Oscillatory model of crassulacean acid metabolism with a dynamic hysteresis switch

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 disc rete element, we use throughout continuous time differential equations whic h more adequately reflect the CAM dynamics. By incorporating results from b oth a complementary and a continuous membrane model, a detailed description of the molecular malate transport in and out of the vacuole through the to noplast membrane is achieved. Our analysis shows that the membrane effectiv ely acts as a hysteresis switch regulating the oscillations. It thus provid es a molecular basis for the circadian clock. The model shows regular endog enous limit cycle oscillations that are stable for a wide range of temperat ures, in a manner that complies well with experimental data. The circadian period length is explained simply in terms of the filling time of the vacuo le. The results emphasize the central role of membrane dynamics for the gen eration of circadian oscillations and thus have general relevance for the e xplanation of biological clocks.