Oscillations in biological systems

At the same time as the Belousov-Zhabotinsky reaction provided a chemical prototype for oscillatory behavior, the first experimental studies on the reaction catalyzed by peroxidase [24] and on the glycolytic system in yeast (to be discussed in Section 111) demonstrated the occurrence of biochemical oscillations in vitro. These advances opened the way to the study of the molecular bases of oscillations in biological systems. 

The general concept of the excitation of coherent oscillations in biological systems, with limited reference to membranes, has been nicely reviewed by Kaiser. A discussion of Frohlich s model is presented in terms of how it possesses the requisite characteristics to undergo various types of phase transitions subsequent to external perturbations. Reference, however, to the specific involvement of biological membranes in such phase transitions is only briefly mentioned. The emphasis in Kaiser s analysis of Frohlich s basic hypothesis is on the idea that stable limit cycle behavior... 

F. Kaiser, Coherent Oscillations in Biological Systems. I. Bifurcation Phenomena and Phase Transitions in an Enzyme-Substrate Reaction with Ferroelectric Behavior, Z. Naturforsch. 33a, 294-304 (1978). 

Fig. 6-5. The evolution of the lagoon s waters in response to oscillations in biological productivity. The results show the adjustment of the system from an initial composition equal to that of seawater. This figure shows isotope ratios, calcium concentration, the saturation index, and productivity.

First model for oscillating system was proposed by Volterra for prey-predator interactions in biological systems and by Lotka for autocatalytic chemical reactions. Lotka s model can be represented as... 

One may wonder whether a purely harmonic model is always realistic in biological systems, since strongly unharmonic motions are expected at room temperature in proteins [30,31,32] and in the solvent. Marcus has demonstrated that it is possible to go beyond the harmonic approximation for the nuclear motions if the temperature is high enough so that they can be treated classically. More specifically, he has examined the situation in which the motions coupled to the electron transfer process include quantum modes, as well as classical modes which describe the reorientations of the medium dipoles. Marcus has shown that the rate expression is then identical to that obtained when these reorientations are represented by harmonic oscillators in the high temperature limit, provided that AU° is replaced by the free energy variation AG [33]. In practice, tractable expressions can be derived only in special cases, and we will summarize below the formulae that are more commonly used in the applications. 

Synchronous processes represent the most demonstrative and unique example of chemical reaction ensembles, arranged in time and space. Interest in synchronous chemical reactions is also so much keener, because in biological systems many processes are synchronous. This means that biochemical reactions are arranged and performed in systems with molecular and permolecular structures, which is the chemist s pipe dream . Studies performed in recent decades have allowed the development of the interaction theory for synchronous chemical reactions at two levels—microscopic and macroscopic. Strictly speaking, parallel reactions may also be taken as synchronous reactions although proceeding simultaneously in the reaction system, they are characterized by the absence of any interaction between them. However, such synchronous reactions are trivial and of no special interest for chemistry. It is of much more importance when they interact and, therefore, induce oscillations in yields of synchronous reaction products. 

Here, we provide new insights that may aid in understanding the variety of oscillations displayed in biological systems and how they may be related to the maintenance or loss of control in such systems. Examples of periodic phenomena abound in biological systems, in many cases due to fluctuations of ligand interacting with a receptor. 

We may conclude that many important biological rhythms originate from positive feedback mechanisms whose nonlinearity is further strengthened by the cooperative nature of the regulatory process. Although the detailed molecular implementation of the feedback process differs in each case, it is the self-amplification with which it is associated that gives rise to instabilities followed by sustained oscillations in biochemical systems as well as in cardiac or neural cells (Goldbeter, 1992). 

H. Pohl, Natural Oscillating Fields of Cells, in Coherent Excitations in Biological Systems (H. Frohlich and F. Kremer, eds.). Springer, Berhn (1983), pp. 199-210. 

It is the most basic and properly explained model of oscillating reactions. In 1921, Lotka proposed a model to explain some oscillatory phenomena in biological systems [29]. This model composed numbers of sequential steps which are presented in Table 1.1. As suggested, the each step referred to a specific mechanism in which the reactant molecules come together to form some useful intermediates and products. 

In most chemical oscillators, it is difficult or impossible to follow the concentrations of more than a small fraction of the reactants and intermediates. Experimental determination of all the rate constants is likewise a forbidding prospect. These difficulties in obtaining a complete set of measurements are even greater in biological systems, where the variety and complexity of relevant... 

Systems of coupled nonlinear oscillators are nsed to explain the dynamics of various biological and physiological systems. This is because most of the interesting phenomena in biological systems occur as a result of the collective behavior of the entities in the system and also becanse we are more interested in the collective dynamics of the systems (macroscopic properties), instead of the dynamics of individual entities. 

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