메뉴 건너뛰기




Volumn 16, Issue 4, 2008, Pages 463-478

Construction and customization of stable oscillation models in biology

Author keywords

Biochemical systems theory; Limit cycle; Model sesign; S system; Stable oscillation

Indexed keywords


EID: 55949121336     PISSN: 02183390     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218339008002502     Document Type: Article
Times cited : (10)

References (38)
  • 1
    • 55949120979 scopus 로고    scopus 로고
    • Edelstein-Keshet L, Mathematical Models in Biology, in SIAM (ed.), Random House, New York, 2005.
    • Edelstein-Keshet L, Mathematical Models in Biology, in SIAM (ed.), Random House, New York, 2005.
  • 2
    • 4544313613 scopus 로고    scopus 로고
    • The ups and downs of modeling the cell cycle
    • Nicholas TI, Andrew WM, The ups and downs of modeling the cell cycle, Curr Biol 14:771-777, 2004.
    • (2004) Curr Biol , vol.14 , pp. 771-777
    • Nicholas, T.I.1    Andrew, W.M.2
  • 3
    • 23944469094 scopus 로고    scopus 로고
    • Systems-level dissection of the cell-cycle oscillator: Bypassing positive feedback produces damped oscillations
    • Pomerening JR, Kim SY, Ferrell JE, Systems-level dissection of the cell-cycle oscillator: bypassing positive feedback produces damped oscillations, Cell 122:565-578, 2005.
    • (2005) Cell , vol.122 , pp. 565-578
    • Pomerening, J.R.1    Kim, S.Y.2    Ferrell, J.E.3
  • 5
    • 0033375755 scopus 로고    scopus 로고
    • Limit cycle models for circadian rhythms based on transcriptional regulation in Drosophila and Neurospora
    • Leloup JC, Gonze D, Goldbeter A, Limit cycle models for circadian rhythms based on transcriptional regulation in Drosophila and Neurospora, J Biol Rhythms 14:433-448, 1999.
    • (1999) J Biol Rhythms , vol.14 , pp. 433-448
    • Leloup, J.C.1    Gonze, D.2    Goldbeter, A.3
  • 6
    • 32144448876 scopus 로고    scopus 로고
    • Bifurcations in a mathematical model for circadian oscillations of clock genes
    • Tsumoto K, Yoshinaga T, Iida H, Kawakami H, Aihara K, Bifurcations in a mathematical model for circadian oscillations of clock genes, J Theor Biol 239:101-122, 2006.
    • (2006) J Theor Biol , vol.239 , pp. 101-122
    • Tsumoto, K.1    Yoshinaga, T.2    Iida, H.3    Kawakami, H.4    Aihara, K.5
  • 8
    • 9344260562 scopus 로고
    • Periodical oxidation of malonic acid in solution (a study of the Belousov reaction kinetics)
    • Zhabotinsky AM, Periodical oxidation of malonic acid in solution (a study of the Belousov reaction kinetics), Biofizika 9:306-311, 1964.
    • (1964) Biofizika , vol.9 , pp. 306-311
    • Zhabotinsky, A.M.1
  • 9
    • 0008849269 scopus 로고    scopus 로고
    • From simple to complex oscillatory behavior in metabolic and genetic control networks
    • Goldbeter A, Gonze D, Houart G, Leloup JC, Halloy J, Dupont G, From simple to complex oscillatory behavior in metabolic and genetic control networks, Chaos 11:247-260, 2001.
    • (2001) Chaos , vol.11 , pp. 247-260
    • Goldbeter, A.1    Gonze, D.2    Houart, G.3    Leloup, J.C.4    Halloy, J.5    Dupont, G.6
  • 10
    • 33750989365 scopus 로고    scopus 로고
    • Oscillatory dynamics arising from competitive inhibition and multisite phosphorylation
    • Chickarmane V, Kholodenko BN, Sauro HM, Oscillatory dynamics arising from competitive inhibition and multisite phosphorylation, J Theor Biol 244:68-76, 2007.
    • (2007) J Theor Biol , vol.244 , pp. 68-76
    • Chickarmane, V.1    Kholodenko, B.N.2    Sauro, H.M.3
  • 14
    • 0023531427 scopus 로고
    • Chemical reaction network structure and the stability of complex isothermal reaction-I. The deficiency zero and deficiency one theorems
    • Feinberg M, Chemical reaction network structure and the stability of complex isothermal reaction-I. The deficiency zero and deficiency one theorems. Chem Eng Sci 42:2229-2268, 1987.
    • (1987) Chem Eng Sci , vol.42 , pp. 2229-2268
    • Feinberg, M.1
  • 15
    • 0016038059 scopus 로고
    • Dynamics of open chemical systems and the algebraic structure of the underlying reaction network
    • Feinberg M, Horn JMF, Dynamics of open chemical systems and the algebraic structure of the underlying reaction network. Chem Eng Sci 29:775-787, 1974.
    • (1974) Chem Eng Sci , vol.29 , pp. 775-787
    • Feinberg, M.1    Horn, J.M.F.2
  • 17
    • 0002674020 scopus 로고
    • Abzweigung einer periodischen Lösung von einer stationären Lösung eines differential systems
    • Hopf E, Abzweigung einer periodischen Lösung von einer stationären Lösung eines differential systems, Ber Math Phys KL Sächs Acad Wiss 94:1-22, 1942.
    • (1942) Ber Math Phys KL Sächs Acad Wiss , vol.94 , pp. 1-22
    • Hopf, E.1
  • 18
    • 0000040998 scopus 로고
    • Introduction to bifurcation theory
    • Crawford JD, Introduction to bifurcation theory. Rev Mod Phys 63:991-1038, 1991.
    • (1991) Rev Mod Phys , vol.63 , pp. 991-1038
    • Crawford, J.D.1
  • 19
    • 0014649230 scopus 로고
    • Biochemical systems analysis. I. Some mathematical properties of the rate law for the component enzymatic reactions
    • Savageau MA, Biochemical systems analysis. I. Some mathematical properties of the rate law for the component enzymatic reactions, J Theor Biol 25:365-369, 1969.
    • (1969) J Theor Biol , vol.25 , pp. 365-369
    • Savageau, M.A.1
  • 20
    • 0014658880 scopus 로고
    • Biochemical systems analysis. II. The steady-state solutions for an n-pool system using a power-law approximation
    • Savageau MA, Biochemical systems analysis. II. The steady-state solutions for an n-pool system using a power-law approximation, J Theor Biol 25:370-379, 1969.
    • (1969) J Theor Biol , vol.25 , pp. 370-379
    • Savageau, M.A.1
  • 21
    • 0014733809 scopus 로고
    • Biochemical systems analysis. III. Dynamic solutions using a power-law approximation
    • Savageau MA, Biochemical systems analysis. III. Dynamic solutions using a power-law approximation, J Theor Biol 26:215-226, 1970.
    • (1970) J Theor Biol , vol.26 , pp. 215-226
    • Savageau, M.A.1
  • 27
    • 33646179187 scopus 로고    scopus 로고
    • A quartet neural system model orchestrating sleep and wakefulness mechanisms
    • Tamakawa Y, Karashima A, Koyama Y, Katayama N, Nakao M, A quartet neural system model orchestrating sleep and wakefulness mechanisms, J Neurophysiol 95:2055-2069, 2006.
    • (2006) J Neurophysiol , vol.95 , pp. 2055-2069
    • Tamakawa, Y.1    Karashima, A.2    Koyama, Y.3    Katayama, N.4    Nakao, M.5
  • 28
    • 0344736694 scopus 로고    scopus 로고
    • A detailed predictive model of the manmalian circadian clock
    • Forger DB, Peskin CS, A detailed predictive model of the manmalian circadian clock. Proc Natl Acad Sci USA 100:14806-14811, 2003.
    • (2003) Proc Natl Acad Sci USA , vol.100 , pp. 14806-14811
    • Forger, D.B.1    Peskin, C.S.2
  • 29
    • 4244101701 scopus 로고
    • Some further studies of nonlinear oscillations in chemical systems
    • Tyson JJ, Some further studies of nonlinear oscillations in chemical systems, J. Chem. Phys. 58:3919-3930, 1973.
    • (1973) J. Chem. Phys , vol.58 , pp. 3919-3930
    • Tyson, J.J.1
  • 30
    • 53349102813 scopus 로고
    • Impulses and physiological states in theoretical models of nerve membrane
    • Fitzhugh R, Impulses and physiological states in theoretical models of nerve membrane, Biophys J 1:445-466, 1961.
    • (1961) Biophys J , vol.1 , pp. 445-466
    • Fitzhugh, R.1
  • 31
    • 6344238035 scopus 로고
    • An active pulse transmission line simulating nerve axon
    • Nagumo J, Arimoto S, Yoshizawa S, An active pulse transmission line simulating nerve axon, Proc IRE 50:2061-2070, 1962.
    • (1962) Proc IRE , vol.50 , pp. 2061-2070
    • Nagumo, J.1    Arimoto, S.2    Yoshizawa, S.3
  • 33
    • 0342349799 scopus 로고
    • Recasting nonlinear differential equations as S-systems: A canonical nonlinear form
    • Savageau MA, Voit EO, Recasting nonlinear differential equations as S-systems: a canonical nonlinear form, Math Biosci 87:83-115, 1987.
    • (1987) Math Biosci , vol.87 , pp. 83-115
    • Savageau, M.A.1    Voit, E.O.2
  • 35
    • 33645796471 scopus 로고    scopus 로고
    • Dynamical principles of two-component genetic oscillators
    • Guantes R, Poyatos JF, Dynamical principles of two-component genetic oscillators, PLoS Comput Biol 2:e30, 2006.
    • (2006) PLoS Comput Biol , vol.2
    • Guantes, R.1    Poyatos, J.F.2
  • 36
    • 0037041888 scopus 로고    scopus 로고
    • Synthetic gene network for entraining and amplifying cellular oscillations
    • Hasty J, Dolnik M, Rottschafer V, Collins JJ, Synthetic gene network for entraining and amplifying cellular oscillations, Phys Rev Lett 88:148101, 2002.
    • (2002) Phys Rev Lett , vol.88 , pp. 148101
    • Hasty, J.1    Dolnik, M.2    Rottschafer, V.3    Collins, J.J.4
  • 37
    • 1242274449 scopus 로고    scopus 로고
    • Detection of multistability, bifurcations, and hysteresis in a large class of biological positive-feedback systems
    • Angeli D, Ferrell JEJ, Sontag ED, Detection of multistability, bifurcations, and hysteresis in a large class of biological positive-feedback systems, Proc Natl Acad Sci USA 101:1822-1827, 2004.
    • (2004) Proc Natl Acad Sci USA , vol.101 , pp. 1822-1827
    • Angeli, D.1    Ferrell, J.E.J.2    Sontag, E.D.3
  • 38
    • 31144466208 scopus 로고    scopus 로고
    • Smooth bistable S-system
    • Voit EO, Smooth bistable S-system, IEE Proc Syst Biol 152:207-213, 2005.
    • (2005) IEE Proc Syst Biol , vol.152 , pp. 207-213
    • Voit, E.O.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.