Computational and Modeling Strategies for Cell Motility - Computational Modeling of Biological Systems - page 290

Fig. 6 The profile of the cell conformation at t D 80 contrasted with the initial shape at t D 0:1
for tangential membrane-cortical layer anchoring energy with ˛ 1 D 0:1;˛ 2 D 0

6 Conclusion

We have surveyed recent theoretical and numerical developments that are relevant
to modeling of cell motility. We have integrated many of these advances into
a phase field model of the cell with multiple substructures (the ambient fluid,
bilayer membrane, nematic cortical layer, and internal cytosol) with an activation
potential in the cortical layer that resolves chemical-mechanical transduction. For
this chapter, we have imposed the activation domains, amplitudes, and timescales,
which in the future will be triggered by biochemical processes. The simulated phase
field model exhibits plausible cell morphology dynamics, which are only a cartoon
at this point. To make the model and simulations more biologically relevant, we plan
to use experimental characterizations of the physical properties of the membrane,
cortical layer, cytoplasm, and nucleus, and biochemical kinetics of reacting and
diffusing G protein species which trigger activation and deactivation.

Acknowledgments Wang's research is partly supported by National Science Foundation grants
CMMI-0819051 and DMS-0908330. Yang's research is supported in part by the army re-
search office (ARO) W911NF-09-1-0389. Forest's research is supported in part by grants NSF
DMS-0908423 and DMS-0943851.