Additional file 4: of Modeling the ascorbate-glutathione cycle in chloroplasts under light/dark conditions

Simulated progress curves under NADP + -limiting and high-light conditions in the presence of 1.3 μM MDAR. Parametric conditions as indicated in Fig. 10B. (TIF 1938 kb

Additional file 1: of Modeling the ascorbate-glutathione cycle in chloroplasts under light/dark conditions

Fitting the average daily global clear-sky solar irradiance data to Eq. ( 11 ). Data were taken from [13] after considering these parameters: geographic coordinates = 40° 25' 0'' North, 3° 42' 1'' West (Madrid, Spain), month = September, inclination of plane = 35° and orientation (azimuth) of plane = 0°. Dots represent the real solar irradiance data (adapted so that the photoperiod starts at time = 0) and the line corresponds to the nonlinear regression analysis. Data were fitted by the SigmaPlot Scientific Graphing Software for Windows, version 13.0 (2014, Systat Software, Inc.). (TIF 187 kb

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

Elemental biochemical processes involved in the energy status of cells.

<p>The synthesis sources of ATP are coupled to energy-consumption processes through a network of enzymatic reactions which, interconverting ATP, ADP and AMP, shapes a permanent cycle of synthesis-degradation for the adenine nucleotides. This dynamic functional structure defines the elemental processes of the adenylate energy network, a thermodynamically open system able to accept, store, and supply energy to cells.</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

Additional file 3: of Modeling the ascorbate-glutathione cycle in chloroplasts under light/dark conditions

Simulated progress curves under NADP + -limiting and high-light conditions in the presence of 2 μM MDAR. Parametric conditions as indicated in Fig. 10A. (TIF 1806 kb

Numerical analysis for the model of the adenylate energy system.

<p>a–c: (cf. Scenario I in text) In y-axis we are plotting the max and the min of the different variables α, β and γ. For situations with no oscillations (stable fixed point colored in solid black lines) the max and the min are coincident. For situations with oscillations, the max and the min of the oscillations are plotted separately; in blue we are coloring the max of the oscillation, in red, its minimum value. is the control parameter. The numerical integration shows simple solutions. For small values () the adenine nucleotide concentrations present different stable steady states which lose stability at a Hopf bifurcation at ∼1. For , the attractor is a stable limit cycle. d–f: (Scenario II) The delay r₂ is the control parameter. The numerical bifurcation analysis reveals that the temporal structure is complex, emerging 5 Hopf bifurcations as well as a secondary bifurcation of Neimark-Sacker type. Two pairs of Hopf bifurcations are connected in the parameter space. A third supercritical Hopf bifurcation occurs at r₂∼71.94, rapidly followed by another Hopf bifurcation, subcritical, at r₂∼72.83. This marks the beginning of the region where the system is multi-stable. The last Hopf bifurcation, born at r₂∼72.83, which is subcritical exhibiting the presence of several Torus bifurcations, occurs on a branch of limit cycles when a pair of complex-conjugated Floquet multipliers, leave the unit circle. Branches of stable (resp. unstable) steady states are represented by solid (resp. dashed) black lines; branches of stable (resp. unstable) limit cycles are represented by the max of the oscillation in blue and the minimum in red and by solid (resp. dashed). Hopf bifurcation points are black dots labeled H; Torus bifurcation points are blue dots labeled TR. The bifurcation parameters (Scenario I) and r₂ (Scenario II) are represented on the horizontal axis. The max and min values of each variable are represented on the vertical axis.</p