# Mathematical Prediction Of On-off Switches In Cell Division Proven

A team of Virginia Tech researchers has experimentally verified the predictions of a mathematical model concerning the regulation of irreversible transitions into and out of mitosis (the division of genetic material during the cell cycle). The commitment to mitosis must be an all-or-nothing decision; otherwise deleterious mutations result. This research highlights the power of pairing experimental and computational biology to understanding complex processes. Mathematical modeling of the cell cycle and other biological events may someday lead to previously unidentified targets for therapy of cancer and other diseases.

The article, "Hysteresis drives cell-cycle transitions in Xenopus Laevis egg extracts," will be published in the Proceedings of the National Academy of Sciences online edition the week of Dec. 30,2002 through Jan. 3, 2003 (article #02-5349 at www.pnas.org). It is the first collaborative publication between Virginia Tech biologists Jill Sible and John Tyson. Sible is corresponding author.

Tyson, a university distinguished professor, has been developing mathematical models to describe the cell cycle for many years, but only recently have experimentalists collaborated to test the validity of these models. His comprehensive model describing DNA synthesis and nuclear division in cell-free extracts from frog eggs was published in 1993.

In this project, the researchers set out to test predictions made by the mathematical model regarding specific levels of the protein cyclin required to regulate cell division, or mitosis. The experimental challenges were quantitative. "We had to be very precise," says Sible. "We found that, qualitatively and quantitatively, we were able to validate three key predictions of the model regarding the amount of cyclin required to start, maintain, and stop mitosis."

Cells enter mitosis by activating the enzyme Cdc2 and leave mitosis when Cdc2 activity drops. Cdc2 is activated by accumulation of its partner, cyclin, and inactivated when cyclin is destroyed.

What ensures that Cdc2 is irreversibly turned ON or OFF at mitotic entry and exit, respectively? Does the switch function like a buzzer or a toggle?

"A buzzer is ON when one pushes hard enough on its button and stops buzzing when one lets go. A toggle likewise switches on when one pushes hard enough on the lever in one direction, but it will stay on when one lets go," says Tyson. "To switch a toggle off, one must push the lever with sufficient force in the opposite direction. Engineers call this sort of behavior hysteresis."

By manipulating the concentration of cyclin in cytoplasmic extracts prepared from frog eggs, the Virginia Tech investigators pushed the "button" for Cdc2 to see how the switch responded. To turn Cdc2 ON and trigger entry into mitosis required a push of at least 40 units of cyclin. When they let up on the pressure (by letting cyclin concentration drop to 30 or even 20 units of cyclin), the switch stayed ON, that is, Cdc2 remained active and mitosis persisted. To turn the switch OFF (inactivate Cdc2 and exit mitosis), required cyclin levels to drop to 16 units or less. These experiments demonstrated that the control system is bi-stable and hysteretic.

What regulates these irreversible switches has been a big question, Sible explains. "Others have published mathematical models of the cell cycle that function without hysteresis. It was not until we put our model to the test that we could determine that hysteresis is the basis of the switches that start and stop mitosis."

These experiments were performed in cell-free extracts derived from frog eggs. The frog egg extract system is the most simple eukaryotic cell cycle system but is representative of cell cycles in other organisms including humans. "We know from many years of research, including that resulting in the 2001 Nobel Prize in Physiology or Medicine, (awarded to Leland H. Hartwell, R. Timothy Hunt, and Paul M. Nurse for their discoveries of key regulators of the cell cycle), that cell cycle components are similar in frog and human cells," says Sible.

The researchers' ultimate goal is to build a mathematical model of the human cell cycle that would likewise reveal underlying principles of cell regulation and be predictive. "Many predictions in the model we tested were not intuitive. The belief is that a comprehensive mathematical model of the human cell cycle would present a new understanding of its regulation and suggest novel ways to control disorders such as cancer," says Sible." For example, cell cycle 'checkpoints' guard dividing cells from mistakes that may lead to cancer. Sible continues, "We saw something relevant but subtle in our simple system. If we raised the cyclin level modestly (beyond what was needed to trigger mitosis), we eliminated the checkpoint that normally halts the cell cycle if there is something wrong with the DNA."

Co-authors of the PNAS article are Wei Sha, who completed her master's degree with Sible and is now a Ph.D. student at the Virginia Bioinformatics Institute at Virginia Tech; Jonathan Moore of the Cancer Research United Kingdom London Research Institute; Katherine Chen, a senior research scientist at Virginia Tech; Antonio Lassaletta, an undergraduate student in mechanical engineering who is studying with Sible; and Chung-Seon Yi, a postdoctoral associate with Tyson.

Source: Virginia Tech. January 2003.

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