A three dimensional model of cell movement in multicellular systems
Eiriker Palsson

ABSTRACT
A mathematical model for cell movement in multicellular systems has
been developed that allows us to simulate and visualize, in three
dimensions, individual cell movements in a number of multicellular
systems. These include cell movement during, aggregation and slug
stage, of {\it Dictyostelium discoideum}, embryogenesis, limb
formation and wound healing.  The building blocks of the model are
individual cells, and each cell has certain given properties. The
basic properties are that a cell deforms under force (either stretch
or compress), while conserving its volume, it adheres to other cells
and it can generate an active motive force. The response of a cell
depends on its internal parameter state, and on the information it
receives from its external environment, which includes neighbor cells,
the extracellular matrix and chemical signals.  The movement and
deformation of each cell is then determined by summing up all the
forces that a cell experiences from its surroundings, and using that
force in the equations of motion.

Here I introduce this model and and show examples of its applications and
compare the results with experimental data. Among the simulations I show,
is how different cell types can sort out based solely on differences in
adhesion. The results are compared to cell sorting experiments done by
Steinberg et.al [1,2] on within the range of the experimental values. I
also present results from simulations of {\it Dictyostelium} movements. 
First I show simulations of the aggregation stage, where cells are
aggregating chemotactically, towards a signaling center, in response to
cAMP waves. In these simulations one can observe stream formation and how
the mound arises due to the inward motion of the cells towards the
signaling center. I will also present simulations of 2-D slugs, where
where I studied the affect cell adhesion and cell chemotaxis have on the
soring of Prespore and Prestalk cells in the slug. These findings will be
compared to observations of 2-D slugs done by Bonner[3]. 

[1] M. S. Steinberg, Reconstruction of tissues by dissociated cells,
Science, 141:401-408, 1963.

[2] R. Foty {\it et al} Surface tension of embryonic tissues predict
their mutual envelopment, Development, 122:1611-1620, 1996.

[3] J. Bonner, A Way of following individual cells in the migrating slugs 
of {\it Dictyostelium discoideum}, PNAS, Vol. 95, pp. 9355-9359, 1998