Thermodynamics and Energetics of the Tonoplast Membrane Operating as a Hysteresis Switch in an Oscillatory Model of Crassulacean Acid Metabolism

The observed endogenous circadian rhythm in plants performing Crassulacean acid metabolism is effected by malate transport at the tonoplast membrane. Experimental and theoretical work asks for a hysteresis switch, regulating this transport via the ordering state of the membrane. We apply a schematic molecular model to calculate the thermally averaged order parameter of the membrane lipid structure in its dependence on external parameters temperature and area per molecule. The model shows a first order structural phase transition in a biologically relevant temperature range. Osmotic consequences of malate accumulation can trigger a transition between the two phases by changing the surface area of the cell vacuole. Estimation of the energy needed to expand the vacuole under turgor pressure because of osmotic changes while acidifying shows that energy needed as latent heat for the calculated change between phases can easily be afforded by the cell. Thus, malate content and the coexisting two phases of lipid order, showing hysteretic behavior, can serve as a feedback system in an oscillatory model of Crassulacean acid metabolism, establishing the circadian clock needed for endogenous rhythmicity. Received: 2 September 1997/Revised: 24 April 1998