Math helps biologists find size of clot-forming cells

Using computational modeling, UC Davis mathematicians have developed a mathematical design for figuring out why platelets, the cells that form blood clots, are the size and shape that they are. Platelets are important for healing wounds, but having too many can cause strokes and other conditions.

Greater knowledge of how they form and behave could have wide implications. According to study co-author Alex Mogilner, UC Davis professor of mathematics and of neurobiology, physiology and behavior, an understanding of platelet behavior could be important for medicine.

“There has to be a certain number of them [platelets], and they have to be 2-3 microns in diameter for humans,” Mogilner said. “There is a number of disorders associated with either too many platelets, resulting in life-threatening thrombi [blood clots] or too few platelets, resulting in equally dangerous excessive bleeding.”

In addition to holding implications for physiology and medicine, this study is important for modeling the physical forces inside of cells.

Mogilner, along with UC Davis postdoctoral scholars Jie Zhu and Kun-Chun Lee, developed a mathematical model of the forces inside the cells that turn into platelets in order to predict their final size and shape.

“We find that smaller cells always have to overcome a higher force in the hooping filaments [surrounding the cells] to start the deformation,” Zhu said. “Therefore, the size of final platelets could be determined by the barrier force in the filaments — cells will stop dividing if the barrier is too high.”

The balance of the forces within these cells could provide insight into their form, which dictates their function.

“One of the fundamental questions of cell biology is: what determines size and shape of cells?” Mogilner said. “There is a number of mechanisms [within cells], including the [mechanical] force-balance, which we confirmed for platelets.”

Zhu likens the bending elastic filaments in these cells to the experience of drinking out of a water bottle.

“These interesting findings reminded us of a scene that most people probably have experienced when drinking bottled water: If you try to suck the water out without letting air flow in the bottle, the plastic wall of the bottle will collapse inward, often forming a barbell-shaped cross-section,” Zhu said.

This barbell shape is important in understanding platelets, as it is the shape these cells take in an intermediate stage, as discovered by Mogilner’s collaborators, the Joseph Italiano team at Harvard Medical School. While Mogilner and his colleagues took a computational approach, the Harvard team took an experimental one.

The Harvard team found that the pre-platelet cell transitioned from a circular to the barbell shape before splitting into two daughter cells.

“In coming up with a mathematical model, it is always nice to have some experimental data,” Lee said. “It is like watching a baseball being thrown across a baseball park making an arc; it makes sense because it fits our physical intuition and experience.”

RACHEL KUBICA can be reached at science@theaggie.org.