Model definition The cell model
Your goal is to make a model of a crawling cell that migrates on a flat substrate via random motility and under the influence of a chemotactic signal, or chemoattractant. The cell is inclined to move from a lower to a higher concentration of chemoattract-ants, or signaling molecule. To account for the probability effects involved in cell locomotion, you will build randomness into the speed and direction calculations for your cell. Therefore as your cell crawls up the chemoattractant gradient, it won't necessarily do so in a straight line.
Like a living cell beginning its migration on a coverslip, your cell will start off as a 10 |im spheroid that has been flattened around the edges. You could call it a lymphocyte, but it could just as easily be another type of motile cell that crawls using the three-stage mechanism shown in Figure 16.03. For simplicity, the cell will produce a single pseudopod at the start of each locomotion cycle and retract a single one at end of the cycle. We will introduce the technique shortly for setting up your cell to deform. This will be the key Maya technique you' ll learn and apply in this chapter. Below is a list of parameters you'll build into the model:
- Leading pseudopod protrusion rate.
- Traction (cell center translocation) rate.
- Trailing pseudopod retraction rate.
- Wait time—the time spent sitting still between crawl cycles.
From these four parameters, a fifth will emerge:
5. Linear migration speed of the whole cell.
Without adhering to the substrate, a cell cannot generate the traction required to move. We can represent cell-substrate adhesions in Maya by fixing the location of different portions of the cell surface—by fixing the joints—at appropriate times during
the crawl cycle. Finally, to make the cell center clearly visible as it moves about the scene, you will couple a smaller sphere—the nucleus—to the cell body.
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