Cell cycle oscillations

J. R. Pomerening, S. Y. Kim, and J. E. Eerrell, Jr. Systems-level dissection of the cell-cycle oscillator Bypassing positive feedback produces damped oscillations. Cell 122, 565-578 (2005). 

The cell cycle oscillator is one of the best studied cellular signaling networks in terms of kinetic models. Readers are encouraged to consult the very readable paper [198] and book chapter [197] by John Tyson and his colleagues. For a succinct review of recent studies of various oscillations in cell biology, see [120],... 

Pomerening JR, Sontag ED, Ferrell Jr JE. Building a cell cycle oscillator hysteresis and bistability in the activation of Cdc2. Nat. Cell Biol. 2003 5 346-351. 

Growth-factor control of the cell cycle oscillator(s)... 

Duboc P, Marison IW, von Stockar U (1996) Physiology of Saccharomyces cerevisiae during Cell Cycle Oscillations. J Biotechnol 51 57-72... 

Figure 14 Estimation of the biomass formation rate from the carbon, degree of reduction and enthalpy balances during cell cycle oscillations at a dilution rate of 0.10 h. (Redrawn from Reference [53] with permission of the author and publisher).

Gabrielli, B. G., Roy, L. M., Gautier, J., Philippe, M., and Mailer, J. L. (1992a). A afc2-related kinase oscillates in the cell cycle independently of cyclins G2/M and cdc2. J. Biol. Chem. 267 1969-1975. 

Some of the main examples of biological rhythms of nonelectrical nature are discussed below, among which are glycolytic oscillations (Section III), oscillations and waves of cytosolic Ca + (Section IV), cAMP oscillations that underlie pulsatile intercellular communication in Dictyostelium amoebae (Section V), circadian rhythms (Section VI), and the cell cycle clock (Section VII). Section VIII is devoted to some recently discovered cellular rhythms. The transition from simple periodic behavior to complex oscillations including bursting and chaos is briefly dealt with in Section IX. Concluding remarks are presented in Section X. 

The cell cycle is a key process that recurs in a periodic manner. Early cell cycles in amphibian embryos are driven by a mitotic oscillator. This oscillator produces the repetitive activation of the cyclin-dependent kinase cdkl, also known as cdc2 [131]. Cyclin synthesis is sufficient to drive repetitive cell division cycles in amphibian embryonic cells [132]. The period of these relatively simple cell cycles is of the order of 30 min. In somatic cells the cell cycle becomes longer, with durations of up to 24 h or more, owing to the presence of checkpoints that ensure that a cell cycle phase is properly completed before the cell progresses to the next phase. The cell cycle goes successively through the phases Gl, S (DNA replication), G2, and M (mitosis) before a new cycle starts in Gl. After mitosis cells can also enter a quiescent phase GO, from which they enter Gl under mitogenic stimulation. 

The interplay between oscillations and bistability has been addressed in detailed molecular models for the cell cycles of amphibian embryos, yeast and somatic cells [138-141]. The predictions of a detailed model for the cell cycle in yeast were successfully compared with observations of more than a hundred mutants [142]. Other theoretical studies focus on the dynamical properties of particular modules of the cell cycle machinery such as that controlhng the Gl/S transition [143]. 

If the cell cycle in amphibian embryonic cells appears to be driven by a limit cycle oscillator, the question arises as to the precise dynamical nature of more complex cell cycles in yeast and somatic cells. Novak et al. [144] constructed a detailed bifurcation diagram for the yeast cell cycle, piecing together the diagrams obtained as a function of increasing cell mass for the transitions between the successive phases of the cell cycle. In these studies, cell mass plays the role of control parameter a critical mass has to be reached for cell division to occur, provided that it coincides with a surge in cdkl activity which triggers the G2/M transition. 

The periodic recurrence of cell division suggests that globally the cell cycle functions like an autonomous oscillator. An extended model incorporating the sequential activation of the various cyclin-dependent kinases, followed by their inactivation, shows that even in the absence of control by cell mass, this sequence of biochemical events can operate as a limit cycle oscillator [145]. This supports the union of the two views of the cell cycle as dominoes and clock [146]. Because of the existence of checkpoints, however, the cell cycle stops at the end of certain phases before engaging in the next one. Thus the cell cycle looks more like an oscillator that slows down and makes occasional stops. A metaphor for such behavior is provided by the movement of the round plate on the table in a Chinese restaurant, which would rotate continuously under the movement imparted by the participants, were it not for frequent stops. 

R. R. Klevecz, J. Bolen, G. Forrest, and D. B. Murray, A genomewide oscillation in transcription gates DNA replication and cell cycle. Proc. Natl. Acad. Sci. USA 101, 1200-1205 (2004). 

Oscillating changes in the activity of the cell cycle machinery, with protein kinases as the most important component... 

Entry into and the course of mitosis are primarily determined by the activity of the CDC2 kinase. The CDC2 kinase in the active form exists as a complex with cychn B and, together with the cyclin, forms the mitosis promoting factor, MPF. The activity of MPF oscillates in the cell cycle and is the triggering factor for entry of the cell into M phase. 

The top panels in Fig. 10.2 show the oscillations in the fraction of cells in the different cell cycle phases, as a function of time, in the absence of entrainment by the circadian clock. In the case considered, the duration of the cell cycle is 22 h, and the variability V is equal to 0% (Fig. 10.2a) or 15% (Fig. 10.2b). When variability is set to zero, no desynchronization occurs and the oscillations in the successive phases of the cell cycle are manifested as square waves that keep a constant amplitude in a given phase. Conversely, when variability increases up to 15% in the absence of entrainment (Fig. 10.2b), the amplitude of the oscillations decreases, reflecting enhanced desynchronization. 

The cell cycle automaton model permits us to clarify the reason why circadian delivery of 5-FU is least or most toxic when it peaks at 4 a.m. or 4 p.m., respectively. Indeed, the model allows us to determine the position of the peak in S-phase cells relative to that of the peak in 5-FU. As shown in Fig. 10.5, 5-FU is least cytotoxic when the fraction of S-phase cells oscillates in antiphase with 5-FU (when 5-FU peaks at 4 a.m.) and most toxic when both oscillate in phase (when 5-FU peaks at 4 p.m). Intermediate cytotoxicity is observed for other circadian patterns of 5-FU (when the drug peaks at 10 a.m. or 10 p.m.), for which the peak of 5-FU partially overlaps with the peak of S-phase cells. For the continuous infusion of 5-FU, the peak in S-phase cells necessarily occurs in the presence of a constant amount of 5-FU. Hence, the constant delivery pattern is nearly as toxic as the circadian pattern peaking at 4 p.m. 

To some extent the idea of resonance is also present in the case of circadian 5-FU delivery. Indeed, the circadian patterns of 5-FU which peak at 4 a.m. or 4 p.m. correspond to oscillations that are, respectively, in antiphase or in corresponding phase with the circadian variation of the fraction of cells in S phase. This effect can be seen even for cell cycle durations that differ from 24 h, because of the entrainment of the cell cycle by the circadian clock. 

Interestingly, FIA can also be operated without an injection and gives valuable results. To this end we stained the DNA within yeast cells removed at a minute flux from a reactor and were able to quantify the amount of DNA online thus giving evidence for the cell-cycle dependence of oscillations [397]. 

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