메뉴 건너뛰기




Volumn 55, Issue 3, 2007, Pages 331-352

An equation-free approach to analyzing heterogeneous cell population dynamics

Author keywords

[No Author keywords available]

Indexed keywords

ACETALDEHYDE; ADENOSINE TRIPHOSPHATE; GLUCOSE; NICOTINAMIDE ADENINE DINUCLEOTIDE;

EID: 34548081500     PISSN: 03036812     EISSN: 14321416     Source Type: Journal    
DOI: 10.1007/s00285-007-0086-6     Document Type: Article
Times cited : (20)

References (56)
  • 3
    • 0036216388 scopus 로고    scopus 로고
    • Maximum likelihood estimation of discretely sampled diffusions: A closed-form approximation approach
    • 1
    • Aït-Sahalia Y. (2002). Maximum likelihood estimation of discretely sampled diffusions: a closed-form approximation approach. Econometrica 70(1): 223-262
    • (2002) Econometrica , vol.70 , pp. 223-262
    • Aït-Sahalia, Y.1
  • 4
    • 0026666852 scopus 로고
    • Synchrony and mutual stimulation of yeast cells during fast glycolytic oscillations
    • Aon M.A., Cortassa S., Westerhoff H.V. and Dam K. (1992). Synchrony and mutual stimulation of yeast cells during fast glycolytic oscillations. J. Gen. Microbiol. 138: 2219-2227
    • (1992) J. Gen. Microbiol. , vol.138 , pp. 2219-2227
    • Aon, M.A.1    Cortassa, S.2    Westerhoff, H.V.3    Van Dam, K.4
  • 5
    • 0042378381 scopus 로고    scopus 로고
    • Laplacian eigenmaps for dimensionality reduction and data representation
    • 6
    • Belkin M. and Niyogi P. (2003). Laplacian eigenmaps for dimensionality reduction and data representation. Neural Comput. 15(6): 1373-1396
    • (2003) Neural Comput. , vol.15 , pp. 1373-1396
    • Belkin, M.1    Niyogi, P.2
  • 6
    • 0001059908 scopus 로고
    • Phase relationship of glycolytic intermediates in yeast cells with oscillatory metabolic control
    • Betz A. and Chance B. (1965). Phase relationship of glycolytic intermediates in yeast cells with oscillatory metabolic control. Arch. Biochem. Biophys. 109: 585-594
    • (1965) Arch. Biochem. Biophys. , vol.109 , pp. 585-594
    • Betz, A.1    Chance, B.2
  • 7
    • 0034092437 scopus 로고    scopus 로고
    • How yeast cells synchronize their glycolytic oscillations: A perturbation analytic treatment
    • Bier M., Bakker B.M. and Westerhoff H.V. (2000). How yeast cells synchronize their glycolytic oscillations: a perturbation analytic treatment. Biophys. J. 78: 1087-1093
    • (2000) Biophys. J. , vol.78 , pp. 1087-1093
    • Bier, M.1    Bakker, B.M.2    Westerhoff, H.V.3
  • 8
    • 0000214973 scopus 로고
    • Properties and kinetics of reduced pyridine nucleotide fluorescence of the isolated and in vivo rat heart
    • Chance B., Williamson J.R., Jamieson D. and Schoener B. (1965). Properties and kinetics of reduced pyridine nucleotide fluorescence of the isolated and in vivo rat heart. Biochem. J. 341: 357-377
    • (1965) Biochem. J. , vol.341 , pp. 357-377
    • Chance, B.1    Williamson, J.R.2    Jamieson, D.3    Schoener, B.4
  • 9
    • 0033581959 scopus 로고    scopus 로고
    • Sustained oscillations in living cells
    • Dano S., Sorensen P.G. and Hynne F. (1999). Sustained oscillations in living cells. Nature 402: 320-322
    • (1999) Nature , vol.402 , pp. 320-322
    • Dano, S.1    Sorensen, P.G.2    Hynne, F.3
  • 10
    • 0021983604 scopus 로고
    • Long term oscillations in glycolysis
    • Das J. and Busse H.G. (1985). Long term oscillations in glycolysis. J. Biochem. 97: 719-727
    • (1985) J. Biochem. , vol.97 , pp. 719-727
    • Das, J.1    Busse, H.G.2
  • 11
    • 0025909052 scopus 로고
    • Analysis of the dynamics of relaxation type oscillation in glycolysis of yeast extracts
    • Das J. and Busse H.G. (1991). Analysis of the dynamics of relaxation type oscillation in glycolysis of yeast extracts. Biophys. J. 60: 363-379
    • (1991) Biophys. J. , vol.60 , pp. 363-379
    • Das, J.1    Busse, H.G.2
  • 12
    • 0035964634 scopus 로고    scopus 로고
    • Solution of stochastic partial differential equations using Galerkin finite element techniques
    • 48
    • Deb M.K., Babuška I.M. and Oden J.T. (2001). Solution of stochastic partial differential equations using Galerkin finite element techniques. Comput. Methods Appl. Mech. Eng. 190(48): 6359-6372
    • (2001) Comput. Methods Appl. Mech. Eng. , vol.190 , pp. 6359-6372
    • Deb, M.K.1    Babuška, I.M.2    Oden, J.T.3
  • 14
    • 0344736694 scopus 로고    scopus 로고
    • A detailed predictive model of the mammalian circadian clock
    • 25
    • Forger D.B. and Peskin C.S. (2003). A detailed predictive model of the mammalian circadian clock. PNAS 100(25): 14806-14811
    • (2003) PNAS , vol.100 , pp. 14806-14811
    • Forger, D.B.1    Peskin, C.S.2
  • 15
    • 0041428215 scopus 로고    scopus 로고
    • Projective methods for stiff differential equations: Problems with gaps in their eigenvalue spectrum
    • 4
    • Gear C.W. and Kevrekidis I.G. (2002). Projective methods for stiff differential equations: Problems with gaps in their eigenvalue spectrum. SIAM J. Sci. Comput. 24(4): 1091-1106
    • (2002) SIAM J. Sci. Comput. , vol.24 , pp. 1091-1106
    • Gear, C.W.1    Kevrekidis, I.G.2
  • 16
    • 0037408148 scopus 로고    scopus 로고
    • Telescopic projective methods for parabolic differential equations
    • 1
    • Gear C.W. and Kevrekidis I.G. (2003). Telescopic projective methods for parabolic differential equations. J. Comput. Phys. 187(1): 95-109
    • (2003) J. Comput. Phys. , vol.187 , pp. 95-109
    • Gear, C.W.1    Kevrekidis, I.G.2
  • 17
    • 0037104864 scopus 로고    scopus 로고
    • Coarse integration/bifurcation analysis via microscopic simulators: Micro-Galerkin methods
    • Gear C.W., Kevrekidis I.G. and Theodoropoulos C. (2002). Coarse integration/bifurcation analysis via microscopic simulators: micro-Galerkin methods. Comput Chemical Engineering 26: 941-963
    • (2002) Comput Chemical Engineering , vol.26 , pp. 941-963
    • Gear, C.W.1    Kevrekidis, I.G.2    Theodoropoulos, C.3
  • 18
    • 24644471938 scopus 로고    scopus 로고
    • Projecting to a slow manifold: Singularly perturbed systems and legacy codes
    • 3. (electronic)
    • Gear C.W., Kaper T.J., Kevrekidis I.G. and Zagaris A. (2005). Projecting to a slow manifold: singularly perturbed systems and legacy codes. SIAM J. Appl. Dyn. Syst. 4(3): 711-732 (electronic)
    • (2005) SIAM J. Appl. Dyn. Syst. , vol.4 , pp. 711-732
    • Gear, C.W.1    Kaper, T.J.2    Kevrekidis, I.G.3    Zagaris, A.4
  • 19
    • 0032496593 scopus 로고    scopus 로고
    • Probabilistic characterization of transport in heterogeneous porous media
    • Ghanem R. (1998). Probabilistic characterization of transport in heterogeneous porous media. Comput. Methods Appl. Mech. Eng. 158: 3-4
    • (1998) Comput. Methods Appl. Mech. Eng. , vol.158 , pp. 3-4
    • Ghanem, R.1
  • 21
    • 0015084446 scopus 로고
    • Metabolic coupling and synchronization of NADH oscillations in yeast cell populations
    • Ghosh A.K., Chance B. and Pye E.K. (1971). Metabolic coupling and synchronization of NADH oscillations in yeast cell populations. Arch. Biochem. Biophys. 145: 319-331
    • (1971) Arch. Biochem. Biophys. , vol.145 , pp. 319-331
    • Ghosh, A.K.1    Chance, B.2    Pye, E.K.3
  • 23
    • 0015419716 scopus 로고
    • Dissipative structures for an allosteric model. Application to glycolytic oscillations
    • Goldbeter A. and Lefever R. (1972). Dissipative structures for an allosteric model. Application to glycolytic oscillations. Biophys. J. 12: 1302-1315
    • (1972) Biophys. J. , vol.12 , pp. 1302-1315
    • Goldbeter, A.1    Lefever, R.2
  • 24
    • 6344263666 scopus 로고    scopus 로고
    • Modeling the synchronization of yeast respiratory oscillations
    • 3
    • Henson M.A. (2004). Modeling the synchronization of yeast respiratory oscillations. J. Theoret. Biol. 231(3): 443-458
    • (2004) J. Theoret. Biol. , vol.231 , pp. 443-458
    • Henson, M.A.1
  • 25
    • 0036901566 scopus 로고    scopus 로고
    • Cell population modeling of yeast glycolytic oscillations
    • Henson M.A., Muller D. and Reuss M. (2002). Cell population modeling of yeast glycolytic oscillations. Biochem. J. 368: 433-446
    • (2002) Biochem. J. , vol.368 , pp. 433-446
    • Henson, M.A.1    Muller, D.2    Reuss, M.3
  • 26
    • 34548059545 scopus 로고    scopus 로고
    • Differential equations, dynamical systems, and an introduction to chaos
    • 2nd edn. Elsevier/Academic Press, Amsterdam
    • Hirsch, M.W., Smale, S., Devaney, R.L.: Differential equations, dynamical systems, and an introduction to chaos. In: Pure and Applied Mathematics (Amsterdam), vol. 60, 2nd edn. Elsevier/Academic Press, Amsterdam (2004)
    • (2004) Pure and Applied Mathematics (Amsterdam) , vol.60
    • Hirsch, M.W.1    Smale, S.2    Devaney, R.L.3
  • 27
    • 0035846723 scopus 로고    scopus 로고
    • Full-scale model of glycolysis in Saccharomyces cerevisiae
    • Hynne F., Dano S. and Sorensen P. (2001). Full-scale model of glycolysis in Saccharomyces cerevisiae. Biophys. Chem. 94: 121-163
    • (2001) Biophys. Chem. , vol.94 , pp. 121-163
    • Hynne, F.1    Dano, S.2    Sorensen, P.3
  • 28
    • 4244125097 scopus 로고
    • Oscillations of nucleotides and glycolytic intermediates in aerobic suspensions of Ehrlich ascites tumor cells
    • Ibsen K.H. and Schiller K.W. (1967). Oscillations of nucleotides and glycolytic intermediates in aerobic suspensions of Ehrlich ascites tumor cells. Biochem. Biophys. Acta 799: 291-297
    • (1967) Biochem. Biophys. Acta , vol.799 , pp. 291-297
    • Ibsen, K.H.1    Schiller, K.W.2
  • 30
    • 85128858890 scopus 로고    scopus 로고
    • Equation-free, coarse-grained multiscale computation: Enabling microscopic simulators to perform system-level analysis
    • 4
    • Kevrekidis I.G., Gear C.W., Hyman J.M., Kevrekidis P.G., Runborg O. and Theodoropoulos C. (2003). Equation-free, coarse-grained multiscale computation: enabling microscopic simulators to perform system-level analysis. Commun. Math. Sci. 1(4): 715-762
    • (2003) Commun. Math. Sci. , vol.1 , pp. 715-762
    • Kevrekidis, I.G.1    Gear, C.W.2    Hyman, J.M.3    Kevrekidis, P.G.4    Runborg, O.5    Theodoropoulos, C.6
  • 31
    • 3042720018 scopus 로고    scopus 로고
    • Equation-free: The computer-assisted analysis of complex, multiscale systems
    • 7
    • Kevrekidis I.G., Gear C.W. and Hummer G. (2004). Equation-free: the computer-assisted analysis of complex, multiscale systems. AIChE J. 50(7): 1346-1354
    • (2004) AIChE J. , vol.50 , pp. 1346-1354
    • Kevrekidis, I.G.1    Gear, C.W.2    Hummer, G.3
  • 32
    • 0000821240 scopus 로고
    • Oscillatory starch degradation and fermentation in the green algae chlamydomonas reinhardii
    • Kreuzberg K. and Martin W. (1984). Oscillatory starch degradation and fermentation in the green algae chlamydomonas reinhardii. Biochem. Biophys. Acta 799: 291-297
    • (1984) Biochem. Biophys. Acta , vol.799 , pp. 291-297
    • Kreuzberg, K.1    Martin, W.2
  • 34
    • 0035506770 scopus 로고    scopus 로고
    • A stochastic projection method for fluid flow. i: Basic formulation
    • Maitre O.L., Knio O., Reagan M., Najm H. and Ghanem R. (2001). A stochastic projection method for fluid flow. i: basic formulation. J. Comp. Phys. 173: 481-511
    • (2001) J. Comp. Phys. , vol.173 , pp. 481-511
    • Maitre, O.L.1    Knio, O.2    Reagan, M.3    Najm, H.4    Ghanem, R.5
  • 35
    • 2942555049 scopus 로고    scopus 로고
    • Uncertainty propagation using Wiener-Haar expansions
    • Maitre O.L., Knio O., Najm H. and Ghanem R. (2004). Uncertainty propagation using Wiener-Haar expansions. J. Comp. Phys. 197: 28-57
    • (2004) J. Comp. Phys. , vol.197 , pp. 28-57
    • Maitre, O.L.1    Knio, O.2    Najm, H.3    Ghanem, R.4
  • 36
    • 0034815606 scopus 로고    scopus 로고
    • Cellular communication and coupling within the suprachiasmatic nucleus
    • Michel S. and Colwell C.S. (2001). Cellular communication and coupling within the suprachiasmatic nucleus. Chronobiol. Int. 18: 579-600
    • (2001) Chronobiol. Int. , vol.18 , pp. 579-600
    • Michel, S.1    Colwell, C.S.2
  • 37
    • 33748533822 scopus 로고    scopus 로고
    • An equation-free approach to coupled oscillator dynamics: The kuramoto model example
    • Moon S.J. and Kevrekidis I.G. (2006). An equation-free approach to coupled oscillator dynamics: the kuramoto model example. Int. J. Bifurcations Chaos 16: 2043-2052
    • (2006) Int. J. Bifurcations Chaos , vol.16 , pp. 2043-2052
    • Moon, S.J.1    Kevrekidis, I.G.2
  • 39
    • 33745342032 scopus 로고    scopus 로고
    • Difusion maps, spectral clustering and reaction coordinates of dynamical systems
    • 1
    • Nadler B., Lafon S., Coifman R.R. and Kevrekidis I.G. (2006). Difusion maps, spectral clustering and reaction coordinates of dynamical systems. Appl. Comput. Harmon. Anal. 21(1): 113-127
    • (2006) Appl. Comput. Harmon. Anal. , vol.21 , pp. 113-127
    • Nadler, B.1    Lafon, S.2    Coifman, R.R.3    Kevrekidis, I.G.4
  • 40
    • 0037299084 scopus 로고    scopus 로고
    • Uncertainty propagation in reacting-flow simulations through spectral analysis
    • Reagan M., Najm H., Knio O., Ghanem R. and Lemaitre O. (2003). Uncertainty propagation in reacting-flow simulations through spectral analysis. Combust. Flame 132: 545-555
    • (2003) Combust. Flame , vol.132 , pp. 545-555
    • Reagan, M.1    Najm, H.2    Knio, O.3    Ghanem, R.4    Lemaitre, O.5
  • 42
    • 0028345016 scopus 로고
    • Yeast cells with a specific cellular make-up and an environment that removes acetaldehyde are prone to sustained glycolytic oscillations
    • Richard P., Diderich J.A., Bakker B.M., Teusink B., van Dam K. and Westerhoff H.V. (1994). Yeast cells with a specific cellular make-up and an environment that removes acetaldehyde are prone to sustained glycolytic oscillations. FEBS Lett. 341: 223-226
    • (1994) FEBS Lett. , vol.341 , pp. 223-226
    • Richard, P.1    Diderich, J.A.2    Bakker, B.M.3    Teusink, B.4    Van Dam, K.5    Westerhoff, H.V.6
  • 43
    • 0030025877 scopus 로고    scopus 로고
    • Acetaldehyde mediates the synchronization of sustained glycolytic oscillations in populations of yeast cells
    • Richard P., Bakker B.M., Teusink B., van Dam K. and Westerhoff H.V. (1996). Acetaldehyde mediates the synchronization of sustained glycolytic oscillations in populations of yeast cells. Eur. J. Biochem. 235: 238-241
    • (1996) Eur. J. Biochem. , vol.235 , pp. 238-241
    • Richard, P.1    Bakker, B.M.2    Teusink, B.3    Van Dam, K.4    Westerhoff, H.V.5
  • 45
    • 0016829888 scopus 로고
    • Stabilization of energy charge, generation of oscillation and multiple steady states in energy metabolism as a result of purely stoichiometric regulation
    • Selkov E.E. (1975). Stabilization of energy charge, generation of oscillation and multiple steady states in energy metabolism as a result of purely stoichiometric regulation. Eur. J. Biochem. 59: 151-157
    • (1975) Eur. J. Biochem. , vol.59 , pp. 151-157
    • Selkov, E.E.1
  • 46
    • 0039592729 scopus 로고    scopus 로고
    • From Kuramoto to Crawford: Exploring the onset of synchronization in populations of coupled oscillators
    • 1-4. Bifurcations, patterns and symmetry
    • Strogatz S.H. (2000). From Kuramoto to Crawford: exploring the onset of synchronization in populations of coupled oscillators. Physica D 143(1-4): 1-20. Bifurcations, patterns and symmetry
    • (2000) Physica D , vol.143 , pp. 1-20
    • Strogatz, S.H.1
  • 48
    • 0034730149 scopus 로고    scopus 로고
    • Coarse stability and bifurcation analysis using time-steppers: A reaction-diffusion example
    • 18
    • Theodoropoulos C., Qian Y.-H. and Kevrekidis I.G. (2000). Coarse stability and bifurcation analysis using time-steppers: a reaction-diffusion example. PNAS 97(18): 9840-9843
    • (2000) PNAS , vol.97 , pp. 9840-9843
    • Theodoropoulos, C.1    Qian, Y.-H.2    Kevrekidis, I.G.3
  • 49
    • 34250367538 scopus 로고    scopus 로고
    • A computational model for intercellular synchronization in the mammalian circadian clock
    • accepted for publication
    • To, T.-L., Henson, M.A., Herzog, E.D., Doyle III, F.J.: A computational model for intercellular synchronization in the mammalian circadian clock. Biophys. J. (accepted for publication)
    • Biophys. J.
    • To, T.-L.1    Henson, M.A.2    Herzog, E.D.3    Doyle Iii, F.J.4
  • 50
    • 0023857649 scopus 로고
    • Fructose 2,6-bisphosphate and glycolytic oscillations in skeletal muscle extracts
    • Tornheim K. (1988). Fructose 2,6-bisphosphate and glycolytic oscillations in skeletal muscle extracts. J. Biol. Chem. 263: 2619-2624
    • (1988) J. Biol. Chem. , vol.263 , pp. 2619-2624
    • Tornheim, K.1
  • 52
    • 0030857292 scopus 로고    scopus 로고
    • Dynamics of two-component biochemical systems in interacting cells: Synchronization and desynchronization of oscillations and multiple steady states
    • Wolf J. and Heinrich R. (1997). Dynamics of two-component biochemical systems in interacting cells: Synchronization and desynchronization of oscillations and multiple steady states. Biosystems 43: 1-24
    • (1997) Biosystems , vol.43 , pp. 1-24
    • Wolf, J.1    Heinrich, R.2
  • 53
    • 0034650451 scopus 로고    scopus 로고
    • Effect of cellular interaction on glycolytic oscillations in yeast: A theoretical investigation
    • Wolf J. and Heinrich R. (2000). Effect of cellular interaction on glycolytic oscillations in yeast: A theoretical investigation. Biochem. J. 345: 321-334
    • (2000) Biochem. J. , vol.345 , pp. 321-334
    • Wolf, J.1    Heinrich, R.2
  • 54
    • 0034088868 scopus 로고    scopus 로고
    • Transduction of intracellular and intercellular dynamics in yeast glycolytic oscillations
    • Wolf J., Passarge J., Somsen O.J.G., Snoep J.L., Heinrich R. and Westerhoff H.L. (2000). Transduction of intracellular and intercellular dynamics in yeast glycolytic oscillations. Biophys. J. 78: 1145-1153
    • (2000) Biophys. J. , vol.78 , pp. 1145-1153
    • Wolf, J.1    Passarge, J.2    Somsen, O.J.G.3    Snoep, J.L.4    Heinrich, R.5    Westerhoff, H.L.6
  • 55
    • 0037249229 scopus 로고    scopus 로고
    • The wiener-askey polynomial chaos for stochastic differential equations
    • 2
    • Xiu D.B. and Karniadakis G.E. (2002). The wiener-askey polynomial chaos for stochastic differential equations. SIAM J. Sci.Comput. 24(2): 619-644
    • (2002) SIAM J. Sci.Comput. , vol.24 , pp. 619-644
    • Xiu, D.B.1    Karniadakis, G.E.2
  • 56
    • 19944390619 scopus 로고    scopus 로고
    • An equation-free approach to uncertain quantification in dynamical systems
    • 3
    • Xiu D.B., Ghanem R. and Kevrekidis I.G. (2005). An equation-free approach to uncertain quantification in dynamical systems. IEEE Comput. Sci. Eng. J. (CiSE) 7(3): 16-23
    • (2005) IEEE Comput. Sci. Eng. J. (CiSE) , vol.7 , pp. 16-23
    • Xiu, D.B.1    Ghanem, R.2    Kevrekidis, I.G.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.