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

Abstract

The mechanism of endogenous circadian photosynthesis oscillations of plants performing crassulacean acid metabolism (CAM) is investigated in terms of a nonlinear theoretical model. Blasius et al. used throughout continuous time differential equations which adequately reflect the CAM dynamics. 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. In this paper, we pay attention to the approximation of the fast modes of the CAM dynamics. Using the zero-epsilon approximation of the slow manifold, we derive the critical manifold that is defined by two algebraic nonlinear equations. The critical manifold allows us to give the algebraic estimate of the order of the tonoplast membrane. The dynamic equation of the order of the tonoplast membrane includes the nonlinear function that gives the equilibrium value of the lipid order of tonoplast functions as a hysteresis switch. We identify the nonlinear function with the measurement signals. Using the basis function expansion of the nonlinear and the critical manifold, we propose an adaptive observer to estimate the tonoplast order and the nonlinear function.

Modeling and Identification of Crassulacean Acid Metabolism Using Experimental Data

“…In the references (8),(9) , we defined an identification problem of the delay sequence of the CO2 uptake as follows: Estimate the parameters 𝛼 𝑘 ′ 𝑠 and 𝐿 𝑘 ′s so as to minimize the objective function 𝑃(𝑡) at time 𝑡:…”

“…• 𝜀, 𝜏: time constants The nonlinear function 𝑔(𝑧, 𝑇) is approximated via the third-order spline interpolation from the figure shown in the reference (8) . The function is shown in Fig.…”

Informing the improvement and biodesign of crassulacean acid metabolism via system dynamics modelling

“…Significant progress has been made in computational modelling of C 3 and C 4 photosynthesis over the past 30+ yr with integrative models encompassing a suite of physiological and biochemical reactions and transport processes involved in CO 2 uptake, photosynthesis, Calvin cycle activity, and carbohydrate partitioning (von Caemmerer, 2013;Zhu et al, 2013). Previous efforts to model CAM have been limited to a few variables related to CO 2 concentration, malate concentration, temperature and light intensity (Blasius et al, 1999;Matsuo et al, 2013). The SD model presented by Owen & Griffiths captures the inherent plasticity that exists both within and between CAM species in the magnitude and duration of nocturnal and daytime gas exchange (Borland et al, 2011).…”