Parameters Identification of Mathematical Model of the Fission Yeast Cell Cycle Control Using Evolutionary Strategy
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.
[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.
[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.
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:60863", author = "A. Ghaffari and A. S. Mostafavi", title = "Parameters Identification of Mathematical Model of the Fission Yeast Cell Cycle Control Using Evolutionary Strategy", 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", volume = "2", number = "8", pages = "1001-7", }
