title: The cell division cycle: a physiologically plausible dynamic model can exhibit chaotic solutions.
abstract: A mitotic oscillator with one slowly increasing variable (tau L of the order of hours) and one rapidly increasing variable (tau R of the order of minutes) modulated by a timer (ultradian clock) gives an auto-oscillating solution: cells divide when this relaxation oscillator reaches a critical threshold to initiate a rapid phase of the limit cycle. Increasing values of the velocity constant in the slow equation give quasi-periodic, chaotic and periodic solutions. Thus dispersed and quantized cell cycle times are consequences of a chaotic trajectory and have a purely deterministic basis. This model of the dispersion of cell cycle times contrasts with many previous ones in which cell cycle variability is a consequence of stochastic properties inherent in a sequence of many thousands of reactions or the random nature of a key transition step.
authors.affiliation: Microbiology Group (PABIO), University of Wales College of Cardiff, UK.
authors.forename: D
authors.initials: D
authors.lastname: Lloyd
authors.forename: A L
authors.initials: AL
authors.lastname: Lloyd
authors.forename: L F
authors.initials: LF
authors.lastname: Olsen
mesh_terms: D000204:Activity Cycles; D002453:Cell Cycle / Q000502:physiology*; D002455:Cell Division / Q000502:physiology*; D003198:Computer Simulation; D008433:Mathematics; D008954:Models, Biological; D013997:Time Factors