Values of the kinetic parameters used to simulate some of the dynamics of the adenylate energy system.

<p>Values of the kinetic parameters used to simulate some of the dynamics of the adenylate energy system.</p

Emergence of oscillations in the AEC (Scenario II).

<p>Different oscillatory behavior appears when varying r₂, controlling the ADP time delays. (a) For r₂ = 37 s the AEC periodically oscillates with a very low relative amplitude of 0.045. (b–c) Existence of complex AEC oscillatory patterns for: (b) r₂ = 72 s and (c) r2 = 94 s. (d–e) AEC transitions between different oscillatory behavior and steady state patterns for several r₂ values. (d) 50 s, 27 s, 30 s, 32 s, 33 s, 72 s, 52 s. (e) 50 s, 27 s, 30 s, 32 s, 34 s, 36 s, 33 s, 36 s, 38 s, 40 s.</p

AEC dynamics under low production of ATP.

<p>AEC values as a function of time. At very small values (), which represents a strong reduction of the ATP synthesis due to low substrate intake, the dynamic of the adenylate energy system shows a steady state behavior that slowly starts to descend, in a monotone way, up to reach the lowest energy values (AEC ∼0.59) at which the steady state loses stability and oscillatory patterns emerge with a decreasing trend. Finally, when the maximum of the energy charge oscillations reaches a very small value (AEC ∼0.28) the adenylate system suddenly collapses after 12,000 seconds of temporal evolution.</p

Dynamical solutions of Scenario I.

<p>For  = 1.02 (normal activity for the ATP synthesis), periodic oscillations emerge. (a) ATP concentrations. (b) ADP concentrations. (c) AMP concentrations. (d) The Gibbs free energy change for ATP hydrolysis to ADP. (e) The total adenine nucleotide (TAN) pool. It can be observed that ATP and ADP oscillate in anti-phase (the ATP maximum concentration corresponds to the ADP minimum concentration). Likewise, it is noted that the total adenine nucleotide pool shows very small amplitude of only 0.27 and a period around 65 s. (f) ATP transitions between different periodic oscillations and a steady state pattern for several values of (0.97, 1.08, 1.02, 0.97). Maxima and minima values per oscillation are shown in y-axis.</p