Cardiac oscillations

Thanks to the studies of Hodgkin Huxley, which culminated in 1952 with the publication of a series of articles, of which the last was of theoretical nature, the physicochemical bases of neuronal excitability giving rise to the action potential were elucidated. Soon after, Huxley (1959) showed how a nerve cell can generate a train of action potentials in a periodic manner (see also Connor, Walter McKown, 1977 Aihara Matsumoto, 1982 Rinzel Ermentrout, 1989). Even if the properties of the ionic channels involved have not yet been fully elucidated, cardiac oscillations originate in a similar manner from the pacemaker properties of the specialized, electrically excitable tissues of the heart (Noble, 1979,1984 Noble Powell, 1987 Noble, DiFrancesco Denyer, 1989 DiFrancesco, 1993). These examples remained the only biological rhythms whose molecular mechanism was known to some extent, until the discovery of biochemical oscillations. 

Glass, L., M.R. Guevara, A. Shrier R. Perez. 1983. Bifurcation and chaos in a periodically stimulated cardiac oscillator. Physica 7D 89-101. 

Biological and physiological systems are typical complex systems, which provide examples of aperiodicity and chaos [1-7]. Aperiodic cardiac oscillations are reflected in ECG for different cases of arrhythmia Fig. (12.1). Similarly, chaotic, aperiodic and noisy oscillations are observed in EEC in specific cases as shown in Fig. (12.2). Closely allied with chemical oscillations are membrane oscillations which have considerable relevance in physiological processes including neurological and cardiac disorders in the context of detection and control. 

Until the 1950s, the rare periodic phenomena known in chemistry, such as the reaction of Bray [1], represented laboratory curiosities. Some oscillatory reactions were also known in electrochemistry. The link was made between the cardiac rhythm and electrical oscillators [2]. New examples of oscillatory chemical reactions were later discovered [3, 4]. From a theoretical point of view, the first kinetic model for oscillatory reactions was analyzed by Lotka [5], while similar equations were proposed soon after by Volterra [6] to account for oscillations in predator-prey systems in ecology. The next important advance on biological oscillations came from the experimental and theoretical studies of Hodgkin and Huxley [7], which clarified the physicochemical bases of the action potential in electrically excitable cells. The theory that they developed was later applied [8] to account for sustained oscillations of the membrane potential in these cells. Remarkably, the classic study by Hodgkin and Huxley appeared in the same year as Turing s pioneering analysis of spatial patterns in chemical systems [9]. 

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). 

Kurz FT, Aon MA, O Rourke B et al (2010) Spatio-temporal oscillations of individual mitochondria in cardiac myocytes reveal modulation of synchronized mitochondrial clusters. Proc Natl Acad Sci U S A 107 14315-14320... 

These oscillations set the stage for the development of torsades de pointes, a potentially lethal cardiac arrhythmia. 

There are three types of muscle cells smooth, skeletal, and cardiac. In all types of muscle, contraction occurs via an actin myosin sliding filament system, which is regulated by oscillations in intracellular calcium levels. 

The last part of chapter 9 is devoted to a study of intracellular Ca waves. Computer simulations show that the model based on CICR can account for the two types of wave seen in the experiments in different cell types (Dupont Goldbeter, 1992b, 1994). When the period of the oscillations is of the order of 1 s, as in cardiac cells, the wave takes the... 

Glycolytic oscillations have recently been demonstrated in yet another type of cell, belonging to the cardiac tissue (O Rourke et al, 1994). Here, the physiological function of glycolytic oscillations is unknown, but it is likely that they may give rise to certain forms of arrhythmia, since they can modulate the membrane potential in these cells. In a similar manner, oscillations of intracellular Ca (see chapter 9) in heart cells provide another source of cardiac arrhythmia. 

An analogous explanation at the molecular level can be proposed for the spontaneous emergence of the cardiac rhythm at a precise stage of embryonic development. This appearance of one of the most remarkable biological rhythms results from the fact that in the course of development cells in nodal tissues of the heart acquire the capability to generate periodically, in an autonomous manner, the electrical signal that initiates cardiac contraction (Fukii, Hirota Kamino, 1981). As for the neurons, the variation of certain ionic conductances would endow these cells with the property of oscillating spontaneously, while other cardiac cells would only be excitable (DeHaan, 1980). 

Li Rinzel, 1994). The latter reductions therefore yield a minimal model for Ca oscillations, like the earlier, two-pool minimal model considered below, which takes into account only CICR and not the inhibition of Ca " release at high levels of cytosolic Ca. A one-pool version of this model in which Ca and IP3 behave as co-agonists for Ca " release is presented in section 9.4. A model based on the bellshaped calcium dependence of the ryanodine-sensitive calcium channel was recently proposed for calcium dynamics in cardiac myocytes (Tang Othmer, 1994b). 

The waveform of the oscillations predicted by the model for cytosolic Ca (fig. 9.7) resembles that of the spikes observed for a number of cells stimulated by external signals. In particular, the rise in cytosolic Ca is preceded by a rapid acceleration that starts from the basal level although it originates from a different, nonelectrical mechanism, this pattern, which is reminiscent of the pacemaker potential that triggers autonomous spiking in nerve and cardiac cells (DiFrancesco, 1993), has been observed (Jacob et al, 1988) in epithelial cells stimulated by histamine (see fig. 9.3). As in the model by Meyer Stryer (1988), the oscillations of Ca " in the intracellular store have a saw-tooth appearance (see the dashed ctirve in fig. 9.7). Here, however, the phenomenon does... 

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