## Mathematical model of the cell division cycle of fission yeast.(English)Zbl 0992.92022

Summary: Much is known about the genes and proteins controlling the cell cycle of fission yeast. Can these molecular components be spun together into a consistent mechanism that accounts for the observed behavior of growth and division in fission yeast cells? To answer this question, we propose a mechanism for the control system, convert it into a set of 14 differential and algebraic equations, study these equations by numerical simulation and bifurcation theory, and compare our results to the physiology of wild-type and mutant cells.
In wild-type cells, progress through the cell cycle $$(\text{G1}\to\text{S}\to\text{G2}\to\text{M})$$ is related to cyclic progression around a hysteresis loop, driven by cell growth and chromosome alignment on the metaphase plate. However, the control system operates much differently in double-mutant cells, wee1, cdc25$$\Delta$$ which are defective in progress through the latter half of the cell cycle (G2 and M phases). These cells exhibit ‘quantized’ cycles (interdivision times clustering around 90, 160, and 230 min). We show that these quantized cycles are associated with a supercritical Hopf bifurcation in the mechanism, when the wee1 and cdc25 genes are disabled.

### MSC:

 92C37 Cell biology 93C95 Application models in control theory 65C20 Probabilistic models, generic numerical methods in probability and statistics
Full Text:

### References:

 [1] A. Murray and T. Hunt,The Cell Cycle(W. H. Freeman, New York, 1993). [2] Kohn, Mol. Biol. Cell 10 pp 2703– (1999) [3] Chen, Mol. Biol. Cell 11 pp 369– (2000) [4] Nurse, Nature (London) 344 pp 503– (1990) [5] Fisher, Semin. Cell Biol. 6 pp 73– (1995) [6] Nasmyth, Trends Genet. 12 pp 405– (1996) [7] Hayles, Cell 78 pp 813– (1994) [8] Fisher, EMBO J. 15 pp 850– (1996) [9] Stern, Trends Genet. 12 pp 345– (1996) [10] Zachariae, Genes Dev. 13 pp 2039– (1999) [11] Yamaguchi, EMBO J. 19 pp 3968– (2000) [12] Blanco, EMBO J. 19 pp 3945– (2000) [13] Novak, Philos. Trans. R. Soc. London, Ser. B 353 pp 2063– (1998) [14] Yamaguchi, Mol. Biol. Cell 8 pp 2475– (1997) [15] Kitamura, Mol. Biol. Cell 9 pp 1065– (1998) [16] Moreno, Nature (London) 367 pp 236– (1994) [17] Correabordes, Cell 83 pp 1001– (1995) [18] Martin-Castellanos, EMBO J. 15 pp 839– (1996) [19] Benito, EMBO J. 17 pp 482– (1998) [20] Martin-Castellanos, Mol. Biol. Cell 11 pp 543– (2000) [21] Russell, Cell 49 pp 559– (1987) [22] Lundgren, Cell 64 pp 1111– (1991) [23] Aligue, J. Biol. Chem. 272 pp 13320– (1997) [24] Millar, Cell 68 pp 407– (1992) · Zbl 0756.30034 [25] Shirayama, EMBO J. 17 pp 1336– (1998) [26] Novak, J. Cell. Sci. 106 pp 1153– (1993) [27] Nasmyth, Science 274 pp 1643– (1996) [28] J. J. Tyson and B. Novak, J. Theor. Biol. (in press). [29] Nurse, Philos. Trans. R. Soc. London, Ser. B 341 pp 449– (1993) [30] Rhind, Curr. Opin. Cell Biol. 10 pp 749– (1998) [31] Kim, Science 279 pp 1045– (1998) [32] Since Wee1 has a backup enzyme (Mik1), the rate of tyrosine-phosphorylation is not zero in wee1- cells; hence, we reduce kwee from 1.3 to 0.3 for the numerical simulations in Fig. 5. [33] Nurse, Nature (London) 256 pp 457– (1975) [34] Sveiczer, J. Cell. Sci. 112 pp 1085– (1999) [35] Millar, EMBO J. 11 pp 4933– (1992) [36] Goldbeter, Proc. Natl. Acad. Sci. U.S.A. 78 pp 6840– (1981) [37] P. A. Fantes, inCell Cycle Clocks, edited by L. N. J. Edmunds (Marcel Dekker, New York, 1984), p. 233. [38] Nurse, Genetics 96 pp 627– (1980) [39] Fantes, Nature (London) 279 pp 428– (1979) [40] Tyson, Proc. Natl. Acad. Sci. U.S.A. 88 pp 7328– (1991) [41] Novak, J. Theor. Biol. 165 pp 101– (1993) [42] Tyson, J. Theor. Biol. 173 pp 283– (1995) [43] Novak, Proc. Natl. Acad. Sci. U.S.A. 94 pp 9147– (1997) [44] Novak, Biophys. Chem. 72 pp 185– (1998) [45] Sveiczer, Proc. Natl. Acad. Sci. U.S.A. 97 pp 7865– (2000)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.