Regulation of modular Cyclin and CDK feedback loops by an E2F transcriptionoscillator in the mammalian cell cycle

Orit Lavi; Doron Ginsberg; Yoram Louzoun

doi:10.3934/mbe.2011.8.445

Article Contents

2011, Volume 8, Issue 2: 445-461. Doi: 10.3934/mbe.2011.8.445

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Regulation of modular Cyclin and CDK feedback loops by an E2F transcription oscillator in the mammalian cell cycle

1.
Department of Mathematics, Bar Ilan University, Ramat Gan 52900
2.
Life Science Faculty, Bar Ilan University, Ramat Gan 52900

Received: April 2010

Revised: October 2010

Published: March 2011

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Abstract

The cell cycle is regulated by a large number of enzymes and transcription factors. We have developed a modular description of the cell cycle, based on a set of interleaved modular feedback loops, each leading to a cyclic behavior. The slowest loop is the E2F transcription and ubiquitination, which determines the cycling frequency of the entire cell cycle. Faster feedback loops describe the dynamics of each Cyclin by itself. Our model shows that the cell cycle progression as well as the checkpoints of the cell cycle can be understood through the interactions between the main E2F feedback loop and the driven Cyclin feedback loops. Multiple models were proposed for the cell cycle dynamics; each with differing basic mechanisms. We here propose a new generic formalism. In contrast with existing models, the proposed formalism allows a straightforward analysis and understanding of the dynamics, neglecting the details of each interaction. This model is not sensitive to small changes in the parameters used and it reproduces the observed behavior of the transcription factor E2F and different Cyclins in continuous or regulated cycling conditions. The modular description of the cell cycle resolves the gap between cyclic models, solely based on protein-protein reactions and transcription reactions based models. Beyond the explanation of existing observations, this model suggests the existence of unknown interactions, such as the need for a functional interaction between Cyclin B and retinoblastoma protein (Rb) de-phosphorylation.

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Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

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References

[1]	B. Alberts, A. Johnson, J. Lewis, M. Raff, K. Roberts and P. Walter, "Molecular Biology of the Cell," fifth edition, Garland Science, a member of the Taylor and Francis Group, 29 West 35th Street, New York, NY, 2007.
[2]	T. Bashir, N. V. Dorrello, V. Amador, D. Guardavaccaro and M. Pagano, Control of the scf(skp2-cks1) ubiquitin ligase by the apc/c(cdh1) ubiquitin ligase, Nature, 428 (2004), 190-193.doi: 10.1038/nature02330.
[3]	D. Bech-Otschir, M. Seeger and W. Dubiel, The cop9 signalosome: At the interface between signal transduction and ubiquitin-dependent proteolysis, J. Cell Sci., 115 (2002), 467-73.
[4]	C. Berthet, E. Aleem, V. Coppola, L. Tessarollo and P. Kaldis, Cdk2 knockout mice are viable, Curr. Biol., 13 (2003), 1775-1785.doi: 10.1016/j.cub.2003.09.024.
[5]	M. Bilodeau, H. Talarmin, G. Ilyin, C. Rescan, D. Glaise, S. Cariou, P. Loyer, C. Guguen-Guillouzo and G. Baffet, Skp2 induction and phosphorylation is associated with the late g1 phase of proliferating rat hepatocytes, FEBS Lett, 452 (1999), 247-253.doi: 10.1016/S0014-5793(99)00629-8.
[6]	M. Brandeis, I. Rosewell, M. Carrington, T. Crompton, M. A. Jacobs, J. Kirk, J. Gannon and T. Hunt, Cyclin b2-null mice develop normally and are fertile whereas cyclin b1-null mice die in utero, Proc. Natl. Acad. Sci. U.S.A., 95 (1998), 4344-4349.doi: 10.1073/pnas.95.8.4344.
[7]	K. C. Chen, L. Calzone, A. Csikasz-Nagy, F. R. Cross, B. Novak and J. J. Tyson, Integrative analysis of cell cycle control in budding yeast, Mol. Biol. Cell, 15 (2004), 3841-3862.doi: 10.1091/mbc.E03-11-0794.
[8]	L. Chen, R. Wang, T. J. Kobayashi and K. Aihara, Dynamics of gene regulatory networks with cell division cycle, Phys. Rev. E Stat. Nonlin. Soft Matter Phys., 70 (2004), 011909.doi: 10.1103/PhysRevE.70.011909.
[9]	M. Cheng, P. Olivier, J. A. Diehl, M. Fero, M. F. Roussel, J. M. Roberts and C. J. Sherr, The p21(cip1) and p27(kip1) cdk 'inhibitors' are essential activators of cyclin d-dependent kinases in murine fibroblasts, Embo. J., 18 (1999), 1571-1583.doi: 10.1093/emboj/18.6.1571.
[10]	S. Chu, J. DeRisi, M. Eisen, J. Mulholland, D. Botstein, P. O. Brown and I. Herskowitz, The transcriptional program of sporulation in budding yeast, Science, 282 (1998), 699-705.doi: 10.1126/science.282.5389.699.
[11]	J. Culotti and L. H. Hartwell, Genetic control of the cell division cycle in yeast. 3. seven genes controlling nuclear division, Exp. Cell Res., 67 (1971), 389-401.doi: 10.1016/0014-4827(71)90424-1.
[12]	S. J. D'Souza, A. Vespa, S. Murkherjee, A. Maher, A. Pajak and L. Dagnino, E2f-1 is essential for normal epidermal wound repair, J. Biol. Chem., 277 (2002), 10626-10632.doi: 10.1074/jbc.M111956200.
[13]	H. L. Ford and A. B. Pardee, Cancer and the cell cycle, J. Cell Biochem., Suppl. 32-33 (1999), 166-172.doi: 10.1002/(SICI)1097-4644(1999)75:32+<166::AID-JCB20>3.0.CO;2-J.
[14]	A. Fotovati, K. Nakayama and K. I. Nakayama, Impaired germ cell development due to compromised cell cycle progression in skp2-deficient mice, Cell Div., 1 (2006), 4.doi: 10.1186/1747-1028-1-4.
[15]	J. M. Galan and M. Peter, Ubiquitin-dependent degradation of multiple f-box proteins by an autocatalytic mechanism, Proc. Natl. Acad. Sci. U.S.A., 96 (1999), 9124-9129.doi: 10.1073/pnas.96.16.9124.
[16]	T. S. Gardner, M. Dolnik and J. J. Collins, A theory for controlling cell cycle dynamics using a reversibly binding inhibitor, Proc. Natl. Acad. Sci. U.S.A., 95 (1998), 14190-14195.doi: 10.1073/pnas.95.24.14190.
[17]	Y. Geng, W. Whoriskey, M. Y. Park, R. T. Bronson, R. H. Medema, T. Li, R. A. Weinberg and P. Sicinski, Rescue of cyclin d1 deficiency by knockin cyclin e, Cell, 97 (1999), 767-777.doi: 10.1016/S0092-8674(00)80788-6.
[18]	Y. Geng, Q. Yu, E. Sicinska, M. Das, J. E. Schneider, S. Bhattacharya, W. M. Rideout, R. T. Bronson, H. Gardner and P. Sicinski, Cyclin e ablation in the mouse, Cell, 114 (2003), 431-443.doi: 10.1016/S0092-8674(03)00645-7.
[19]	M. Glotzer, A. W. Murray and M. W. Kirschner, Cyclin is degraded by the ubiquitin pathway, Nature, 349 (1991), 132-138.doi: 10.1038/349132a0.
[20]	A. Goldbeter, A minimal cascade model for the mitotic oscillator involving cyclin and cdc2 kinase, Proc. Natl. Acad. Sci. U.S.A., 88 (1991), 9107-9111.doi: 10.1073/pnas.88.20.9107.
[21]	C. H. Golias, A. Charalabopoulos and K. Charalabopoulos, Cell proliferation and cell cycle control: A mini review, Int. J. Clin. Pract., 58 (2004), 1134-1141.doi: 10.1111/j.1742-1241.2004.00284.x.
[22]	D. Gong, J. R. Pomerening, J. W. Myers, C. Gustavsson, J. T. Jones, A. T. Hahn, T. Meyer and J. Ferrell, Cyclin a2 regulates nuclear-envelope breakdown and the nuclear accumulation of cyclin b1, Curr. Biol., 17 (2007), 85-91.doi: 10.1016/j.cub.2006.11.066.
[23]	J. W. Harper and S. J. Elledge, Skipping into the e2f1-destruction pathway, Nat. Cell Biol., 1 (1999), E5-7.doi: 10.1038/8952.
[24]	L. H. Hartwell, Genetic control of the cell division cycle in yeast. ii. genes controlling dna replication and its initiation, J. Mol. Biol., 59 (1971), 183-194.doi: 10.1016/0022-2836(71)90420-7.
[25]	L. H. Hartwell, J. Culotti and B. Reid, Genetic control of the cell-division cycle in yeast. i. detection of mutants, Proc. Natl. Acad. Sci. U.S.A., 66 (1970), 352-359.doi: 10.1073/pnas.66.2.352.
[26]	A. Hershko, The ubiquitin system for protein degradation and some of its roles in the control of the cell division cycle, Cell Death Differ., 12 (2005), 1191-1197.
[27]	A. Hershko and A. Ciechanover, The ubiquitin system, Annual Rev. Biochem., 67 (1998), 425-4-79.
[28]	I. Hoffmann, G. Draetta and E. Karsenti, Activation of the phosphatase activity of human cdc25a by a cdk2-cyclin e dependent phosphorylation at the g1/s transition, Embo. J., 13 (1994), 4302-4310.
[29]	K. Iwamoto, Y. Tashima, H. Hamada, Y. Eguchi and M. Okamoto, Mathematical modeling and sensitivity analysis of g1/s phase in the cell cycle including the dna-damage signal transduction pathway, Biosystems, 94 (2008), 109-117.doi: 10.1016/j.biosystems.2008.05.016.
[30]	T. Jacks, A. Fazeli, E. M. Schmitt, R. T. Bronson, M. A. Goodell and R. A. Weinberg, Effects of an rb mutation in the mouse, Nature, 359 (1992), 295-300.doi: 10.1038/359295a0.
[31]	S. Jirawatnotai, D. S. Moons, C. O. Stocco, R. Franks, D. B. Hales, G. Gibori and H. Kiyokawa, The cyclin-dependent kinase inhibitors p27kip1 and p21cip1 cooperate to restrict proliferative life span in differentiating ovarian cells, J. Biol. Chem., 278 (2003), 17021-17027.doi: 10.1074/jbc.M301206200.
[32]	M. B. Kastan and J. Bartek, Cell-cycle checkpoints and cancer, Nature, 432 (2004), 316-323.doi: 10.1038/nature03097.
[33]	D. Knapp, L. Bhoite, D. J. Stillman and K. Nasmyth, The transcription factor swi5 regulates expression of the cyclin kinase inhibitor p40sic1, Mol. Cell Biol., 16 (1996), 5701-5707.
[34]	C. Koch and K. Nasmyth, Cell cycle regulated transcription in yeast, Curr. Opin. Cell Biol., 6 (1994), 451-459.doi: 10.1016/0955-0674(94)90039-6.
[35]	D. M. Koepp, J. W. Harper and S. J. Elledge, How the cyclin became a cyclin: Regulated proteolysis in the cell cycle, Cell, 97 (1999), 431-434.doi: 10.1016/S0092-8674(00)80753-9.
[36]	K. W. Kohn, Molecular interaction map of the mammalian cell cycle control and dna repair systems, Mol. Biol. Cell, 10 (1999), 2703-2734.
[37]	U. Kossatz, N. Dietrich, L. Zender, J. Buer, M. P. Manns and N. P. Malek, Skp2-dependent degradation of p27kip1 is essential for cell cycle progression, Genes Dev., 18 (2004), 2602-2607.doi: 10.1101/gad.321004.
[38]	O. Lavi and Y. Louzoun, What cycles the cell? - robust autonomous cell cycle models, Math Med Biol, 26 (2009), 337-359.doi: 10.1093/imammb/dqp016.
[39]	J. Lisztwan, A. Marti, H. Sutterluty, M. Gstaiger, C. Wirbelauer and W. Krek, Association of human cul-1 and ubiquitin-conjugating enzyme cdc34 with the f-box protein p45(skp2): Evidence for evolutionary conservation in the subunit composition of the cdc34-scf pathway, EMBO J., 17 (1998), 368-383.doi: 10.1093/emboj/17.2.368.
[40]	A. J. Lotka, "Elements of Physical Biology," Williams and Wilkins, Baltimore, 1925.
[41]	J. W. Ludlow, C. L. Glendening, D. M. Livingston and J. A. DeCarprio, Specific enzymatic dephosphorylation of the retinoblastoma protein, Mol. Cell Biol., 13 (1993), 367-372.
[42]	C. Lukas, C. S. Sorensen, E. Kramer, E. Santoni-Rugiu, C. Lindeneg, J. M. Peters, J. Bartek and J. Lukas, Accumulation of cyclin b1 requires e2f and cyclin-a-dependent rearrangement of the anaphase-promoting complex, Nature, 401 (1999), 815-818.doi: 10.1038/44611.
[43]	M. Malumbres, R. Sotillo, D. Santamaria, J. Galan, A. Cerezo, S. Ortega, P. Dubus and M. Barbacid, Mammalian cells cycle without the d-type cyclin-dependent kinases cdk4 and cdk6, Cell, 118 (2004), 493-504.doi: 10.1016/j.cell.2004.08.002.
[44]	A. Marti, C. Wirbelauer, M. Scheffner and W. Krek, Interaction between ubiquitin-protein ligase scfskp2 and e2f-1 underlies the regulation of e2f-1 degradation, Nat. Cell Biol., 1 (1999), 14-19.doi: 10.1038/8984.
[45]	A. Montagnoli, F. Fiore, E. Eytan, A. C. Carrano, G. F. Draetta, A. Hershko and M. Pagano, Ubiquitination of p27 is regulated by cdk-dependent phosphorylation and trimeric complex formation, Genes Dev., 13 (1999), 1181-1189.doi: 10.1101/gad.13.9.1181.
[46]	D. O. Morgan, Regulation of the apc and the exit from mitosis, Nat. Cell Biol., 1 (1999), E47-53.doi: 10.1038/10039.
[47]	M. C. Morris, A. Heitz, J. Mery, F. Heitz and G. Divita, An essential phosphorylation-site domain of human cdc25c interacts with both 14-3-3 and cyclins, J. Biol. Chem., 275 (2000), 28849-28857.doi: 10.1074/jbc.M002942200.
[48]	M. Murphy, M. G. Stinnakre, C. Senamaud-Beaufort, N. J. Winston, C. Sweeney, M. Kubelka, M. Carrington, C. Brechot and J. Sobczak-Thepot, Delayed early embryonic lethality following disruption of the murine cyclin a2 gene, Nat. Genet., 15 (1997), 83-86.doi: 10.1038/ng0197-83.
[49]	K. Nakayama, N. Ishida, M. Shirane, A. Inomata, T. Inoue, N. Shishido, I. Horii, D. Y. Loh and K. Nakayama, Mice lacking p27(kip1) display increased body size, multiple organ hyperplasia, retinal dysplasia, and pituitary tumors, Cell, 85 (1996), 707-720.doi: 10.1016/S0092-8674(00)81237-4.
[50]	K. I. Nakayama, S. Hatakeyama and K. Nakayama, Regulation of the cell cycle at the g1-s transition by proteolysis of cyclin e and p27kip1, Biochem. Biophys. Res. Commun., 282 (2001), 853-860.doi: 10.1006/bbrc.2001.4627.
[51]	P. Nash, X. Tang, S. Orlicky, Q. Chen, F. B. Gertler, M. D. Mendenhall, F. Sicheri, T. Pawson and M. Tyers, Multisite phosphorylation of a cdk inhibitor sets a threshold for the onset of DNA replication, Nature, 414 (2001), 514-521.doi: 10.1038/35107009.
[52]	R. Norel and Z. Agur, A model for the adjustment of the mitotic clock by cyclin and mpf levels, Science, 251 (1991), 1076-1078.doi: 10.1126/science.1825521.
[53]	P. Nurse, A long twentieth century of the cell cycle and beyond, Cell, 100 (2000), 71-78.doi: 10.1016/S0092-8674(00)81684-0.
[54]	D. A. Orlando, C. Y. Lin, A. Bernard, J. Y. Wang, J. E. Socolar, E. S. Iversen, A. J. Hartemink and S. B. Haase, Global control of cell-cycle transcription by coupled cdk and network oscillators, Nature, 453 (2008), 944-947.doi: 10.1038/nature06955.
[55]	M. Peter, The regulation of cyclin-dependent kinase inhibitors (ckis), Prog. Cell Cycle Res., 3 (1997), 99-108.
[56]	J. M. Peters, Scf and apc: The yin and yang of cell cycle regulated proteolysis, Curr. Opin. Cell Biol., 10 (1998), 759-768.doi: 10.1016/S0955-0674(98)80119-1.
[57]	B. Pfeuty and K. Kaneko, Minimal requirements for robust cell size control in eukaryotic cells, Phys. Biol., 4 (2007), 194-204.doi: 10.1088/1478-3975/4/3/006.
[58]	S. Prinz, E. S. Hwang, R. Visintin and A. Amon, The regulation of cdc20 proteolysis reveals a role for apc components cdc23 and cdc27 during s-phase and early mitosis, Curr. Biol., 8 (1998), 750-760.doi: 10.1016/S0960-9822(98)70298-2.
[59]	F. Puntoni and E. Villa-Moruzzi, Phosphorylation of protein phosphatase-1 isoforms by cdc2-cyclin b in vitro, Mol. Cell. Biochem., 171 (1997), 115-120.doi: 10.1023/A:1006892103306.
[60]	Z. Qu, W. R. MacLellan and J. N. Weiss, Dynamics of the cell cycle: Checkpoints, sizers, and timers, Biophys. J., 85 (2003), 3600-3611.doi: 10.1016/S0006-3495(03)74778-X.
[61]	T. Reis and B. A. Edgar, Negative regulation of de2f1 by cyclin-dependent kinases controls cell cycle timing, Cell, 117 (2004), 253-264.doi: 10.1016/S0092-8674(04)00247-8.
[62]	J. M. Roberts and C. J. Sherr, Bared essentials of cdk2 and cyclin E, Nat. Genet., 35 (2003), 9-10.doi: 10.1038/ng1234.
[63]	J. Rudolph, Targeting the neighbor's pool, Mol. Pharmacol., 66 (2004), 780-782.doi: 10.1124/mol.104.004788.
[64]	D. Santamaria, C. Barriere, A. Cerqueira, S. Hunt, C. Tardy, K. Newton, J. F. Caceres, P. Dubus, M. Malumbres and M. Barbacid, Cdk1 is sufficient to drive the mammalian cell cycle, Nature, 448 (2007), 811-815.doi: 10.1038/nature06046.
[65]	C. J. Sherr and J. M. Roberts, Living with or without cyclins and cyclin-dependent kinases, Genes Dev., 18 (2004), 2699-2711.doi: 10.1101/gad.1256504.
[66]	P. Sicinski, J. L. Donaher, S. B. Parker, T. Li, A. Fazeli, H. Gardner, S. Z. Haslam, R. T. Bronson, S. J. Elledge and R. A. Weinberg, Cyclin d1 provides a link between development and oncogenesis in the retina and breast, Cell, 82 (1995), 621-630.doi: 10.1016/0092-8674(95)90034-9.
[67]	M. J. Solomon, M. Glotzer, T. H. Lee, M. Philippe and M. W. Kirschner, Cyclin activation of p34cdc2, Cell, 63 (1990), 1013-1024.doi: 10.1016/0092-8674(90)90504-8.
[68]	M. J. Solomon and P. Kaldis, Regulation of cdks by phosphorylation, Results Probl. Cell Differ., 22 (1998), 79-109.
[69]	P. T. Spellman, G. Sherlock, M. Q. Zhang, V. R. Iyer, K. Anders, M. B. Eisen, P. O. Brown, D. Botstein and B. Futcher, Comprehensive identification of cell cycle-regulated genes of the yeast saccharomyces cerevisiae by microarray hybridization, Mol. Biol. Cell, 9 (1998), 3273-3297.
[70]	K. Sriram, G. Bernot and F. Kepes, A minimal mathematical model combining several regulatory cycles from the budding yeast cell cycle, IET Syst. Biol., 1 (2007), 326-341.doi: 10.1049/iet-syb:20070018.
[71]	T. T. Su and J. Stumpff, Promiscuity rules? The dispensability of cyclin E and Cdk2, Sci. STKE, 2004 (2004), pe11.doi: 10.1126/stke.2242004pe11.
[72]	M. Sugimoto, N. Martin, D. P. Wilks, K. Tamai, T. J. Huot, C. Pantoja, K. Okumura, M. Serrano and E. Hara, Activation of cyclin d1-kinase in murine fibroblasts lacking both p21(Cip1) and p27(Kip1), Oncogene, 21 (2002), 8067-8074.doi: 10.1038/sj.onc.1206019.
[73]	S. Tamrakar, E. Rubin, and J. W. Ludlow, Role of prb dephosphorylation in cell cycle regulation, Front Biosci., 5 (2000), D121-137.doi: 10.2741/Tamrakar.
[74]	O. Tetsu and F. McCormick, Proliferation of cancer cells despite Cdk2 inhibition, Cancer Cell, 3 (2003), 233-245.doi: 10.1016/S1535-6108(03)00053-9.
[75]	J. E. Toettcher, A. Loewer, G. J. Ostheimer, M. B. Yaffe, B. Tidor and G. Lahav, Distinct mechanisms act in concert to mediate cell cycle arrest, Proc. Natl. Acad. Sci. U.S.A., 106 (2009), 785-790.doi: 10.1073/pnas.0806196106.
[76]	J. J. Tyson and B. Novak, Regulation of the eukaryotic cell cycle: Molecular antagonism, hysteresis, and irreversible transitions, J. Theor. Biol., 210 (2001), 249-263.doi: 10.1006/jtbi.2001.2293.
[77]	S. van den Heuvel and N. J. Dyson, Conserved functions of the prb and e2f families, Nat. Rev. Mol. Cell Biol., 9 (2008), 713-724.doi: 10.1038/nrm2469.
[78]	H. C. Vodermaier, Apc/c and scf: Controlling each other and the cell cycle, Curr. Biol., 14 (2004), R787-796.doi: 10.1016/j.cub.2004.09.020.
[79]	V. Volterra, "Animal Ecology," Chapman R. N., McGraw-Hill, New York., 1931, 409-448.
[80]	R. Wasch and F. R. Cross, Apc-dependent proteolysis of the mitotic cyclin clb2 is essential for mitotic exit, Nature, 418 (2002), 556-562.doi: 10.1038/nature00856.
[81]	J. Weinstein, Cell cycle-regulated expression, phosphorylation, and degradation of p55cdc. a mammalian homolog of cdc20/fizzy/slp1, J. Biol. Chem., 272 (1997), 28501-28511.doi: 10.1074/jbc.272.45.28501.
[82]	M. L. Whitfield, G. Sherlock, A. J. Saldanha, J. I. Murray, C. A. Ball, K. E. Alexander, J. C. Matese, C. M. Perou, M. M. Hurt, P. O. Brown and D. Botstein, Identification of genes periodically expressed in the human cell cycle and their expression in tumors, Mol. Biol. Cell, 13 (2002), 1977-2000.
[83]	L. Wu, C. Timmers, B. Maiti, H. I. Saavedra, L. Sang, G. T. Chong, F. Nuckolls, P. Giangrande, F. A. Wright, S. J. Field, M. E. Greenberg, S. Orkin, J. R. Nevins, M. L. Robinson and G. Leone, The E2f1-3 transcription factors are essential for cellular proliferation, Nature, 414 (2001), 457-462.doi: 10.1038/35106593.
[84]	M. Xu, K. A. Sheppard, C. Y. Peng, A. S. Yee and H. Piwnica-Worms, Cyclin a/Cdk2 binds directly to e2f-1 and inhibits the dna-binding activity of e2f-1/dp-1 by phosphorylation, Mol. Cell Biol., 14 (1994), 8420-8431.
[85]	K. Yang, M. Hitomi and D. W. Stacey, Variations in cyclin d1 levels through the cell cycle determine the proliferative fate of a cell, Cell Div., 1 (2006), 32.doi: 10.1186/1747-1028-1-32.
[86]	W. Zachariae and K. Nasmyth, Whose end is destruction: Cell division and the anaphase-promoting complex, Genes Dev., 13 (1999), 2039-2058.doi: 10.1101/gad.13.16.2039.
[87]	H. Zhang, R. Kobayashi, K. Galaktionov and D. Beach, P19skp1 and p45skp2 are essential elements of the cyclin A-CDK2 S phase kinase, Cell, 82 (1995), 915-925.doi: 10.1016/0092-8674(95)90271-6.
[88]	J. Zhang, X. Dong, Y. Fujimoto and H. Okamura, Molecular signals of mammalian circadian clock, Kobe J. Med. Sci., 50 (2004), 101-109.
[89]	L. Zhang and C. Wang, F-box protein skp2: A novel transcriptional target of e2f, Oncogene, 25 (2006), 2615-2627.doi: 10.1038/sj.onc.1209286.
[90]	P. Zhou and P. M. Howley, Ubiquitination and degradation of the substrate recognition subunits of scf ubiquitin-protein ligases, Mol. Cell, 2 (1998), 571-580.doi: 10.1016/S1097-2765(00)80156-2.