Oscillation autonomous biochemical

In this paper I shall discuss, in a general way, some basic dynamical properties of biochemical reaction schemes that are subjected to an external perturbation that oscillates in time. The first part of this paper will deal with the ways in which a weak external oscillating stimulus is able to alter the concentrations of metabolites in a biochemical system. This part will, in particular, consider what happens when the reaction system already oscillates in a limit cycle mode due to non-linearities in its reaction kinetics. It will be shown that such an autonomous biochemical oscillator may exhibit an enhanced sensitivity to a narrow range of externally applied frequencies. 

Although these arguments have been presented for reaction systems whose rates are forced by an external oscillator, they remain true for autonomous biochemical oscillations where ot and are nonlinear functions of metabolite concentrations. That is, the rate of removal of a labeled compound through a reaction step whose rate is oscillating due to nonlinear kinetics will be enhanced over an equivalent system that maintains the same mean chemical flux and mean concentrations of metabolites but does not oscillate. This has been demonstrated numerically ( 6) on the reaction system (1) from the previous section using the full kinetic equations... 

IIIC) 1973 Vavilin, V. A., Zhabotinskii, A. M., Zaikin, A. N. A Study of a Self-Oscillatory Chemical Reaction, I. The Autonomous System, In Biological and Biochemical Oscillations (Ed. B. Chance), 71-79... 

The periodic recurrence of cell division suggests that globally the cell cycle functions like an autonomous oscillator. An extended model incorporating the sequential activation of the various cyclin-dependent kinases, followed by their inactivation, shows that even in the absence of control by cell mass, this sequence of biochemical events can operate as a limit cycle oscillator [145]. This supports the union of the two views of the cell cycle as dominoes and clock [146]. Because of the existence of checkpoints, however, the cell cycle stops at the end of certain phases before engaging in the next one. Thus the cell cycle looks more like an oscillator that slows down and makes occasional stops. A metaphor for such behavior is provided by the movement of the round plate on the table in a Chinese restaurant, which would rotate continuously under the movement imparted by the participants, were it not for frequent stops. 

Ingalls, B. (2004) Autonomously oscillating biochemical systems parametric sensitivity of extrema and period. Syst. Biol. 1, 62-70. 

Fig. 7.5. Incorporating the variation of biochemical parameters into the description of the evolution of the mechanism of intercellular communication in D. dis-coideum. The sigmoidal increase observed during the 6h that follow the beginning of starvation for adenylate cyclase (

Ohmori, T. and Yang, R.Y.K. (1994) Autonomous pH oscillations in an immobilized papain membrane system. Biotechnal. Appl. Biochem., 20, 67-78. 

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