Oscillatory influx

What is the relative development in time with the GA-controlled variation of the EBR of the two types of systems, one with constant influx of glucose, the other with an oscillatory influx of glucose, with average influx the same as in the constant influx case ... 

In the oscillatory influx of glucose, we drive the initially stable focus with a given period (frequency) and amplimde of the imposed sinusoidal glucose oscillation (a =... 

Fig. 10.5 Plot of the ATP/ADP ratio versus (a) the numher of generations in the GA, (h) for the oscillatory influx of glucose with the amplitude 0.5 mM/min (deterministic case), (c) the numher of generations for the constant influx of glucose. In (a) and (c), the highest value of the ATP/ADP ratio among 24 individuals at each generation by the GA is plotted and shows that systems with the constant influx of glucose take about double the generations necessary to reach the autonomous oscillation than systems with the oscillatory influx of glucose. (From [11].)...

The imposition of an oscillatory influx of glucose on the reaction mechanism shown in fig. 10.3, initially in a state of no oscillations (in a node or a focus), may have... 

Fig. 10.6 The frequency density versus number of generations to reach the bifurcation (a) the oscillatory influx (average 30) and (b) the constant influx (average 59). (From [11].)...

These equations were solved numerically and in Fig. 15.5 we show the ratio of the efficiency as defined in (15.29) for an oscillatory influx of reactants to that efficiency for a steady (constant) influx vs. w, the frequency of the oscillatory influx, (15.25). The autonomous system, with a steady influx, is in a stable focus, that is the autonomous system on being perturbed briefly returns to the stable state with an oscillatory component. In order to emphasize the effects of an oscillatory influx, conditions were chosen for the steady influx such that only 10% of the heat input is converted to work. 

We see that substantial increases in efficiency can be achieved with an oscillatory influx, as much as 30% for the conditions chosen. Variations in the ratio of efficiencies shown in Fig. 15.5 depend both on the amplitue and frequency of the periodic perturbation of the input (and output) flux. The increase in the ratio of frequencies at certain frequencies u> are related to resonance phenomena and appropriate phase relations of the response of the system to the oscillatory influx. At higher amplitudes of oscillatory perturbations there are two resonance peaks (an issue we shall re-visit in later chapters in which we dicuss perturbing chemical reactions). 

Fig. 15.5. Plot of the ratio of the efficiency, (15.29), for the case of an oscillatory influx into the CSTR, to that for a steady influx, vs. the frequency of the oscillatory influx cj, for four different amplitudes of perturbation , (15.25), the smallest being 0.1 (dotted line), and the largest 0.4 (solid line). The symbol uJo denotes the frequency of the damped oscillation in the autonomous system. From [4]...

Measurements consist of the temperature of the products and their chemical composition. Typical results are shown in Fig. 15.9 in plots of an oscillatory influx and the temperature of the reaction products vs. time. 

Protons are pumped in living systems to establish a proton gradient, and the energy necessary for this pumping is frequently provided by the hydrolysis of ATP, in which ADP and phosphate are formed [7]. In this section, we study a model of a proton pump found in the plasma membrane of plants [8-12] and include the coupling of potassium and calcium ion transport. As in prior examples, we calculate the thermodynamic efficiency [13] of the proton pump with a constant influx of ATP and compare that to the thermodynamic efficiency with an oscillatory influx of ATP, the average of which is the same as the constant concentration of ATP. 

In formulating the mechanism of the proton pump, we require the presence of certain nonlinearities to find the possibility of changing the dissipation, or the efficiency, with an oscillatory input of ATP. The minimum elements of a proton pump, although nonlinear, lead only to monotone relaxation kinetics, and thus only to decreases in efficiency upon imposition of an oscillatory influx of ATP. However, by including the coupling of other ion transport processes, such as those of potassium and calcium, the mechanism of the proton pump behaves like a damped oscillator, which has been observed in experiments... 

With that property a change in efficiency, increases and decreases, is feasible with an oscillatory influx of ATP. 

The relative efficiency is clearly a function of the frequency of the ATP oscillatory influx, with increases in certain ranges of frequency and decreases... 

Fig. 17.9. Plot of the phase difference between the Gibbs free energy change and the rate of the HRP reaction in units of 2n for the data presented in Fig. 17.7a. The darkened symbols denote the region of oscillatory influx of O2 (from [15])...

Fig. 17.10. Plots of average NADH concentrations triangles) and average dissipation (diamonds) vs. time for the data shown in Figs. 17.7a and 17.7b, respectively. Darkened symbols designate regions of oscillatory influx of O2 (from [15])...

Li Z, Hatton GI 1996 Oscillatory bursting of phasically firing rat supraoptic neurones in low-Ca medium Na influx, cytosolic Ca and gap junctions. J Physiol 496 379-394... 

Glycosides increase intracellular sodium and also extracellular potassium by inhibitory actions on sodium potassium ATPase. Thus, with chronic therapy, because intracellular sodium is increased, phase 0 may be blunted slightly. The increase in extracellular potassium results in a decrease in the rate of repolarization and thus a decrease in the slope of phase 3 of the action potential, and a skewed appearance. This results in a longer time for the membrane to repolarize and, accordingly, an increase in the effective refractory period. Because the objective of the drug is to increase the influx of calcium, the faster influx of calcium results in a shortened phase 2, because a shorter time is required for the membrane to reach the equilibrium potential for calcium. Finally, phase 4 is elevated and increased in slope, due to the alterations in sodium and potassium concentration. This, with chronic therapy, and particularly as toxicity is approached, results in delayed oscillatory afterpotentials (see Figure). 

The first GA search was for oscillations in the possible reaction mechanisms given that the GA may vary the influx bromide and bromate concentrations over ranges that include the observations in [28]. For that purpose we used the so-called NFT rate coefficients. Under these conditions, no oscillations were found in any of the three possible three-step mechanisms. The GA reveals that there are two different groups of oscillatory mechanisms in the four-step and five-step sets. The first group of reaction sets of elementary steps consists of the reactions (1,2,4,5), (1,2,4,5,6), and (1,2,4,5,7). For this group, the form of the oscillations is shifted only in phase among these three reaction mechanisms thus, the four-step (1,2,4,5) is an irreducible mechanism and the elementary steps 6 or 7 are not essential for an oscillatory mechanism. 

In the earlier chapter, we have discussed the emergence of time-order in chemical reactions in continuously stirred tank reactor (CSTR) and have discussed the concept of negative and positive feedback for occurrence of oscillatory reactions. In this respect, experimental studies of oscillatory reactions in batch reactors have been investigated in great depth which has provided convincing evidence for the important role of auto-catalytic and inhibitory reactions in oscillatory reactions. Rate of internal production is controlled by the influx of reactants from external source. 

In (a) and (b) there is an efficiency increase of 1.008 and 1.08, respectively, in comparing the oscillatory input flux with constant input flux the temperature variation and the flux are in phase. In (c) the efficiency is 0.976 and the temperature variation and the flux are not in phase. The changes in efficiency are smaller here than in the calculations. Fig. 15.5, since the possible conversion to work, for constant influx, is more efficient here (about 26%) compared to about 10% in the example in the calculations. Further experiments are... 

Many chemical and biochemical reactions can be in an oscillatory regime in which the concentrations of intermediates and products vary in a regular oscillatory way in time the oscillations may be sinusoidal but usually are not. Sustained oscillations require an open system with a continuous influx of reactants in a closed system oscillations may occur initially when the sjretem is far from equilibrium, but disappear as the system approaches equilibrium. A simple example of an oscillatory reaction is the Selkov model [1]... 

Fig. 16.5. Plot of the period of the chemical oscillation, T, vs. the total adenine nucleotide concentration for various values of influx conditions. The points of marginal stability, the transitions from non-oscillatory to oscillatory conditions, are on the extreme left of each curve. From [7]...

The efficiency for this model of a proton pump has been calculated [13] for different parameters in the stationary state mode and for a range of frequencies and amplitudes of ATP influx in the oscillatory mode. In Fig. 17.5, from [13], we plot the ratio of the efficiency in the oscillatory mode to that in the stationary mode vs. the ratio of the frequency of the ATP oscillation to the frequency of the autonomous system, the damped oscillator. 

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