Oscillatory model of crassulacean acid metabolism with a dynamic hysteresis switch

Abstract

The mechanism of endogenous circadian photosynthesis oscillations of plants performing crassulacean acid metabolism (CAM) is investigated in terms of a nonlinear theoretical model. Unlike previous CAM models containing a discrete element, we use throughout continuous time di¡erential equations which more adequately re£ect the CAM dynamics. By incorporating results from both a complementary and a continuous membrane model, a detailed description of the molecular malate transport in and out of the vacuole through the tonoplast membrane is achieved. Our analysis shows that the membrane e¡ectively acts as a hysteresis switch regulating the oscillations. It thus provides a molecular basis for the circadian clock. The model shows regular endogenous limit cycle oscillations that are stable for a wide range of temperatures, in a manner that complies well with experimental data. The circadian period length is explained simply in terms of the ¢lling time of the vacuole. The results emphasize the central role of membrane dynamics for the generation of circadian oscillations and thus have general relevance for the explanation of biological clocks.

Spatiotemporal variation of metabolism in a plant circadian rhythm: The biological clock as an assembly of coupled individual oscillators

“…3a). This typical limit-cycle behavior has short and long time constants (15) that are reflected in periods of fast and slow change in PSII (Fig. 3b).…”

“…From a theoretical point of view, the endogenous rhythm can be reproduced by a minimal model that reduces CAM to three metabolic pools, namely internal CO 2 concentration and cytoplasmic and vacuolar malic acid levels, connected by several feedback loops that regulate malate influx and efflux of the vacuole (14,15). The order state of the tonoplast operates as a beat oscillator or hysteresis switch in the model (16) that allows malic acid transport to and from the cell vacuole to override circadian control of the properties of PEPCase by a regulatory cascade that extends to the level of transcription (8,17,18).…”

Adaptive Estimation of Biological Rhythm in Crassulacean Acid Metabolism with Critical Manifold

“…The malic acid is accumulated to high concentrations of up to several hundred millimolars and stored in the cell sap vacuole [1,2]. During the daytime, malate is remobilized from the vacuole and decarboxylated again [3]. The resulting CO 2 is refixed by RubisCO for photosynthetic assimilation [3].…”

“…During the daytime, malate is remobilized from the vacuole and decarboxylated again [3]. The resulting CO 2 is refixed by RubisCO for photosynthetic assimilation [3]. Blasius et al investigated the mechanism of endogenous circadian photosynthesis oscillations of plants performing CAM in terms of a nonlinear theoretical model [3][4][5].…”

“…CAM plants take up external CO 2 during the night while the stomata are open. The CO 2 is fixed in the plant in the form of organic acids, normally malate, via the enzyme phosphonenolpyruvate carboxylase (PEPc) and stored overnight in the vacuole [3]. The malic acid is accumulated to high concentrations of up to several hundred millimolars and stored in the cell sap vacuole [1,2].…”