Parameters Identification of Mathematical Model of the Fission Yeast Cell Cycle Control Using Evolutionary Strategy

Authors: A. Ghaffari, A. S. Mostafavi

Abstract:

Complex assemblies of interacting proteins carry out most of the interesting jobs in a cell, such as metabolism, DNA synthesis, mitosis and cell division. These physiological properties play out as a subtle molecular dance, choreographed by underlying regulatory networks that control the activities of cyclin-dependent kinases (CDK). The network can be modeled by a set of nonlinear differential equations and its behavior predicted by numerical simulation. In this paper, an innovative approach has been proposed that uses genetic algorithms to mine a set of behavior data output by a biological system in order to determine the kinetic parameters of the system. In our approach, the machine learning method is integrated with the framework of existent biological information in a wiring diagram so that its findings are expressed in a form of system dynamic behavior. By numerical simulations it has been illustrated that the model is consistent with experiments and successfully shown that such application of genetic algorithms will highly improve the performance of mathematical model of the cell division cycle to simulate such a complicated bio-system.

Keywords: Cell cycle, Cyclin-dependent kinase, Fission yeast, Genetic algorithms, Mathematical modeling, Wiring diagram

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1078013

References:

[1] Mitchison, J.M. The Biology of the Cell Cycle. Cambridge, United Kingdom : Cambridge University Press, 1971.
[2] Murray, A. and Hunt, T. The Cell Cycle. An introduction. New York : W.H. Freeman & Co., 1993.
[3] Nasmyth, K. At the heart of the budding yeast cell cycle. Trends Genet, 1996, pp. 405-412.
[4] Mendenhall, M.D. and Hodge, A.E. "Regulation of Cdc28 cyclin dependent protein kinase activity during the cell cycle of the yeast Saccharomyces cerevisia," Microbiol. Mol. Biol. Rev., 1998, pp. 1191- 1243.
[5] Nurse, P. "The Josef Steiner Lecture: CDKs and cell-cycle control in fission yeast: relevance to other eukaryotes and cancer," Int. J. Cancer, 1997, pp. 71: 507-508.
[6] Moser, B.A. and Russell, P. "Cell cycle regulation in Schizosaccharomyces pombe," Curr. Opin. Microbiol. 2000, pp. 3: 631- 638.
[7] Aguda, B. D. "A quantitative analysis of the kinetics of the G(2) DNA damage checkpoint system," Proc. Natl. Acad. Sci. USA, 1999, pp. 96: 11352-11357.
[8] Aguda, B. D. and Tang., Y. "The kinetic origins of the restriction point in the mammalian cell cycle," Cell Prolif. 1999, pp. 32: 321-335.
[9] Chen, K. C., A. Csikasz-Nagy, B. Gyorffy, J. Val, B. Novak, and J. J. Tyson. "Kinetic analysis of a molecular model of the budding yeast cell cycle." Mol. Biol. Cell. , 2000, pp. 11: 369-391.
[10] Gardner, T. S., Dolnik, M. and Collins, J. J. "A theory for controlling cell cycle dynamics using a reversibly binding inhibitor," Proc. Natl. Acad. Sci. USA. 1998, pp. 95: 14190-14195.
[11] Goldbeter, A. "A minimal cascade model for the mitotic oscillator involving cyclin and cdc2 kinase." Proc. Natl. Acad. Sci. USA., 1991, pp. 88: 9107-9111.
[12] Hatzimanikatis, V., K. H. Lee, and J. E. Bailey. "A mathematical description of regulation of the G1-S transition of the mammalian cell cycle." Biotech. Bioeng, 1999: pp. 65: 631-637.
[13] Novak, B., and J. J. Tyson. "Modeling the control of DNA replication in fission yeast." Proc. Natl. Acad. Sci. USA, 1997, pp. 94: 9147-9152.
[14] Sveiczer, A., A. Csikasz-Nagy, B. Gyorffy, J.J. Tyson, and B. Novak. "Modelling the fission yeast cell cycle: Quantized cycle times in wee1- cdc25- mutant cells ." Cell Biology, 2000, pp. 7865-7870.
[15] Thron, C. D. "Bistable biochemical switching and the control of the events of the cell cycle." Oncogene, 1997, pp. 15:317-325.
[16] Tyson, J. J. "Cell cycle controls," in Computational Cell Biolog,. C. P. Fall, E. S. Marland, J. M. Wagner, and J. J. Tyson, Eds. New York, Berlin: Springer, 2002, pp. 261-284.
[17] Tyson, J., K. Chen, and B. Novak. "Network dynamics and cell physiology," Macmillan Magazines Ltd, December 2001, pp. 908-916.
[18] Tyson, J. J., and B. Novak. "Regulation of the eukaryotic cell cycle: molecular antagonism, hysteresis, and irreversible transitions." J. Theor. Biol., 2001, pp. 210:249-263.
[19] Obeyesekere, M. N., E. S. Knudsen, J. Y. J. Wang, and S. O. Zimmerman. "A mathematical model of the regulation of the G(1) phase of Rb+/+ and Rb-/- mouse embryonic fibroblasts and an osteosarcoma cell line." Cell Prolif., 1997, pp. 30:171-194.
[20] Qu, Z., J. N. Weiss, and W. R. MacLellan. "Regulation of the mammalian cell cycle: a model of the G1-to-S transition." Am. J. Physiol. Cell Physiol, 2003, pp. 284:C349-C364.
[21] Novak, B., A. Csikasz-Nagy, B. Gyorffy, K. Chen, and J. J. Tyson. "Mathematical model of the fission yeast cell cycle with checkpoint controls at the G1/S, G2/M and metaphase/anaphase transitions." Biophysical Chemistry, 1998, pp. 72: 185-200.
[22] Fisher, D., and P. Nurse. "Cyclins of the fission yeast Schizosaccharomyces pombe." Semin. Cell Biol., 1995, pp. 6(2): 73-78.
[23] Fisher, D., and P. Nurse. "A single fission yeast mitotic cyclin B p34cdc2 kinase promotes both S-phase and mitosis in the absence of G1 cyclins." EMBO J., 1996, pp. 15(4): 850-860.
[24] S. Moreno, J. Hayles, and P. Nurse, Regulation of p34. cdc2. protein kinase during mitosis. Cell, 58, pp. 361-372, 1989.
[25] V. W. Porto, "Evolutionary computation approaches to solving problems in neural computaion", in Handbook of Evolutionary Computation", Back, T., Fogel, D. B., and Michalewicz, Z. (eds). Institute of Physics Publishing and New York: Oxford University Press, pp. D1.2:1-D1.2:6.
[26] X. Yao, "Evolving Artificial Neural Networks", Proceedings of IEEE, 87(9), pp. 1423-1447, Sept. 1999.
[27] K. Balakrishnan, and V. Honavar, "Evolutionary Design of Neural Architectures-A Preliminary Taxonomy and Guide to Literature", Report CS-TR # 95-01, Dept. of Computer Science, Iowa State University, Jan. 1995.
[28] Nurse, P. "Coupling M phase and S phase: controls maintaining the dependence of mitosis on chromosome replication," cell 65, 1991, pp. 921-923.
[29] Nurse, P., and P.A. Fantes. "Cell cycle controls in fission yeast: a genetic analysis ." in The Cell Cycle, by P.C.L. John, Ed., Campridge: Cambridge University Press, 1981, pp. 85-98.
[30] B. Stern, and P. Nurse, "Fission yeast pheromone blocks S-phase by inhibiting the G1 cyclin B-p34cdc2 kinase," EMBO J. 1997 February 3, pp. 16(3): 534-544.