Relaxation oscillator cell cycle

Experiments carried out on mitosis in Physarum polycephalum (Kaufmann Wille, 1975 Tyson Sachsenmaier, 1978) did not allow a definitive conclusion in favour of one of the two views. The difficulty came from the fact that, short of the identification of the true biochemical variables driving the cell cycle, it was difficult to demonstrate the existence of a limit cycle in Physarum. Experiments based on the fusion of two plasmodia taken at different phases of the mitotic cycle or on the effect of heat shocks aimed at demonstrating the existence of a singular point from which the limit cycle would be reached with an indefinite phase (Winfree, 1974,1980,1987). These experiments did not allow the distinction to be made between a limit cycle characterized by relaxation oscillations and a discontinuous mechanism of the type discussed above. 

Control cycle is one depolarization and repolarization of the transmembrane voltage. Control wave (or slow wave) is the continuing rhythmic electrical activity recorded at any one site. It was assumed to be generated by the smooth muscle cells behaving like a relaxation oscillator at that site. However, recent evidence [Hara et al, 1986 Suzuki et al. 1986 Barajas-Lopez et al, 1989 Serio et al, 1991] indicates that it is generated by a system of interstitial cells of Cajal (ICC) and smooth muscle cells at that site. ECA is the totality of the control waves recorded at one or several sites. Response Potentials (or spikes) are the rapid oscillations of transmembrane voltage in the depolarized state of smooth muscle cells. They are associated with muscular contraction and their occurrence is assumed to be in response to a control cycle when acetylcholine is present. ERA is the totality of the groups of response potentials at one or several sites. 

Wille, 1975). The division cycle occurs in these cells with a periodicity close to 12 h. Mixing experiments relying on the fusion of plasmodia taken at different times over the cycle showed phase advances or delays that would be typical of the behaviour expected if mitosis were driven by a continuous oscillator of a moderate relaxation nature (Kauffman, 1974 Kauffman Wille, 1975 Wille, Scheffey Kau an, 1977). Implicit in the limit cycle description is the assumption that one of the variables of the oscillator behaves as a mitogenic factor once this variable exceeds a certain threshold, mitosis would ensue. A specific prediction of the limit cycle model of mitosis is that finely tuned perturbations may transiently suppress oscillations. In this case, mitosis would eventually resume, with undefined phase, possibly after a delay corresponding to a few cycles in which the mitogenic factor oscillates below its threshold level. As the trajectory followed by the oscillator eventually approaches the asymptotic limit cycle, mitosis would occur when the threshold is again exceeded. 

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