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Circadian rhythm makes physiology and behaviors of organisms adapt to the day and night cycle in the environment. Recent experiment indicated a PER-TIM interval timer in Drosophila melanogaster cytoplasm. In this paper, we present a possible mathematical model for this interval timer. The characters of the model are the formation of big clusters, fast exchange and different functions of phosphorylation of different sites. The experimental results on features of the PER-TIM interval timer of mild type and perL mutant and on the existence of three different types of temporal profiles of nuclear accumulation of PER and TIM in single cells are reproduced by our simulations.
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Keywords:
- PER-TIM /
- circadian clock /
- interval timer
[1] Bell-Pedersen D, Cassone V M, Earnest D J, Golden S S, Hardin P E, Thomas T L, Zoran M J 2005 Nat. Rev. Genet. 6 544
[2] Allada R, Chung B Y 2010 Annu. Rev. Physiol. 72 605
[3] Rutter J, Reick M, McKnight S L 2002 Annu. Rev. Biochem. 71 307
[4] Levi F, Schibler U 2007 Ann. Rev. Pharmacol. Toxicol. 47 593
[5] Williams J, A Sehgal A 2001 Annu. Rev. Physiol. 63 729
[6] Gallego M, Virshup D M 2007 Nat. Rev. Mol. Cell Biol. 8 139
[7] Emberly E, Wingreen N 2006 Phys. Rev. Lett. 96 038303
[8] Tomita J, Nakajima M, Kondo T, Iwasaki H 2005 Science 307 251
[9] Nakajima M, Imai K, Ito H, Nishiwaki T, Murayama Y, Iwasaki H, Oyama T, Kondo T 2005 Science 308 414
[10] Li C, Chen X, Wang P, Wang W 2009 PLoS Comput. Biol. 5 e1000568
[11] Curtin K D, Huang Z J, Rosbash M 1995 Neuron 14 365
[12] Sehgal A, Rothenfluh-Hilfiker A, Hunter-Ensor M, Chen Y, Myers M P, Young M W 1995 Science 270 808
[13] Gekakis N, Saez L, Delahaye-Brown A M, Myers M P, Sehgal A, Young M W, Weitz C J 1995 Science 270 811
[14] Allada R, Emery P, Takahashi J S, Rosbash M 2001 Annu. Rev. Neurosci. 24 1091
[15] Meyer P 2006 Science 311 226
[16] Kuczenski R S, Hong K C, Garcia-Ojalvo J, Lee K H 2007 PLoS Comput. Biol. 3 e154
[17] Holmberg C I, Tran S E, Eriksson J E, Sistonen L 2002 Trends Biochem. Sci. 27 619
[18] Ermentrout B, Mahajan A 2003 APPL. MECH. REV. 56 B53
[19] Shafer O T, Rosbash M, Truman J W 2002 J. Neurosci. 22 5946
[20] Kivimae S, Saez L, Young M W 2008 PLoS Biol. 6 e183
[21] Fang Y, Sathyanarayanan S, Sehgal A 2007 Genes Dev. 21 1506
[22] Schlosser A, Vanselow J T, Kramer A 2005 Anal. Chem. 77 5243
[23] Park K S, Mohapatra D P, Misonou H, Trimmer J S 2006 Science 313 976
[24] Wu R C, Qin J, Yi P, Wong J, Tsai S Y, Tsai M J, O'Malley B W 2004 Mol. Cell 15 937
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[1] Bell-Pedersen D, Cassone V M, Earnest D J, Golden S S, Hardin P E, Thomas T L, Zoran M J 2005 Nat. Rev. Genet. 6 544
[2] Allada R, Chung B Y 2010 Annu. Rev. Physiol. 72 605
[3] Rutter J, Reick M, McKnight S L 2002 Annu. Rev. Biochem. 71 307
[4] Levi F, Schibler U 2007 Ann. Rev. Pharmacol. Toxicol. 47 593
[5] Williams J, A Sehgal A 2001 Annu. Rev. Physiol. 63 729
[6] Gallego M, Virshup D M 2007 Nat. Rev. Mol. Cell Biol. 8 139
[7] Emberly E, Wingreen N 2006 Phys. Rev. Lett. 96 038303
[8] Tomita J, Nakajima M, Kondo T, Iwasaki H 2005 Science 307 251
[9] Nakajima M, Imai K, Ito H, Nishiwaki T, Murayama Y, Iwasaki H, Oyama T, Kondo T 2005 Science 308 414
[10] Li C, Chen X, Wang P, Wang W 2009 PLoS Comput. Biol. 5 e1000568
[11] Curtin K D, Huang Z J, Rosbash M 1995 Neuron 14 365
[12] Sehgal A, Rothenfluh-Hilfiker A, Hunter-Ensor M, Chen Y, Myers M P, Young M W 1995 Science 270 808
[13] Gekakis N, Saez L, Delahaye-Brown A M, Myers M P, Sehgal A, Young M W, Weitz C J 1995 Science 270 811
[14] Allada R, Emery P, Takahashi J S, Rosbash M 2001 Annu. Rev. Neurosci. 24 1091
[15] Meyer P 2006 Science 311 226
[16] Kuczenski R S, Hong K C, Garcia-Ojalvo J, Lee K H 2007 PLoS Comput. Biol. 3 e154
[17] Holmberg C I, Tran S E, Eriksson J E, Sistonen L 2002 Trends Biochem. Sci. 27 619
[18] Ermentrout B, Mahajan A 2003 APPL. MECH. REV. 56 B53
[19] Shafer O T, Rosbash M, Truman J W 2002 J. Neurosci. 22 5946
[20] Kivimae S, Saez L, Young M W 2008 PLoS Biol. 6 e183
[21] Fang Y, Sathyanarayanan S, Sehgal A 2007 Genes Dev. 21 1506
[22] Schlosser A, Vanselow J T, Kramer A 2005 Anal. Chem. 77 5243
[23] Park K S, Mohapatra D P, Misonou H, Trimmer J S 2006 Science 313 976
[24] Wu R C, Qin J, Yi P, Wong J, Tsai S Y, Tsai M J, O'Malley B W 2004 Mol. Cell 15 937
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