have explicit
representation of energy reserves.
We review the predictions for growth, reproduction and survival, from DEB
models with forcing functions that represent fluctuating food environments.
For the DEB model of S.A.L.M. Kooijman, environmental stochasticity typically
leads to enhanced growth and reduced reproduction. We present analytic approximations
that capture many of the essential features of this variability in individual
performance. These approximations can guide the formulation of statistical
models that will be used to model fish growth in stressed environments. We
speculate on the implications of our findings for the population size distributions
of fish in California coastal wetlands.