  During development, spatio-temporal patterns ranging from checkerboard to
engulfing occur with precise proportions of the respective cell fates. Key
developmental regulators are intracellular transcriptional interactions and
intercellular signaling. We present an analytically tractable mathematical
model based on signaling that reliably generates different cell type patterns
with specified proportions. Employing statistical mechanics, We derived a cell
fate decision model for two cell types. A detailed steady state analysis on the
resulting dynamical system yielded necessary conditions to generate spatially
heterogeneous patterns. This allows the cell type proportions to be controlled
by a single model parameter. Cell-cell communication is realized by local and
global signaling mechanisms. These result in different cell type patterns. A
nearest neighbor signal yields checkerboard patterns. Increasing the signal
dispersion, cell fate clusters and an engulfing pattern can be generated.
Altogether, the presented model allows to reliably generate heterogeneous cell
type patterns of different kinds as well as desired proportions.
