Table 1.

Distinctive features of ODE-based models addressing CAM diel rhythmicity.

Model	Modified from	Focus	Modifications from previous models	Main achievements
Nungesser et al., 1984	–	Interaction between light and metabolite pools.	–	Reproduced CAM behavioral parameters such as content of malic acid, starch, Glc6P and PEP, CO2-exchange, and Ci.
Lüttge and Beck, 1992	Nungesser et al., 1984	CAM rhythmicity, light and temperature.	Removed the influence of light on malate transport. Allowed light fluxes to vary arbitrarily. Adjusted parameters to stabilize oscillations for runs longer than a day/night cycle.	Reproduced a stable rhythmicity in normal dark–light cycles and in continuous light. Predicted accurately a change to chaos as irradiance and temperature is increased.
Grams et al., 1996	Lüttge and Beck, 1992	Effect of irradiance and temperature on CAM rhythmicity.	Included the saturation of CO2 fixation at high irradiance and high Ci. Included three different modes of modeling malate transport: influx, efflux, and influx near maximum capacity.	Predicted accurately that high irradiances gradually make oscillations disappear and that rhythm displays a smaller amplitude upon re-initiation. Reproduced the effect of below-range temperature halting rhythmicity.
Grams et al., 1997	Grams et al., 1996	Low and high temperature effect on CAM rhythmicity.	Influx, efflux and influx near maximum capacity were modeled as a function of temperature.	Reproduced accurately the phase displacement upon re-initiation of CAM rhythmicity after out-of-range temperature treatments.
Blasius et al., 1997	Lüttge and Beck, 1992; Grams et al., 1996	Effects of temperature as a continuous functional dependency.	Reduced to four the number of metabolite pools modeled. Added an algorithm to simulate continuous temperature variations.	The model exhibits robustness against functional changes in its structure. Increases in light intensity under continuous light increased the oscillation frequency but did not disrupt the rhythmicity. Higher temperatures resulted in slower oscillations.
Blasius et al., 1998	Blasius et al., 1997	Constructing a minimal skeleton model.	Removed the starch pool Added a respiration term into the analysis Adjusted the ratio of cytoplasm/vacuole volume to match an experimentally determined value.	Showed that only malate in the vacuole, malate in the cytoplasm and Ci in the earlier model are dynamically independent Showed that PEPC phosphorylation cannot sustain CAM rhythmicity on its own Provided evidence that CAM rhythmicity relies on a hysteresis switch at the tonoplast.
Blasius et al., 1999	Blasius et al., 1998	Implementation of a continuous hysteresis switch	Included a dynamic switch, using an equation that simulates membrane dynamics.	The appearance of unstable steady states allows the system to reproduce more closely experimental data More accurate simulation of phase I.
Wyka et al., 2004	Blasius et al., 1999	Testing the effect of removing ambient CO2	Tested both experimentally and computationally different durations and moments for CO2 removal.	The model did not reproduce experimental results. Simulating CO2 removal for a time period led to a phase shift in oscillations, while in vivo the oscillations kept as normal.
Owen and Griffiths, 2013	Nungesser et al., 1984; Blasius et al., 1999	Identifying key flow junctions, metabolic feedbacks and parameters that limit CO2 uptake over the diel cycle.	Implemented a system dynamics approach. Included a wider set of elements, regulatory interactions in the model and parameters, including carbonic anhydrase reaction, the switch between PEPC and Rubisco. carboxylation, transpiration and mesophyll conductance.	Modifying a number of parameters including vacuolar capacity, stomatal and mesophyll conductance as well as switches from PEPC to Rubisco activity allowed the initial model fitted to K. draigemontiana to replicate Agave tequilana behavior in terms of CO2 uptake.