Kaneko discusses numerous possibilities of coupling the oscillators. In all circumstances the phase diagram has regions of fixed factors, oscillations, and undefined or chaos. This can be for being expected in the bifurcation of your perform as proven in Figure 6. The tough boundary in our phase diagram at ? 2 is always to be expected as shown in Figure seven. The fact that the oscillations get started prior to two. 5 is due to the fact that the thresholding and signal transfer changes the dynamics. The areas within the phase diagram labeled n are for n cycle, or odd attractor. In mapping this phase diagram to glycolytic oscillations we’d not anticipate all threshold values to be legitimate. If we set the threshold to 0. 5 then the bifurcation param eter represents the glucose dosage and we’ve two cycles above a tiny variety until the four cycles followed by continued boost from the glucose results in n cycles.
A 4 cycle on this phase space would look like a doubled 2 cycle, amplitude modulated glycolytic oscillator, and an n cycle would search like an amplitude or fre quency modulated 2 cycle or 4 cycle. These types of modulations are already observed by Hess et al. and von Klitzing and Betz. Mitochondrial transition We now flip our awareness towards the mitochondria and take a look at the original source the potential implications from glycolytic oscillations on mitochondrial stability. Its known that the glycolytic os cillations result in very similar pH oscillations. But these oscillations are about ? two out of phase. This has implications around the polarization from the mitochon drial membrane. The cell has buffer mechanisms to minimize pH imbalance, but an excessive amount of polarization of your mitochondrial membrane will cause the mitochondria to break down. The phase lag in pH can lead to a probable dilemma. Galante et al.
showed that a rise this article of protons to an assay of heart mitochondria benefits within a lower inside the Michaelis Menten price continual Km, and an increase within the forward velocity, Vf, from the response The ratio of Vf Km displays an real phase transition at pH seven. five. The authors did not discuss the significance of this phase transition. Later on operate by Aromolaran et al. showed waves of Ca2 ions traversing the cell because of a localized ATP perturb ation. These waves can traverse the whole cell inside thirty seconds far faster than diffusion. Other operate by Ramanujand and Herman present a nonlinear scaling of glucose metabolism in regular and cancer cells, the place the scaling exponent is dif ferent for both types of cells. That is analogous to our observed variation as being a func tion of glucose. Lastly, Aon et al. describe experiments on percolation and criticality in mitochondrial networks of the cell.