Abstract
The paper reviews a series of models for circadian clocks and discusses their conclusions and predictions. Attention is focused on Pittendrigh's empirical model, two mathematical models by the author and Winfree's work.
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Literature
Andronov, A. A., A. A. Vitt and S. E. Khaikin. 1966.Theory of Oscillators. Oxford: Pergamon.
Aschoff, J. (Ed.) 1965.Circadian Clocks. Amsterdam: North-Holland.
Bünning, E. 1973.The Physiological Clock, 3rd ed. Springer, Berlin.
Engelmann, W., H. G. Karlsson and A. Johnsson. 1973. “Phase Shifts in theKalanchoe Petal Rhythm Caused by Light Pulses of Different Durations.”Int. J. Chronobiol.,1, 147–156.
Hastings, J. W. and H.-G. Schweiger (Eds.) 1976.The Molecular Basis of Circadian Rhythms. Berlin: Dahlem Konferenzen.
Johnsson, A. and H. G. Karlsson. 1972. “A Feedback Model for Biological Rhythms: I. Mathematical Description and Properties of the Model.”J. Theor. Biol.,36, 153–174.
Karlsson, H. G. and A. Johnsson. 1972. “A Feedback Model for Biological Rhythms: II. Comparisons with Experimental Results, Especially on the Petal Rhythm ofKalanchoe”J. Theor. Biol.,36, 175–194.
Menaker, M. (ed.). 1971.Biochronometry, Nat. Acad. Sci., Washington, D.C.
Minorsky, N. 1962.Nonlinear Oscillations. Princeton, N.J.: Van Nostrand-Reinhold.
Njus, D., F. M. Sulzman and J. W. Hastings. 1974. “Membrane Model for the Circadian Clock.”Nature,248, 116–120.
Njus, D. 1976. “Experimental approaches to membrane models.” InThe Molecular Basis of Circadian Rhythms (J. W. Hastings and H.-G. Schweiger, Eds.), Dahlem Konferenzen, Berlin, pp. 283–294.
Ottesen, E. A. 1965.B.A. Thesis, Princeton University.
Ottesen, E. A., C. S. Pittendrigh and S. Daan. 1976. Unpublished manuscript.
Pavlidis, T. 1965. “A New Model for Simple Neural Nets and its Application in the Design of a Neural Oscillator.”Bull. Math. Biophys.,27, 215–229.
—. 1967a. “A Mathematical Model for the Light Affected System in the Drosophila Eclosion Rhythm.”Bull. Math. Biophys.,29, 291–310.
—. 1967b. “A Model for Circadian Clocks.”Bull. Math. Biophys.,29, 781–791.
—. 1968. “Studies on Biological Clocks: A Model for the Circadian Rhythms of Nocturnal Organisms.” InLectures on Mathematics in Life Sciences (M. Gerstenhaber, Ed.), American Math. Soc., Providence, R.I., pp. 88–112.
—. 1971. “Populations of Biochemical Oscillators as Circadian Clocks.”J. Theor. Biol.,33, 319–338.
—. 1973a. “The Free Run Period of Circadian Rhythms and Phase Response Curves.”Am. Natur.,107, 524–530.
—. 1973b.Biological Oscillators: Their Mathematical Analysis. New York: Academic Press.
Pavlidis, T. 1976. “Spatial and Temporal Organization of Populations of Oscillators.” InThe Molecular Basis of Circadian Rhythms (J. W. Hastings and H.-G. Schweiger, Eds.), Dahlem Konferenzen, Berlin.
Pittendrigh, C. S. 1965. “The Circadian Oscillation inDrosophila Pseudoobscura Pupae: A Model for the Photoperiodic Clock.”Z. Pflantenphysiol.,54, 275–307.
—. 1974. “Circadian Organization in Cells and the Circadian Organization of Multicellular Systems.” InNeurosciences Third Study Program (F. O. Schmitt and F. G. Worden, Eds.), Cambridge, Mass.: M.I.T. Press.
Pittendrigh, C. S. 1976. “Circadian Clocks: What are They?” InThe Molecular Basis of Circadia Rhythms (J. W. Hastings and H.-G. Schweiger, Eds.), Dahlem Konferenzen, Berlin, pp. 11–48.
Swade, R. H. 1969. “Circadian Rhythms in Fluctuating Light Cycles: Toward a New Model of Entrainment.”J. Theor. Biol.,24, 227–239.
Tyson, J. I., S. G. A. Alivisatos, F. Grün, T. Pavlidis, O. Richter and F. W. Schneider. 1976. “Mathematical Background Group Report.” InThe Molecular Basis of Circadian Rhythms (J. W. Hastings and H.-G. Schweiger, Eds.), Dahlem Konferenzen, Berlin, pp. 85–108.
Wever, R. 1965. “A Mathematical Model for Circadian Rhythms.” InCircadian Clocks (Aschoff, J., Ed.) Amsterdam: North-Holland, pp. 47–63.
Winfree, A. T. 1970. “Integrated View of resetting a Circadian Clock.”J. Theor. Biol.,28, 327–374.
—. 1971. “Corkscrews and Singularities in Fruitflies: Resetting Behavior of the Circadian Eclosion Rhythm.” InBiochronometry (M. Menaker, Ed.), Nat. Acad. Sci., Washington, D.C., pp. 81–109.
—. 1973. “Resetting the Amplitude ofDrosophila's Circadian Chronometer.”J. Comp. Physiol.,85, 105–140.
—. 1975. “Unclocklike Behavior of Biological Clocks.”Nature,253, 315–319.
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Pavlidis, T. What do mathematical models tell us about circadian clocks?. Bltn Mathcal Biology 40, 625–635 (1978). https://doi.org/10.1007/BF02460734
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DOI: https://doi.org/10.1007/BF02460734