Cell-based, mathematical models help
make sense of morphogenesis—i.e. cells organizing into
shape and pattern—by capturing cell behavior in simple, purely
descriptive models. Cell-based models then predict the
tissue-level patterns the cells produce collectively. The first
step in a cell-based modeling approach is to isolate
sub-processes, e.g. the patterning capabilities of one or a
few cell types in cell cultures. Cell-based models can then
identify the mechanisms responsible for patterning in vitro.
This review discusses two cell culture models of morphogenesis
that have been studied using this combined
experimental-mathematical approach: chondrogenesis (cartilage
patterning) and vasculogenesis (de novo blood vessel growth). In
both these systems, radically different models can equally
plausibly explain the in vitro patterns. Quantitative
descriptions of cell behavior would help choose between
alternative models. We will briefly review the experimental
methodology (microfluidics technology and traction force
microscopy) used to measure responses of individual cells to their
micro-environment, including chemical gradients, physical forces
and neighboring cells. We conclude by discussing how to include
quantitative cell descriptions into a cell-based model: the
Cellular Potts model.