1. Introduction
In the research of plant response to the environment, it is often necessary to investigate the responses of photosynthetic traits, such as phytoremediation of pollutants, saline, ozone stress, climate change [1] [2] [3] [4] . However, the complex processes of photosynthesis are affected by many other internal and external factors/processes such as water relations, lights, energy balance, low and high lights, and nitrogen metabolism [5] . Moreover, CO2 fixation, mitochondrial respiration and photorespiration involve processes where CO2 fluxes occur simultaneously [6] , making the investigation of photosynthesis under different environmental conditions very challenging and often leading to the over-parameterization of photosynthetic models [7] . Some of the model parameters are difficult to estimate, such as CO2 compensation point (
), daytime respiration (Rd), mesophyll conductance (gm) [8] (Table 1). Furthermore, multiple parameters are needed to comprehensively describe the responses of photosynthesis to the environment [9] .
Photosynthesis can be roughly divided into two components, the biochemical process, and the CO2 diffusion process [2] [10] [11] . The biochemical process includes Rubisco carboxylation, the regeneration of CO2 receptor RuBP, and utilization and transport of photosynthates [12] . The FvCB photosynthesis model is based on Rubisco enzyme kinetics and biochemical metrology [13] and is widely used to scale photosynthesis from chloroplast and leaf level to ecosystem and global levels, such as in the Earth System Models [14] . The parameters involved in the biochemical process include the maximum rate of RuBP carboxylation (Vcmax), maximum photosynthetic electron transport rate (Jmax), apparent carboxylation efficiency (ACE, estimated from A/Ci), and apparent quantum yield (AQY, estimated from light response curve (LRC) (Table 1) [15] . The Ball Berry type models have established a linear relationship between net photosynthetic rate (An) and stomatal conductance (gs) to incorporate the CO2 diffusion process (gs = g0 + g1 × An × f(D)/Ca) [16] . Parameters related to CO2 diffusion include gs and mesophyll conductance (gm) (Table 1) [17] . Although these models provide a good explanation of photosynthetic responses to specific environmental factors, the mechanisms and parameters that coordinate biochemical and CO2 diffusion simultaneously are rarely reported. The actual growth environment conditions are complex and variable, particularly under the scenario of climate change [18] .
The biochemical model FvCB of photosynthesis explains the demand function of photosynthesis, while the CO2 diffusion model Ball-Berry describes the supply
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Table 1. Definition of abbreviation.
function of photosynthesis (Figure 1(a)) [10] . The demand function is the relationship between net CO2 assimilation rate and CO2 concentration inside the leaf (A/Ci response curve) or in the chloroplast (A/Cc response curve); The supply function is the line connecting the ambient on the X-axis (Ca) to the corresponding internal CO2 concentration on the A/Ci or A/Cc (i.e., Ci or Cc) with the corresponding diffusion conductance to CO2 as the slope [19] . The actual net photosynthetic rate (An) is the rate at the intersection of the two functions [10] [20] , as shown in Figure 1(a). We know that RuBP regeneration depends on light-driven electron transport and Rubisco activity. CO2 diffusion is mainly controlled by gs, which itself is influenced by the environment (such as soil moisture condition and atmospheric water vapor pressure deficit) [10] . The demand and supply functions together can integrate the physical, biochemical and photochemical limitations to CO2 diffusion and assimilation at different segments of the photosynthetic pathway, including the CO2 assimilation capacity in the chloroplast [19] [21] . Therefore, the demand function and supply functions of photosynthesis should reflect the coordination between plants and multiple environmental factors. However, there is still a lack of suitable and easy-to-measure parameters to represent the actual coordination between CO2 demand and supply in the photosynthetic process.
The supply function and demand function of photosynthesis are not only embedded in the A/Ci curve but also in other photosynthetic measurements such as the Laisk measurement [22] . The Laisk method is used to determine CO2 compensation points and daytime mitochondrial respiration in the leaf. The method uses photosynthetic CO2 response curves at low CO2 concentrations (i.e., the initial part of the A/Ci) measured under three sub-saturation light intensities [23] . According to the FvCB model, the three truncated-A/Ci curves should theoretically intersect each other at a common point where the X and Y values are the intercellular CO2 compensation point (
) and the daytime respiration (Rd), respectively [24] . The intersections of the supply function and the demand function with the same Ca be fitted into a regression line (Figure 1(b)). The analysis of the coordination between demand function and supply function may help us to better understand the responses of photosynthesis changes in environmental conditions.
Photosynthesis is catalyzed by Rubisco with CO2 and RuBP as substrates and the photosynthetic rate is the CO2 fixation rate under a given photosynthetically active radiation (PAR) and Ca. Theoretically, there should be a parameter or parameters that describe the intrinsic photosynthetic traits for a given leaf [25] . However, Vcmax and Jmax do not represent the actual photosynthesis capacity of the leaf [26] [27] , The maximum apparent carboxylation efficiency (ACE) is the initial slope of the A/Ci curve at a given PAR, which is related to Rubisco activity [28] [29] . The initial slope of the photosynthetic light response curve (A/L curve) represents the maximum apparent quantum yield (AQY) under the measurement Ca, which is generally considered to be related to photorespiration or
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Figure 1. Demand function and Supply function of photosynthesis in A/Ci curve modified from Figure 9.7. in “Photosynthesis in silico: Understanding complexity from molecules to ecosystems” [20] and Figure 1(b) by Duursma [10] (a). The dark solid line indicates the “demand function” (initial part of A/Ci) the dependence of An on Ci, and the solid line represents the “supply function” describing the CO2 diffusion from ambient (Ca) to intercellular spaces (Ci). The intersection (Ci, An) of the demand and supply curves of photosynthesis means the steady state of these two functions is equal. The intersections of demand and supply curves at 75, 150, and 300 μmol·m−2·s−1 PARs and at 200 μmol·mol−1 Ca (part of the Laisk dataset) can fit into a regression line named DSF (DSF, Demand-Supply Function regression line in (b)). The slope of DSF is ΔAn/ΔCi (dsf). Diagram of the common Laisk method (generated from a single set of measurements on the Populus balsamifera L., see Table S1) (c). P1, P2, P3 are the intersecting points between PAR300 and PAR150, PAR300 and PAR75, PAR150 and PAR75, and point Pmp is the average of P1, P2, P3; Dashed lines DSF100, DSF150, and DSF200 are produced by connecting the Ci points onPAR75, PAR150, and PAR300 lines for three ambient CO2 concentrations: 100, 150, and 200 μmol·mol−1; Ci-dsf 100, Ci-dsf 150 and Ci-dsf 200 are the x-axis intercept of DSF100, DSF150, and DSF200, respectively; Line lv is the proposed auxiliary line perpendicular to the mean line of DSF100, DSF150, and DSF200. (d). Schematic diagram of using the lines in (c) and the reduction to apagoge method to derive point Pv for estimating
and −Rd. Line DSFmean (dashed) represents the average of DSF100, DSF150, and DSF200 in (c). It is assumed that line lv passes point P2 (i.e., the intersecting point of A/Ci lines with the highest and lowest PAR) and intersects with line PAR150 at point Pv150; Pv is the midpoint of line segment P2-Pv150. Whether lv is parallel shifted to the left (lv1) or right (lv2), the sum of line segments formed by the intersections of lv and three A/Ci will increase. Therefore, the line lv passing through P2 intersects the PAR150 (the middle PAR in the Laisk measurement) at point Pv150, and the midpoint (Pv) of the P2Pv150 may be more representative of the point (
, −Rd). The shape of lines in (d) is more realistic relationships between different lines as shown in (c). Please see Table 1 for other explanations.
RuBP regeneration [30] [31] . At present, gs and Ci/Ca are used to assess the limitation of CO2 diffusion to photosynthesis. However, these parameters are very sensitive to changes in by environmental conditions and therefore highly variable [10] . A proper evaluation of environmental effects on the demand and supply functions of photosynthesis, particularly those associated with climate change, will provide insightful information and useful data for ecological and photosynthesis models based on the biochemical and CO2 diffusion algorithms of photosynthesis. However, there is a lack of such information in the literature. The coordination between the demand and supply functions of photosynthesis likely reflects the intrinsic characteristics of plant adaptation to the environment. Based on the measurement of Laisk dataset, We studied the regression lines (defined as the Demand-Supply Function, or DSF) connecting the intersections of the Demand Function and Supply Function of photosynthesis at different PAR under the same CO2 concentration of leaf surface (Ca) (Laisk data according to [32] ) and examined the effect of DSF slope on
and Rd estimations and the relationship of the DSF slope with CO2 diffusion and biochemical characteristics of photosynthesis. We proposed and tested a new method to calculate
and Rd, and a new parameter to describe the coordination between DF and SF under the co-limitation of Rubisco and RuBP regeneration.
2. Materials and Methods
2.1. Plant Materials
Three broadleaf tree species, balsam poplar (Populus balsamifera L.), black cottonwood(Populus trichocarpa Torr. & Gray), and white birch (Betula papyrifera Marsh.) were used for this study. White birch seeds and black cottonwood branch cuttings were collected from trees in the city of Thunder Bay (48˚42'19"N, 89˚26'01"W). Balsam poplar seeds from Kemptville (45˚02"N, 75˚39'W) were obtained from the National Tree Seed Centre in Fredericton, NB, Canada. Balsam poplar and white birth seeds were processed according to The Woody Plant Seed Manual [33] and sown in germination trays in the Lakehead University greenhouse. The cottonwood cuttings were treated with a rooting hormone (Plat Prod Stim Root #3, Plant Products Co. Ltd. Brantford, ON, CA) before being planted. The cuttings were misted continuously in a polyethylene tent during the period of root induction in the greenhouse. The seedlings and rooted cuttings were transplanted into 3.5 L plastic pots filled with peat moss and vermiculite (1:1, v:v). The plants were watered as needed to keep the growing medium moist and fertilized twice a week with 75 mg·L−1 of a fertilizer solution (All-Purpose, 24-8-16 N-P-K fertilizer, Plant Products Co. Ltd. Mississauga, ON, CA). The greenhouse conditions were 23/16˚C day/night temperatures, 16-hour photoperiod and 50% RH. The maximum flux density of photosynthetically active radiation at the canopy level was 500 μmol·m−2·s−1 on a sunny day. The environmental conditions were monitored and controlled using an Argus Titan System (Argus Control Systems Ltd., Surrey, BC, Canada).
2.2. Gas Exchange Measurements and Parameter Estimations
Following two months of growth, six seedlings were randomly selected from each species. The gas exchange of the 1st fully expanded leaf on the terminal shoot sample trees was measured using a PP-Systems CIRAS-3 Portable Photosynthesis System equipped with a PLC3 Universal Leaf Cuvette with automatic climate control and a built-in CFM-3 Chlorophyll Fluorescence Module (PP Systems International, Inc. Amesbury, MA, USA). The photosynthetic responses to CO2, i.e., A/Ci curves, were measured between 9:00 and 16:00. The Laisk script measurements were taken at 200, 150, 100, and 50 μmol·mol−1 CO2 concentration (Ca) and 300, 150, and 75 μmol·m−2·s−1 PAR. Subsequently, full photosynthetic CO2 response curves (A/Ci curves) were measured at 400, 300, 200, 150, 100, 50, 400, 600, 800, 1000, and 1200 μmol·mol−1 CO2 and 1000 μmol·m−2·s−1 PAR. The apparent quantum yield was derived from measurements taken at 400 μmol·mol−1 CO2 and 50, 100, 150, 200, 250 μmol·m−2·s−1 PAR; the slope of the A-Ci response was derived from light response curves (ΔA/ΔCi-lrc, Figure 1(c)). All the measurements were made on the same leaf blade.
The point Pv (novel vertical line method in 2.4 section) and Pmp (conventional average midpoint method in 2.5 section) of the Laisk method (Figure 1(c)) were estimated first and then used to calculate Rd and
(Figure 1(b)). The variable J method [34] was used to calculate gm, where the electron transport (J) was calculated from chlorophyll fluorescence according to Momayyezi’s protocol and Γ* was assumed to equal to
[35] . The chlorophyll fluorescence measurement was taken using the built-in CFM-3 model in the PP Systems CIRAS-3 system.
The A/Ci data were analyzed using the Plantecophysfitaci function of the R package to produce the maximum rate of ribulose-1,5-bisphosphate (RuBP) carboxylation (Vcmax, μmol·m−2·s−1), the maximum rate of photosynthetic electron transport (Jmax, μmol·m−2·s−1) [10] . The initial slope of A/Ci was recorded as the maximum apparent carboxylation efficiency (ACE = ΔA/ΔCi).
2.3. Demand-Supply Functions (DSF)
Figure 1(c) is the Laisk schematic diagram based on actual measurements (Table S1). The three A/Ci lines PAR300, PAR150, and PAR75 (solid line in Figure 1(c)) are the initial linear part of the Demand Functions (DF) at 300, 150 and 75 μmol·m−2·s−1 photosynthetically active radiation (PAR) flux density, respectively; the bold lines are the Supply Functions (SF) at three different ambient CO2 concentration (Ca) of 100, 150 and 200 μmol·mol−1, the slope of which represents the rate of CO2 diffusion from leaf surface (Ca) through stomates into the intercellular space (Ci). The three intersecting points of the three supply functions for the same Ca with their corresponding demand functions measured at the three PARs fall on a straight line which we define as the Demand-Supply Function (DSF) (the three dashed lines, DSF200, DSF150 and DSF100 in Figure 1(c)). The X-intercepts of the three DSFs are designated by their corresponding Ca as Ci-dsf100, Ci-dsf150 and Ci-dsf200 (Figure 1(c)). The purpose of this study was to explore the characteristics and physiological significance of the Demand-Supply Functions.
2.4. Novel Vertical Line Method for Determining
and Rd
The Laisk method assumes that the initial part of three A/Ci curves measured under three unsaturated PAR flux densities will intersect at a common point (
, −Rd), where
represents the CO2 compensation point at intercellular CO2 concentration and Rd represents daytime respiration rate in absence of photorespiration. The method is based on FvCB biochemical model of photosynthesis as A = Vc (Cc − Γ*)/Cc − Rd. Where A is the net rate of CO2 assimilation, Vc represents the Rubisco carboxylation rate, Cc represents CO2 concentration in the chloroplast, Γ* is chloroplast CO2 compensation point [13] [36] . When Cc equals Γ*, A equals -Rd. Here we assume that the gm is infinite as the Laisk method only provides Ci values but not Cc [37] . In reality, however, the three A/Ci lines rarely intersect at a single point. Instead, there are generally three pairwise intersections that form an obtuse triangle (P1P2P3, Figure 1(c)). The conventional protocol uses the average of the three intersecting points (point Pmp in Figure 1(c)) to determine Ci* and −Rd [32] . But the three lines have different weights in terms of slope because of the multiple resistances to CO2 diffusion, enzyme variables [22] . Furthermore, measurement noises can magnify the separation of the intersecting points when the differences in slope between the three lines are small.
The Demand-Supply Functions (DSF) for different Ca that we derived have similar slopes (DSF100, DSF150, and DSF200 in Figure 1(c), to be explained later) and can be used to estimate
and Rd. We proposed to use a line perpendicular to the line with the average slope (DSFmean in Figure 1(d)) of the three DSFs (i.e., lv in Figure 1(c), Figure 1(d)) as an auxiliary line for estimating
and Rd. This line has a negative slope reciprocal to the average slope of DSFs and an unknown intercept. In theory, line lv is also the initial section of an A/Ci curve (demand function) at a certain PAR, similar to PAR300, PAR150, and PAR75 (initial section of A/Ci curves measured at 300, 150, 75 μmol·m−2·s−1 PAR, respectively, in Figure 1(c)). lv is supposed to go through the intersection point (
, −Rd) that all A/Ci curves are theoretically supposed to intersect each other regardless of PAR under which the A/Ci curves are measured.
We use the reduction to absurdity by introducing the vertical line (lv) from Laisk dataset and developed a novel vertical line method (VL) to calculate the point (
, −Rd). Based on the above description, it’s assumed that that line lv should pass through point P2 that the intersection of two A/Ci with the biggest difference in PAR (PAR75 and PAR300, Figure 1(d)). A parallel shift of lv to the left (lv1) or right (lv2) will increase the total length of line segments of P4P5, P4P6, P5P6 which are formed by the intersections of lv and three A/Ci curves, because the total length of P4P6 and P5P6 is always greater than the length of P2Pv150 (Figure 1(d)). According to the FvCB model, these intersections theoretically should converge, when the sum of the distances among the three intersecting points will be minimal and thus the position of line lv is determined. Therefore, after passing the intersecting point P2 between PAR300 and PAR75, line lv will intersect PAR150 at point Pv150, and the midpoint (Pv) of line P2Pv150 will be at or near the theoretical converging point (
, −Rd).
2.5. Comparison of Three Methods for
, Rd and gm Estimation
In addition to the conventional average midpoint method (MP), Walker and Ort [38] proposed a slope-intercept method (SI) for Laisk data analysis. The slope-intercept method treats the slope and intercept of each A/Ci line (initial part of A/Ci curve) as a point (slope, intercept), and the points from multiple A/Ci lines produce a new regression the slope of which equals to −
and the y-intercept of which gives Rd. First, we compared the estimates of
and Rd from the Laisk data set using three methods, i.e., conventional average midpoint method, slope-intercept method and our novel vertical line method, and used the estimated
and Rd to estimate gm. Secondly,
and Rd estimates using Walker’s data (Table S2) were also produced and compared among the three methods; but we only used the lower three (50, 130, 240 mmol·m−2·s−1) of the five PARs because the average midpoint method and the vertical line method can only use for three PARs, and the lower three PARs are more suitable for meeting the sub-saturated light intensity requirement of the Laisk method.
2.6. Assay of Carbonic Anhydrase Activity
The assay of the carbonic anhydrase activity (CAU) was based on the bromothymol blue colorimetry described by Wilbur [39] . 0.2 g leaf blade was ground in 1 ml of 40 mM potassium phosphate buffer (pH = 8.3) using a mortar and pestle on ice. The homogenate was centrifuged for 10 min at 5000 g and 4˚C, 20 μl of the supernatant was added to 1 ml of the buffer solution containing 20 mg·L−1 bromothymol blue as a pH indicator. 1 ml CO2-saturated water of 4˚C was then added and the time (as T) that it took for the Ph of the reaction system to change from 8.3 to 6.3 was recorded. 20 μL buffer solution only was used as control and the time of pH change from 8.3 to 6.3 after adding 1 ml CO2-saturated water was recorded as T0. The carbonic anhydrase activity was calculated as CA (EU) = 10 × (T0 ÷ T − 1).
2.7. Statistical Analysis
The differences in the parameters of the supply and demand function (dsf) among different species were tested using one-way ANOVA. The effects of Lasik calculation methods and species on photosynthetic parameters were tested using two-way ANOVA. Tukey-HSD Post-hoc comparisons were conducted when ANOVA showed a significant effect. Pearson correlation analysis and linear regression were performed to examine the relationships between parameter values estimated from the Pv method and those from the other methods. All the analyses were conducted using R 4.0.4. Principal component analysis (PCA) was applied to photosynthetic parameters using the PCA function from the FactoMineR package.
3. Results
3.1. Characteristics of DSF: Slope and Intercept
The significant differences in the slope of the Demand-Supply Function (DSF) indicated species specificity (Table S3): the lv slope was significantly smaller in black cottonwood than in balsam poplar and white birch (Figure 2(a)); however,
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Figure 2. (a) Variation in the slope of the vertical line (lv) among balsam poplar (bp), black cottonwood (cw) and white birch (wb); (b) Variation in the slope of Demand-Supply Function (dsf) with measurement Ca (100, 150, 200 μmol·m−2·s−1) and species; (c) Frequency distribution of DSF x-axis intercept (Ci-dsf) title to Ca ratio. Means (±SE, n = 6) with different letters in (a) and (b) were significantly different from each other (p ≤ 0.05). Please see Table 1 for other explanations.
the trend for the slope of DSF lines was the opposite, i.e., it was significantly greater in the cottonwood than in balsam poplar and white birch (Figure 2(b)). The DSF slopes of the same species for the ambient CO2 concentration (Ca, from 100 to 200 μmol·mol−1) were not significantly different from each other, suggesting that the DSF lines were approximately parallel to each other (Figure 2(b)). The coefficient of variation in DSF slope and lv slope was much greater in white birch than the other two tree species (Table 2). The ratio of Ci-dsf (DSF intercept on the X-axis) to Ca (Ci-dsf/Ca) in the three species was in a narrow range of 0.96 to 0.97 (Figure 2(c)). This suggests that for a given Ca, the X-axis intercept of the fitting line of the Demand-Supply Function was relatively constant.
3.2. Relationship between DSF Slope and Ci/Ca to gs and Ca
The slope of the Demand-Supply Function (dsf) was inversely related to stomatal conductance (gs) and leaf surface CO2 concentration (Ca) and the relationship varied with species (Figure 3(a) and Figure 3(b)): balsam poplar and white birch had similar trends and had much steeper DSF slopes and smaller stomatal conductance than black cottonwood, and dsf had a strong correlation with and gs (Figure 3(a)) but a weak correlation with Ca (except white birch) (Figure 3(b)). No significant correlation was observed between Ci/Ca and gs (Figure 3(c)). Ci/Ca declined with increases in Ca, however, the relationship was not obviously different between the three species (Figure 3(d)).
3.3. Relationship between dsf and Photosynthetic Parameters
The multivariate relationships between photosynthetic parameters were summarized using two principal components (PCA, Figure 4). dsf and ΔA/ΔCi-lrc
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Table 2. Coefficient of variation (CV) of Rd and
estimates using the conventional average mid-point method (MP), slope-intercept method (SI) and vertical line method (VL) as well as CV for the slopes of lv, dsf100, dsf150, and dsf200. See Table 1 for other explanations.
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Figure 3. Relationships of DSF slope to stomatal conductance (gs) (a) and Ca (b) and relationships of Ci/Ca ratio to gs (c) and Ca (d). The same column or row shares axis labels and units. Please see Table 1 for other explanations.
clustered on the left side of principal component 1 (PC1) while ACE and AQY grouped on the right side, indicating that there might be negative correlations between the two groups (Figure 4). The differences in these four parameters in the three tree species were similar to those in PCA (Table S4 & Figure 4) and there were similarities within the group (dsf and ΔA/ΔCi-lrc, ACE and AQY) while opposite variations between the groups (Figure 4 and Figure 5).
An obvious phenomenon was that dsf and ΔA/ΔCi-lrc almost overlapped in PCA (Figure 4), indicating a close relationship between them. ANOVA analysis verified that dsf and ΔA/ΔCi-lrc (the values of ΔA/ΔCi from different PARs) had no significant difference between different Ca but there were differences among species (Table S5), suggesting that dsf and ΔA/ΔCi-lrc might be species-specific and independent of the measurement conditions (PARs and Ca).
3.4.
, Rd and gm Estimates
and Rd estimates from our new vertical line method (VL) were not significantly different from those estimated using the conventional average midpoint method (MP) and slope-intercept method (SI) for all three tree species (Table S6 and Figure 6(a), Figure 6(b)). However, white birch had significantly lower Rd than black cottonwood and balsam poplar and the variation and coefficient of variation in Rd were much greater for the combination of the MP method and
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Figure 4. Principal Component Analysis (PCA) on balsam poplar (bp), black cottonwood (cw) and white birch (wb) by CAU (carbonic anhydrase activity), Rd (daytime respiration), gm (mesophyll con-ductance), Ci/Ca ratio, Vcmax (maximum rate of ribulose-1,5-bisphosphate carboxylation), ACE (apparent carboxylation efficiency), AQY (apparent quantum yield), Jmax (maximum rate of photosynthetic electron transport rate),
(intercellular CO2 compensation point), dsf (DSF slope = ΔAn/ΔCi) and ΔAn/ΔCi-lrc (slope of An vs Ci under light response curve). Please see Table 1 for other explanations.
birch than the other combinations (Table 2 & Figure 6(a)). There was no significant difference in
among the three species, but the variation and coefficient of variation in
were much larger for the combination of white birch and the MP method (Table 2 & Figure 6(b)). gm estimation was influenced by species and the method of
and Rd estimation (Table S6). White birch had significantly lower gm than in the other two species (Figure 6(c)), and the slope-intercept method produced significantly greater gm estimation than the MP method and vertical line method (Figure 6(d)). The gm calculated by the MP method was slightly smaller than that calculated by the VL method, but the difference was not statistically significant (Figure 6(d)).
Using the three lower PAR curves of Walker’s data, the
and Rd estimates using the three methods were not significantly different from each other and the values from our vertical line method generally fell between those of the other two methods (Table S7). However, the slope-intercept method produced much greater Rd estimates when using 5 PAR curves (0.63) than using 3 curves (0.51) or the other two methods (0.54 and 0.52) (Table S7).
4. Discussion
4.1. Physiological Characteristics of the Demand-Supply Function
The intersecting points of supply functions and demand functions were estimated using the measurements taken under three different PARs but the same Ca and formed a straight line (DSF). The slope of DSF (dsf, dsf = ΔAn/ΔCi, Figure 1(b), Figure S2) represents A response to low PAR at various Ca and its
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Figure 5. The estimates of ACE (apparent carboxylation efficiency (a)), AQY (apparent quantum yield, (b)), ΔAn/ΔCi-lrc (slope of An vs Ci under light response curve (c)) and dsf (DSF slope, (d)) in balsam poplar (bp), black cottonwood (cw) and white birch (wb). Means (±SE, n = 6) with different letters were significantly different from each other (p ≤ 0.05). Please see Table 1 for other explanations.
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Figure 6. The estimates (mean ± SE, n = 6) of Rd (a),
(b), and gm ((c) & (d)) in balsam poplar (bp), black cottonwood (cw) and white birch (wb) using three different methods: the conventional average midpoint method (MP), the slope-intercept method (SI) and our novel vertical line method (VL). The means with different letters are significantly different from each other (p ≤ 0.05). Please see Table 1 for other explanations.
absolute value represents the apparent quantum year of photosynthesis at various Ca and non-saturating PAR (ΔAn/ΔCi-lrc in Figure S1). The apparent carboxylation efficiency (ACE) was derived from the initial slope of A/Ci (ACE = ΔAn/ΔCi, using the same algorithm as for dsf and △An/△Ci-lrc). Furthermore, ACE increased with increases in PAR (Figure S3(a)). Similarly, the apparent quantum yield (AQY) derived from the initial slope of a light response curve represents the quantum yield under a certain Ca and AQY increases with increasing Ca (Figure S3(a)) [30] . Many studies have identified similar patterns in ACE and AQY [38] [40] [41] [42] [43] , limiting the application of ACE and AQY because they can only describe the photosynthetic characteristics under a particular measurement condition (PAR or Ca). Under dynamic environmental conditions, plants can rapidly coordinate CO2 diffusion and biochemical fixation [44] , indicating the existence of internal coordination mechanisms [45] [46] .
The apparent carboxylation efficiency reflects the efficiency of assimilation of the CO2 in the intercellular space under a certain PAR (usually saturating PAR). It is considered to be the ultimate limiting factor of CO2 fixation and is related to the amount and activity of Rubisco [47] . Moreover, ACE increased with increases in PAR (Figure S3(a)), indicating that the actual intrinsic carboxylation efficiency (CEi) of a leaf was co-determined by Rubisco activity (related to Vcmax) and RuBP regeneration (related to Jmax) [48] . Similarly, the initial slope of LRC (AQY) for a certain Ca increased with increases in Ca (Figure S3(b)). The intrinsic quantum yield (QYi) of a leaf may be affected by both Rubisco activity and RuBP regeneration [31] . Vcmax and Jmax (as indicators of photosynthetic capacity) might excert their effects through carboxylation efficiency and quantum yield [25] . These were partially explained by PCA results where ACE and AQY were grouped in the middle region of Vcmax and Jmax. However, other studies have shown that Vcmax and Jmax are independent of gs and CO2 diffusion [48] . To sum up, dsf or ΔAn/ΔCi-lrc may provide a link between CO2 diffusion and biochemical characteristics of photosynthesis because of its close relationships with gs, ACE and AQY.
The values of Laisk measurements are co-limited by Rubisco and RuBP regeneration. The Rubisco restriction is reflected in the linear or initial portion of an A/Ci curve and RuBP regeneration restriction prevents the lines with different PAR from overlapping [49] . Hence, dsf (or ΔAn/ΔCi-lrc) probably acts as an internal coordination mechanism between CO2 diffusion and fixation in photosynthesis when PAR and Ca both change simultaneously [50] . Rubisco limitation and RuBP regeneration limitation often co-exist in the nature, especially under fluctuating light and drought conditions (may cause Ci decrease) [51] . Therefore, results derived from a normal A/Ci (ACE, Vcmax and Jmax) and LRC (AQY) may not be suitable to explain photosynthesis at these conditions.
Another feature of dsf or ΔAn/ΔCi-lrc is that it is independent of gas exchange measurement conditions (lower PAR and Ca). The dsf has little dependence on Ca since the Michaelis–Menten constants for the carboxylase (Kc) are relatively large [29] [52] , which may explain why DSF from different Ca were almost parallel to each other and why there was no significant difference between dsf and ΔAn/ΔCi-lrc. This property allows the use of dsf or ΔAn/ΔCi-lrc to link CO2 supply and biochemical demand of photosynthesis when Rubisco and RuBP regeneration are co-limiting.
4.2. Demand-Supply Function vs Ci/Ca
The supply function reflects the diffusion of CO2 while the demand function reflects the photochemical and biochemical processes of CO2 assimilation as a function of intercellular CO2 concentration (Ci) [20] . Ci acts as a CO2 pool connecting upstream and downstream, which regulates the supply-demand relationship of photosynthesis to a certain extent [53] . Our results showed that Ci/Ca was not closely related to gs within the range of Ca used in this study although it decreased with decreases in Ca to some extent while no significant differences between in species. Woody plants usually adopt a dynamic leaf gas-exchange strategy and do not maintain a constant value of Ci/Ca [9] . Therefore, Ci/Ca was not suitable to describing coordination between CO2 diffusion and photosynthetic biochemistry under the Laisk measurement protocol in the three species. However, the slope of the Demand-Supply function was closely related to gs, and different between the species and thus may better reflect the response of photosynthesis to stomatal conductance.
4.3. The Vertical Line Method Improves
and Rd Estimation
There are concerns about the validity of Laisk method which is widely used to estimate Rd [23] . Our results demonstrate that the novel vertical line method produced more robust estimates of
and Rd than the conventional average midpoint method, especially in white birch. Although the theoretical basis of the Laisk method is the FvCB model, the Rd estimate using the original Laisk method (Laisk 1977) is compromised because decreasing light reduces
which in turn affects the estimate of Rd [36] . The Laisk method uses the initial portion of A/Ci curves under several sub-saturation light intensities. However, it is unknown whether photosynthesis is limited by Rubisco activities or by RuBP regeneration under such measurement conditions . Those partial A/Ci curves theoretically should intersect at a single point defined by (
, −Rd), but different curves have different weights on the determination of the intersecting point [22] . The different A/Ci curves measured in the Laisk Method tend to have similar slopes and a great degree of overlapping. Consequently, the determination of the intersection point and thus
and Rd estimation are more vulnerable to instrument and operation errors [38] .
The conventional average midpoint method directly averages the coordinate values of the pairwise intersecting points of three A/Ci curves and therefore is also prone to errors if the differences in slopes are small [38] . Mean values of
and Rd fluctuate greatly (higher coefficient of variation) when calculated by the average midpoint method in white birch, leading to difficulties for the application of the Laisk method. Our results show that the coefficient of variation of lv slope (from the average DSF slope) of white birch was significantly larger than those of the other two species, and the DSF showed a slightly increasing trend with increases in Ca and was lower in black cottonwood and balsam poplar, suggesting that the poor performance of the Laisk method (i.e., failure to intersect at one point or the intersection was not in the fourth quadrant) in white birch may be related to the coordination of supply and demand functions. The vertical line method produced more robust estimates of
and Rd than the average midpoint method, possibly because the slope of the auxiliary line lv was much larger than those of the initial A/Ci lines in the conventional Laisk method. Deeper slopes generally produce more stable and reliable determinations of the intersecting point [54] .
5. Conclusion
Our results show that the demand-supply function (DSF) concept and the auxiliary line approach that we developed in this study represent a significant enhancement to the conventional Laisk method. The slope of DSF was essentially ΔAn/ΔCi-lrc measured by LRC. Using an auxiliary line perpendicular to DSF can improve the stability of Laisk method for estimating
and Rd. The dsf was negatively correlated with gs, ACE, and AQY, and linked CO2 diffusion limitation and biochemical limitation of photosynthesis. The dsf should be particularly useful for modeling photosynthesis under dynamic other environment conditions (particularly light) than conventional CO2 diffusion (gs, Ci/Ca) and biochemical (Vcmax, Jmax, ACE, AQY) photosynthesis models alone. Our results suggest that dsf (or ΔAn/ΔCi-lrc) may be species specific. Since it was independent of measurement environment conditions (PAR and Ca), DSF can be used to characterize the intrinsic coordination between CO2 diffusion and biochemical carbon fixation in photosynthesis. The ability of photosynthesis and ecological models to consider dynamic, non-saturating light conditions should become more important in the future for predicting plant response to climate change because such an ability will provide more realistic estimates of the dynamic activities of photosynthesis associated with dynamic environmental conditions. Environmental conditions will likely be more dynamic in the future [18] .
Acknowledgements
We want to thank Ms. Keri Pidgen, Greenhouse Manager of Lakehead University for her logistic support and other operational assistance during the experiments. We also thank the National Tree Seed Centre of Canada for providing balsam poplar seeds.
Supplementary Materials
Additional supporting information may be found online in the Supporting Information section at the end of the article.
Supplementary Materials
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Figure S1. An example diagram of light response curve (LRC) measured at 400 μmol·mol−1 ambient CO2 concentration with black cottonwood. (a): An vs. Ci form LRC data and the slope is ΔAn/ΔCi-lrc (slope of An variation vs Ci variation under light response curve). (b): normal LRC with An vs. PAR and the initial slope represent apparent carboxylation efficiency (AQY) for 400 μmol·mol−1 of Ca.
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Figure S2. Schematic of demand-supply function (DSF) slope (dsf) change from −0.2 to −0.1 based on the measurement of an example. Slope of DSF (−0.2) = ΔAn (−0.2)/ΔCi (−0.2) and DSF (−0.1) = ΔAn (−0.1)/ΔCi (−0.1) may reflect the carboxylation efficiency of photosynthesis during the Laisk measurement (PAR from 75 μmol·m−2·s−1 to 300 μmol·m−2·s−1).
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Figure S3. Diagram of A/Ci (a) and light response curve (b) on black cottonwood as an example. The apparent carboxylation efficiency (ACE) increased with the increase of PARs (a), while the apparent quantum yield (AQY) increased with the increase of Ca (b).
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Table S1. Actual Laisk measurements on black cottonwood showing in Figure 2.
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Table S2. A Laisk dataset from Walker’s Supplemental 5 in “An improved approach for measuring the impact of multiple CO2 conductance on the apparent photorespiratory CO2 compensation point through slope-intercept regression.” The unit of Ci was converted from Pa to µmol·mol−1.
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Table S3. ANOVA P-values for the effects of species and Ca (leaf surface CO2 concentration) on DSF (Demand-Supply Function) slope and vertical line (lv) slope. The species were balsam poplar, black cottonwood and white birch. DSFs were for 100, 150 and 200 μmol·m−2·s−1 Ca.
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Table S4. ANOVA P-values for the effects of species on ACE, ΔAn/ΔCi-lrc, AQY, and dsf. See Figure 5 for other explanations.
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Table S5. ANOVA P-values for the effects of species and Ca (leaf surface CO2 concentration) on ΔAn/ΔCi (the slope of a line at the same Ca and different PARs). Species include balsam poplar, black cottonwood and white birch. Here ΔAn/ΔCi involved dsf100, dsf150, dsf200 from Laisk data and ΔAn/ΔCi-lrc from light response curve measurement under 400 μmol·mol−1 Ca.
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Table S6. ANOVA P-value for the effects of estimation method and species on Rd,
and gm based on Laisk dataset. The three estimation methods are the conventional average midpoint method (Laisk, 1977), the slope-intercept method (Walker et al., 2016) and our vertical line method. The species used include balsam poplar, black cottonwood and white birch.
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Table S7. Rd and
estimates using the conventional average midpoint method (MP), the slope-intercept method (SI) and our vertical line method (VL) from the same A/Ci measurements at 50, 130 and 240 μmol·m−2·s−1 PAR (i.e., Walker’s dataset) except for SI-5 which used two additional sets of A/Ci measurements at 420 and 800 μmol·m−2·s−1 PAR.