Cell cycle automaton

Patterns of Anticancer Drug Delivery by Simulations of a Cell Cycle Automaton. Chapter 10 in this book. 

We use these rules to simulate the dynamic behavior of the cell cycle automaton in a variety of conditions. Table 10.1 lists the values assigned in the various figures to the cell cycle length, presence or absence of cell cycle entrainment by the circadian clock, initial conditions, variability of cell phase duration, and probability of quitting the cell cycle. 

TablelO.l Parameter values and initial conditions considered in the various figures based on numerical simulations of the cell cycle automaton model. All figures were established for a uniform distribution of durations of cell cycle phases around a mean value, with variability V. Entrainment The cell...

Fig. 10.2 Waves through cell cycle phases in absence (a, b) or presence (c, d) of entrainment by the circadian clock. The variability of durations for all cell cycle phases is equal to 0% (left column) or 15% (right column). The curves, generated by numerical simulations of the cell cycle automaton model, show the proportions of cells in Cl, S, G2 or M phase as a function of time, for days 10-13. The time step used for simulations is equal to 1 min. The duration of the cell cycle before or in the absence of entrainment is 22 h. The successive phases of the cell cycle have the following mean durations G1 (9 h),...

Coupling the Cell Cycle Automaton to the Circadian Clock... 

The Cell Cycle Automaton Model Relation with Other Types of Cellular Automata... 

In simulating the cell cycle automaton response to 5-FU, we impose a circadian profile of the anticancer medication similar to that used in clinical oncology [30, 31] 5-FU is delivered in a semi-sinusoidal manner from 10p.m. to 10a.m., with a peak at 4 a.m. (Fig. 10.3b). During the remaining hours of the day and night, the drug concentration is set to zero. For comparison, we consider similar drug delivery patterns shifted in time, with peak delivery either at 10 a.m., 4 p.m., or 10 p.m. 

To clarify the reason why different circadian schedules of 5-FU delivery have distinct cytotoxic effects, we used the cell cycle automaton model to determine the time evolution of the fraction of cells in S phase in response to different patterns of circadian drug administration, for a cell cycle variability of 15%. The results, shown in Fig. 10.5, correspond to the case considered in Fig. 10.4, namely, entrainment of a 22-h cell cycle by the circadian clock. The data for Fig. 10.5a clearly indicate why the circadian schedule with a peak at 4 a.m. is the least toxic. The reason is that the fraction of cells in S phase is then precisely in antiphase with the circadian profile of 5-FU. Since 5-FU only affects cells in the S phase, the circadian delivery of the anticancer drug in this case kills but a negligible amount of cells. 

The cases of peak delivery at 10 a.m. (Fig. 10.5b) or 10 p.m. (Fig. 10.5d) are intermediate between the two preceding cases. Overlap between the peak of 5-FU and the peak of cells in S phase is only partial, but it is still greater in the case of the peak at 10 a.m., so that this pattern is the second most toxic, followed by the circadian delivery centered around 10 p.m. The comparison of the four panels Fig. 10.5a-d explains the results of Fig. 10.4a on the marked differences in cytotoxic effects of the four 5-FU circadian delivery schedules. The use of the cell cycle automaton helps clarify the dynamic bases that underlie the distinctive effects of the peak time in the circadian pattern of anticancer drug delivery. 

Fig. 10.7 Scheme of the operation of the cell cycle automaton step by step, from G1 to M phase. 

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. 

The results presented here point to the interest of measuring, both in normal and tumor cell populations, parameters such as the duration of the cell cycle phases and their variability, as well as the presence or absence of entrainment by the circadian clock. As shown by the results obtained with the cell cycle automaton model, these data are crucial for using the model to predict the differential outcome of various anticancer drug delivery schedules on normal and tumor cell populations. In a sub-... 

Here, as in a previous publication [33], we used the cell cycle automaton model to probe the cytotoxic effect of various patterns of circadian or continuous 5-FU delivery. The results provide a framework to account for experimental and clinical observations, and to help us predict optimal modes of drug delivery in cancer chronotherapy. By explaining the differential cytotoxicity of various circadian schedules of 5-FU delivery, the model clarifies the foundations of cancer chronothera-peutics. In view of its versatility and reduced number of parameters, the automaton model could readily be applied to probe the administration schedules of other types of anticancer medications active on other phases of the cell cycle. 

Altinok, A., Levi, F., Goldbeter, A. A cell cycle automaton model for probing circadian patterns of anticancer drug delivery. Adv. Drug Deliv. Rev. 2007,... 

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