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A Coupled Photosynthetic Model of Ice Plant As Facultative CAM plant
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Combined with Stomatal Conductance
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Abstract. Recently ice plant as medicinal plant is well known for diabetes mellitus retardation and its
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production with plant factory is spreading in Asia. Although ice plant is CAM (Crassulacean Acid
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Metabolism), it activates C3 photosynthesis during juvenile period. The objective of this study was to
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develop the photosynthetic model of ice plant during juvenile stage in plant factory. The light saturation and
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compensation points determined by the regression analysis of light curves in ice plant leaves were 609.37
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and 53.17 μmol·m-2·s-1, respectively. The accuracy in light response between negative exponential and non-
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rectangular hyperbola functions was compared. The non-rectangular hyperbola was more accurate with
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complicated parameters, while the negative exponential could more easily acquire the parameters of light
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response curves of ice plant than the non-rectangular hyperbola. The CO2 saturation and compensation points
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determined by the regression analysis of the A-Ci curve were 632.91 and 117.19 μmol·mol-1, respectively.
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The coupled photosynthetic model was combined to simultaneously predict the photosynthesis, stomatal
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conductance, transpiration, and temperature of ice plant leaves. By using Sharkey’s regression method, the
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photosynthetic parameters, maximum carboxylation rate, potential rate of electron transport, and rate of
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triose phosphate utilization were determined as 222.3, 234.9, and 13.0, respectively. The parameters of
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minimum stomatal conductance to water vapor at the light compensation point (b) and empirical coefficient
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(m) for the sensitivity of gs, to A, Cs and hs in the BWB could be solved as 0.0487 and 0.0012 with linear
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regression analysis using measured A-Ci values. The coupled biochemical model was more effective for
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explaining the photosynthesis of ice plant during juvenile stage in plant factory.
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Additional key words: biochemical model, light compensation point, light saturation point,
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Mesembryanthemum crystallinum L., negative exponential curve, non-rectangular hyperbola.
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Introduction
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Since ice plant (Mesembryanthemum crystallinum L.) in the Aizoaceae family contains polyol in leaf
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that has the ability of antioxidant activation, its production in plant factory is spreading in Asia. The ice plant
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is abundant for inositol, -glucan, and various mineral. Especially, inositol is good for the relieving of
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diabetes mellitus (Cha et al., 2014). Commercializing inositol from raw materials of ice plant, the production
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of the ice plant in plant factory is increasing
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Particularly the ice plant was known as Crassulacean Acid Metabolism (CAM) such as cactus. Winter et
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al. (1978) reported seasonal shift from C3 photosynthesis to CAM in the ice plant growing in its natural
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environment. So the ice plant was classified as facultative CAM plant. Recently Cushman (2001) explained
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that the ice plant has C3 photosynthesis during juvenile stage. Under growth environments in plant factory,
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the harvest happens at juvenile stage because the leaves are shrunk during adult stage. Therefore, crop
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modeling and simulation are effective tools for controlling the environments in greenhouses and plant
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factories by optimizing for planned production (Heuvelink, 1999).
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Photosynthetic models are fundamental parts of the crop growth models which are classified into
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descriptive and biochemical types. The descriptive model summaries the photosynthetic characteristics of the
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crop, while the biochemical one is based the reaction rate of photosynthetic enzymes and critical limiting
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rates. The FvCB model for C3 plants developed by Caemmerer and Farquhar (1981) as a biochemical model
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has been widely applied to physiological research (Medlyn et al, 1999). This model has been more
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informative by using the rate of triose phosphate utilization (TPU) and the TPU limitation (Harley et al.,
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1992; Sharkey et al., 2007). However, in this kind of model, actual crop growth conditions in greenhouses
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could not be reflected, for instance, actual state of stomatal openings affecting photosynthetic efficient under
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changing environment conditions. A coupled model of photosynthesis has been developed by combining the
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FvCB model with stomatal conductance (Leuning, 1995; Nikolov et al., 1995) and energy budget balance
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(Kim and Lieth, 2003) models. Ball (1987) suggested that photosynthetic rate has a strong linear relationship
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with stomatal conductance. The coupled photosynthetic model considers the biochemical limitations of CO2
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carboxylation as well as the stomatal limitations to the CO2 supply. Kim and Lieth (2003) developed a
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coupled model of photosynthesis, stomatal conductance, and transpiration for roses.
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Photosynthesis modeling of the ice plant as CAM plant had not been conducted using biochemical
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models but the contents of malate at each growth stage was analyzed for determining CAM activation and
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confirmed that the photosynthesis of the ice plant was conducted like C3 plant during juvenile stage (Winter
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et al., 1978). The objective of this study was to develop descriptive and coupled models of photosynthesis
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and stomatal conductance of the ice plant combined with sub-models of stomatal conductance and energy
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balance.
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Materials and Methods
Plant Materials and Cultivation Conditions
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The seeds of ice plant (Mesembryanthemum crystallinum L.) were sown on a rock-wool tray (600 mm
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×400 mm) on May 12th, 2014 in velno-type greenhouses of Protected Horticulture Research, RDA located at
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Busan in Korea. The seedlings of ice plant with 3-4 leaves were transplanted on polystyrene panels (100 ×
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100 mm, Ф 3cm) on June 2nd, 2014. The nutrient solution for ice plant developed by Jeju National
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University was Ca(NO3)2･4H2O 3.54g, KNO3 4.04g, NH4H2PO4 77g, and MgSO4･7H2O 2.46g in 10L (Cha
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et al., 2014), The nutrient solution of EC 1.5 dS·m-1 were continuously supplied to the hydroponic systems
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(460 mm × 300 mm× 210 mm) using a deep flow technique with a depth of 70 mm. The nutrient solutions
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were supplied for 10 min at one hour interval. The experiment was conducted in a container-type plant
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factory (3 × 12 m), in which
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20oC, 65%, and 400 μmol·m-2·s-1, respectively. The light/dark period was 18h/6h and the photosynthetic
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photon flux density (PPFD) was 150 μmol·m-2·s-1 during the light period. Bar-type LEDs (PGL-PFL600,
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Parus, Cheonan, Korea) with a 3:7 mixture of blue (445 nm) and red (660 nm) were used as artificial light
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sources (30W).
the room temperature, relative humidity, and CO2 concentration were set as
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Photosynthetic Property of Ice Plant Leaves
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The net CO2 assimilation rate and stomatal conductance to water vapor were measured by using a
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portable photosynthesis system (LI-6400, LI-COR, Lincoln, NE, USA) equipped with an infrared gas
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analyzer. The area of leaf clipped by the chamber was 6 cm2. The temperature and relative humidity in the
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leaf chamber was maintained at 25ºC and 45-65%, respectively, during measurements. The net CO2
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assimilation rate as a function of light curve was determined at each step every 3-4 min. PPFDs ranged from
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0 to 1500 μmol·m-2·s-1 at 400 μmol·mol-1 of CO2 concentration. Regression analyses for descriptive models
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were conducted for negative exponential (Evans et al., 1993; eq. 1) and non-rectangular hyperbola (Thornley,
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1976; eq. 2) models, as described below:
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A = Amax *{(1-exp (- α * I / Amax)} - Rd
(eq. 1)
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A = [α * I +Amax - {(α * I + Amax)2 - 4α* I * θ * Amax} 0.5] / 2θ - Rd
(eq. 2)
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where, A is the net CO2 assimilation rate (μmol·m-2·s-1), α parameter is the initial slope, I is the
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photosynthetic photon flux (μmol·m-2·s-1), Amax is the maximum net CO2 assimilation rate (μmol·m-2·s-1), θ is
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the curvature of photosynthetic curve, and Rd is the respiration rate (μmol·m-2·s-1).
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The net CO2 assimilation rate as a function of A-Ci curve was determined at each step every 3-4 min. CO2
concentration ranged from 100 to 1500 μmol·mol-1 at a PPFD of 500 μmol·m-2·s-1.
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Coupled Biochemical Models for Photosynthesis of Ice Plant
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Biochemical models (eqs. 3–6) were used for acquiring the net photosynthetic rate, which has limitations
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of the rates of CO2 carboxylation by Rubisco, Ribulose 1,5-bisphophate (RuBP) regeneration, and triose
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phosphate utilization.
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A = min{𝐴𝑐 , 𝐴𝑗 , 𝐴𝑝 } − 𝑅𝑑
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A𝑐 = 𝑉𝑚𝑎𝑥
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A𝑗 = 4 (𝐶
(eq.5)
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A𝑝 = 3 ∗ 𝑇𝑃𝑈
(eq.6)
𝐶𝑖 − 𝜏 ∗
𝐶𝑖 + 𝐾𝑐 ∗ (1 +
J ∗ (𝐶𝑖 − 𝜏∗ )
∗
𝑖+2𝜏 )
𝑂
)
𝐾𝑜
(eq.3)
(eq.4)
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where, Vmax is the maximum rate of Rubisco carboxylation (μmol·m-2·s-1), Ci is the intercellular CO2
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concentration (μmol·mol-1), τ* is the CO2 compensation point in the absence of Rd (μmol·mol-1), Kc and Ko
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are the Michaelis-Menten constants of Rubisco for CO2 and O2, respectively (μmol·mol-1), O is the oxygen
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partial pressure (μmol·mol-1), J is the electron transport rate (μmol· m-2· s-1), and TPU is the triose phosphate
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utilization rate (μmol· m-2· s-1). The photosynthetic limitation parameters of the ice plant leaves were
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calculated by an Excel macro program developed by Sharkey (2007).
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The intercellular CO2 concentration (Ci) in ice plant leaf was measured by the portable photosynthetic
measurement system. Eq. 7 describes the equation for estimating the Ci (Caemmerer and Farquhar, 1981).
C𝑖 =
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𝐸
(𝑔𝑡𝑐 − 2 ) 𝐶𝑎 − 𝐴
(eq.7)
𝑔𝑡𝑐 + 𝐸/2
here, gtc is the total conductance to CO2 (μmol· mol-1) and E is the transpiration (mol· m-2 · s-1).
The stomatal conductance was described as the BWB model (eq.8; Ball et al., 1987), in which the relative
humidity at leaf surface (hs) was described as a quadratic function.
𝑔𝑠 = 𝑏 + 𝑚 ∗ 𝐴
ℎ𝑠
𝐶
( 𝑠)
𝐶𝑎
(eq. 8)
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where, gs (mol · m-2· s-1) is the stomatal conductance to water vapor, b (mol· m-2· s-1) is the minimum
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stomatal conductance to water vapor at the light compensation point in the BWB model, m is the empirical
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coefficient for the sensitivity of gs, Cs and Ca are the ambient air and leaf surface CO2 concentrations (μmol·
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mol-1). Parameters b and m were estimated by the linear regression in terms of k value of 𝐴
ℎ𝑠 ∙𝐶𝑎
(𝐶𝑠 )
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The leaf temperature was estimated with the energy balance model as a function of gs, boundary layer
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conductance, and the environmental parameters such as air temperature, relative humidity, and radiation
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(Kim and Lieth, 2003). Ci and TL including photosynthetic active radiation (PAR) were used in the FvCB
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model. The net photosynthetic rate (A) and Ci were used in The BWB model. TL was estimated iteratively
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from the energy balance using air temperature, conductance for heat, and water vapor. Initially, TL and Ci
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were assumed to be equal to the air temperature and 0.7Ca, respectively, to obtain and estimate A, and then
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gs.was obtained. Ci could be estimated using A and gs. These processes were conducted iteratively using the
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Newton-Raphson method until Ci and TL became stable. The photosynthetic rates were acquired by inputting
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their parameters and optical characteristics of ice plant to the photosynthetic simulator (Kim and Lieth, 2003).
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Results and Discussion
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Light response curves of ice plant leaves to various light intensities were developed (Fig. 1). The
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photosynthetic rate were increased up to about 200 μmol·m-2·s-1 PPFD and were saturated at about 600
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μmol·m-2·s-1 PPFD. Similarly Sharp et al. (1984) reported the linear relationship between light intensity and
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photosynthetic rate at 100 μmol·m-2·s-1 PPFD
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Parameters of the negative exponential and non-rectangular hyperbola models were estimated by using
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the regression analysis (Table 1; Kim et al., 2003). These parameters showed C3 photosynthetic character
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during the juvenile stage of ice plants grown in plant factory as mentioned by Winter et al.(1978). The non-
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rectangular hyperbola model was more accurate with R2= 0.998 for describing the light curve than the
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negative exponential model with R2=0.994. In addition, the negative exponential model was under-estimated
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in photosynthetic rate compared to the non-rectangular hyperbola model at the range from 400 to 800
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μmol·m-2·s-1 (Fig. 1). Initial slope (α) of the non-rectangular hyperbola was determined 0.0505 from the
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measured photosynthetic rates from 0 to 100 μmol·m-2·s-1 PPFD. The average curvature of the non-
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rectangular hyperbola (eq. 2) for the light response curve was 0.8668 ± 0.035. The residual sum of squares
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between measured and predicted photosynthetic rates was the lower at the non-rectangular hyperbola than
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the negative exponential. The non-rectangular hyperbola predicted more accurately than the negative
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exponential, however the negative exponential could simply summarized the light response curve.
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Regression analysis was conducted by using the measured photosynthetic rates with increases of CO2
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concentration and the negative exponential model (Fig. 2). The y-axis and x-axis values of the intercept as
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the estimates of Rp and Ccomp were 9.30 μmol·m-2·s-1 and 117.19 μmol·m-2·s-1 (Table 2). With the intercellular
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CO2 concentrations of 63.53 and 458.53 μmol·m-2·s-1 at the compensation and saturation points, the
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atmodspheric CO2 concentrations (Ccomp and Csat) were 117.19 and 632.91 μmol·m-2·s-1, respectively (Table
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2). The photosynthetic limitation curve of ice plant (Fig. 3) could be obtained using an Excel macro program
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(Sharkey et al, 2007). The photosynthetic rates were determined by Rubisco carboxylation rate at the range
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of intercellular CO2 concentration from 100 to 150 μmol·mol-1 by the Ribulose 1,5-bisphosphate (RuBP)
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regeneration rate from 150 to 250 μmol·mol-1, and by the triose phosphate utilization rate (TPU) from 250
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to 800 μmol·mol-1. It was concluded that the photosynthetic A-Ci curve of the ice plant for fitting the
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parameters by Sharkey’s method.
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The maximum carboxylation rate (Vmax, μmol·m-2·s-1), the maximum rate of electron transport (J max,
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μmol·m-2·s-1), the TPU (μmol·m-2·s-1), and the mitochondrial respiration in the light (Rd, μmol·m-2·s-1) were
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222.3, 234.9, 13.0, and 6.25, respectively (Table 3). These parameters of ice plant were in the range of
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parameter values of roses calculated by Kim and Lieth (2003). The parameters of minimum stomatal
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conductance to water vapor at the light compensation point (b) and empirical coefficient (m) for the
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sensitivity of gs, to A, Cs and hs in the BWB could be solved with linear regression analysis using measured
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A-Ci values (Fig. 4). The parameter of the m value showing stomatal conductance slope was lower than rose
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and A-Ci curves should be acquired according to various environmental conditions.
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The parameters of minimum stomatal conductance at the light compensation point (b) with the empirical
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coefficient (m) for the sensitivity of gs, to A, Cs and hs in the BWB model could be solved as 0.0487 and
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0.0012 by the linear regression analysis using measured A-Ci values (Fig. 4). The stomatal conductance
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slope (m) of ice plant was lower than those of rose. k value (eq. 9) showed a weak linearity with the stomatal
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conductance in Fig. 4 as reported by Ball et al (1987).
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k=A
ℎ𝑠 𝐶𝑎
𝐶𝑠
(eq. 9)
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The residual sum of squares between measured and predicted photosynthetic rates in the coupled
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biochemical model was bigger than those in the negative exponential model (Table 4). The biochemical
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model underestimated the photosynthetic rate compared to the negative exponential model at a high
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concentration of CO2. However, the coupled biochemical model using temperature, CO2, and stomatal
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conductance was very effective for analyzing the photosynthetic rate during juvenile stage. Even though the
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ice plant belongs to CAM plant, the A-Ci and light curves indicated that its photosynthesis is working as C3
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during juvenile stage.
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Table 1. Photosynthetic parameters of the negative exponential (eq. 1) and non-rectangular hyperbola (eq. 2)
models
calculated
from
the
light
response
curves
of
ice
plant
in
Fig.
1.
Table 2. Photosynthetic parameters of the negative exponential model (eq. 1) calculated from the A-Ci
curves
of
ice
plant
in
Fig.
2.
Table 3. Estimated photosynthetic parameters of the biochemical model of ice plant at a leaf temperature of
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183
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24.8℃.
Table 4. Comparison of the residual sum of squares between the measured and predicted photosynthetic
rates
of
the
negative
exponential
and
biochemical
models
of
ice
plant.
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Fig. 1. Regression response curves of light using negative exponential and non-rectangular hyperbola models
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at a CO2 concentration of 400 μmol·mol-1 in the leaves of ice plant. Vertical bars are the standard errors of
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the means from three replications. A and PPF are the CO2 assimilation rate and the photosynthetic photon
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flux, respectively.
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Fig. 2. Net CO2 assimilation rate (A) as a function of the intercellular CO2 concentration in the leaves of ice
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plant at a photosynthetic photon flux of 500 μmol·m-2·s-1. Vertical bars are the standard errors of the
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means from three replications.
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Fig. 3. Net CO2 assimilation rate (A) as a function of intercellular CO2 concentration in the leaves of ice
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plant at a photosynthetic photon flux of 500 μmol·m-2·s-1. Rubisco, RuBP or TPU limitation are assumed
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for prediction of photosynthesis.
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Fig. 4. Relationship between stomatal conductance (gs) and k value (=A* hs * Ca / Cs) ( R2=0.8467).
b
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and m in eq. 8 were acquired as 0.0487 and 0.0012 with this result under temperature condition from 20 to
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35℃. A, hs, Ca, and Cs mean the net photosynthetic rate, relative humidity of the leaf surface, ambient CO2
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partial pressure, and CO2 partial pressure at the leaf surface, respectively.
.
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