Oscillators, cellular

Figure 7.8 Propagation of BZ reaction fronts in an oscillating cellular flow. Images are shown every flow oscillation period. Left Phase-locked front in which the concentration pattern at the front edge repeats every oscillation period. Right example of an unlocked front. From Paoletti and Solomon (2005b).

Takahashi, J.S., N. Murakami, S.S. Nikaido, B.L. Pratt L.M. Robertson. 1989. The avian pineal, a vertebrate model system of the circadian oscillator Cellular regulation of circadian rhythms by light, second messengers, and macromolecular synthesis. Recent Progr. Horm. Res. 45 279-352. 

Steriade, M. (1999). Cellular substrates of oscillations in corticothalamic systems during states of vigilance. In Handbook of Behavioral State Control, Cellular and Molecular Mechanisms, ed. R. Lydic H. A. Baghdoyan, pp. 327-48. New York, NY CRC Press. 

A. Goldbeter, Biochemical Oscillations and Cellular Rhythms The Molecular Bases of Periodic and Chaotic Behaviour, Cambridge University Press, Cambridge, United Kingdom (1997). 

U. Schibler and F. Naef, Cellular oscillators Rhythmic gene expression and metabolism. Curr. Opin. Cell. Biol. 17, 223 229 (2005). 

On the other hand stable cavitation (bubbles that oscillate in a regular fashion for many acoustic cycles) induce microstreaming in the surrounding liquid which can also induce stress in any microbiological species present [5]. This type of cavitation may well be important in a range of applications of ultrasound to biotechnology [6]. An important consequence of the fluid micro-convection induced by bubble collapse is a sharp increase in the mass transfer at liquid-solid interfaces. In microbiology there are two zones where this ultrasonic enhancement of mass transfer will be important. The first is at the membrane and/or cellular wall and the second is in the cytosol i. e. the liquid present inside the cell. 

From a mathematical point of view, the onset of sustained oscillations generally corresponds to the passage through a Hopf bifurcation point [19] For a critical value of a control parameter, the steady state becomes unstable as a focus. Before the bifurcation point, the system displays damped oscillations and eventually reaches the steady state, which is a stable focus. Beyond the bifurcation point, a stable solution arises in the form of a small-amplitude limit cycle surrounding the unstable steady state [15, 17]. By reason of their stability or regularity, most biological rhythms correspond to oscillations of the limit cycle type rather than to Lotka-Volterra oscillations. Such is the case for the periodic phenomena in biochemical and cellular systems discussed in this chapter. The phase plane analysis of two-variable models indicates that the oscillatory dynamics of neurons also corresponds to the evolution toward a limit cycle [20]. A similar evolution is predicted [21] by models for predator-prey interactions in ecology. 

New examples of cellular rhythms have recently been uncovered (Table II). These include periodic changes in the intracellular concentration of the transcription factor NF-KB and of the tumor suppressors p53, stress-induced oscillations in the transport of the transcription factor Msn2 between cytoplasm and nucleus in yeast, the segmentation clock that is responsible for the... 

Some of the main types of cellular regulation associated with rhythmic behavior are listed in Table III. Regulation of ion channels gives rise to the periodic variation of the membrane potential in nerve and cardiac cells [27, 28 for a recent review of neural rhythms see, for example, Ref. 29]. Regulation of enzyme activity is associated with metabolic oscillations, such as those that occur in glycolysis in yeast and muscle cells. Calcium oscillations originate... 

As indicated above, theoretical models for biological rhythms were first used in ecology to study the oscillations resulting from interactions between populations of predators and preys [6]. Neural rhythms represent another field where such models were used at an early stage The formalism developed by Hodgkin and Huxley [7] stiU forms the core of most models for oscillations of the membrane potential in nerve and cardiac cells [33-35]. Models were subsequently proposed for oscillations that arise at the cellular level from regulation of enzyme, receptor, or gene activity (see Ref. 31 for a detailed fist of references). 

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. 

Glycolytic oscillations in yeast cells provided one of the first examples of oscillatory behavior in a biochemical system. They continue to serve as a prototype for cellular rhythms. This oscillatory phenomenon, discovered some 40 years ago [36, 37] and still vigorously investigated today [38], was important in several respects First, it illustrated the occurrence of periodic behavior in a key metabolic pathway. Second, because they were soon observed in cell extracts, glycolytic oscillations provided an instance of a biochemical clock amenable to in vitro studies. Initially observed in yeast cells and extracts, glycolytic oscillations were later observed in muscle cells and evidence exists for their occurrence in pancreatic p-cells in which they could underlie the pulsatile secretion of insulin [39]. 

The three best-known examples of biochemical oscillations were found during the decade 1965-1975 [40,41]. These include the peroxidase reaction, glycolytic oscillations in yeast and muscle, and the pulsatile release of cAMP signals in Dictyostelium amoebae (see Section V). Another decade passed before the development of Ca " " fluorescent probes led to the discovery of oscillations in intracellular Ca +. Oscillations in cytosolic Ca " " have since been found in a variety of cells where they can arise spontaneously, or after stimulation by hormones or neurotransmitters. Their period can range from seconds to minutes, depending on the cell type [56]. The oscillations are often accompanied by propagation of intracellular or intercellular Ca " " waves. The importance of Ca + oscillations and waves stems from the major role played by this ion in the control of many key cellular processes—for example, gene expression or neurotransmitter secretion. 

Only deterministic models for cellular rhythms have been discussed so far. Do such models remain valid when the numbers of molecules involved are small, as may occur in cellular conditions Barkai and Leibler [127] stressed that in the presence of small amounts of mRNA or protein molecules, the effect of molecular noise on circadian rhythms may become significant and may compromise the emergence of coherent periodic oscillations. The way to assess the influence of molecular noise on circadian rhythms is to resort to stochastic simulations [127-129]. Stochastic simulations of the models schematized in Fig. 3A,B show that the dynamic behavior predicted by the corresponding deterministic equations remains valid as long as the maximum numbers of mRNA and protein molecules involved in the circadian clock mechanism are of the order of a few tens and hundreds, respectively [128]. In the presence of molecular noise, the trajectory in the phase space transforms into a cloud of points surrounding the deterministic limit cycle. 

Clock oscillation occurs first at a cellular level. The clock genes so far identified in mammals are structurally similar to those in Drosophila (Young Kay 2001). This suggests that mammals and Drosophila utilize similar components to generate circadian ( 24 h) rhythms. Mammalian clock research is now showing whether the core feedback loop of clock genes speculated to be present in Drosophila (Hardin et al 1990) is also conserved in mammals. 

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