Compute-Intensive Simulations for Cellular Models - Parallel Computing for Bioinformatics and Computational Biology - page 111

Figure 4.7 A colony of 2048 cells with three cell types. The shade of a cell represents its age,
darker being older.
The matrix is sparse because each cell has relatively few neighbors, but it is not
blocked as cell contacts do not naturally fall into cliques. The system of equations is
readily solved using standard techniques such as Gaussian elimination or conjugate
gradients.
This approach is readily extended to three dimensions. In [65], colonies of dividing
cells in three dimensions were modeled using the above approach, and colonies of
up to 2 16 cells could be run on a desktop machine (see Fig. 4.7). Tests on dividing
colonies of cells found that the conjugate gradients method converged within a few
iterations. Iterating over time then shows the system evolving with cells jostling for
position as they overlap. Hatherley [66] has also used this model with the inclusion
of several cell types in an attempt to understand the positioning of cell types in a
neurosphere.
4.7.2 Extending the Physical Model
There are a variety of ways that the modeling of physical forces may be extended to
give a more realistic model of the development of a colony of cells. These include
modeling different cell types; modeling the cell cycle of growth, division, and death;
chemical signaling between cells; bonding between cells; bonding to the substrate;
ion concentrations on the substrate; and motility of cells. Understanding and mod-
eling each of these processes is a substantial challenge often involving incomplete
information and guesswork, and any number of approaches may be taken.
Cell division in multicellular organisms is controlled by a complex array of signals,
growth factors, and regulatory networks. The cell cycle in eukaryotes is in four phases
[67]. The quiescent phase stage in animal cells may last for years, then in response
to external growth factors and signals, the cell enters the G1 phase. In this phase, if
sufficient stimulation occurs, the cell reaches a point where it is no longer dependent