Accurate photosynthetic parameter estimation at low stomatal conductance: effects of cuticular conductance and instrumental noise

Accurate estimation of photosynthetic parameters is essential for understanding plant physiological limitations and responses to environmental factors from the leaf to the global scale. Gas exchange is a useful tool to measure responses of net CO2 assimilation (A) to internal CO2 concentration (Ci), a necessary step in estimating photosynthetic parameters including the maximum rate of carboxylation (Vcmax) and the electron transport rate (Jmax). However, species and environmental conditions of low stomatal conductance (gsw) reduce the signal-to-noise ratio of gas exchange, challenging estimations of Ci. Previous works showed that not considering cuticular conductance to water (gcw) can lead to significant errors in estimating Ci, because it has a different effect on total conductance to CO2 (gtc) than does gsw. Here we present a systematic assessment of the need for incorporating gcw into Ci estimates. In this study we modeled the effect of gcw and of instrumental noise and quantified these effects on photosynthetic parameters in the cases of four species with varying gsw and gcw, measured using steady-state and constant ramping techniques, like the rapid A/Ci response method. We show that not accounting for gcw quantitatively influences Ci and the resulting Vcmax and Jmax, particularly when gcw exceeds 7% of the total conductance to water. The influence of gcw was not limited to low gsw species, highlighting the importance of species-specific knowledge before assessing A/Ci curves. Furthermore, at low gsw instrumental noise can affect Ci estimation, but the effect of instrumental noise can be minimized using constant-ramping rather than steady-state techniques. By incorporating these considerations, more precise measurements and interpretations of photosynthetic parameters can be obtained in a broader range of species and environmental conditions. Supplementary Information The online version contains supplementary material available at 10.1007/s11120-024-01092-8.


Introduction
Gas exchange is a powerful tool in plant physiology that allows us to understand CO 2 and water relations in plants to compare plant performance in a range of environments (Stinziano and Way 2017;Vincent et al. 2017;Smith et al. 2020), to describe how plants cope with challenging environments (Kumarathunge et al. 2019;Zhu et al. 2020), and to model plant-environment interactions up to the global scale (Oleson et al. 2013;Rogers et al. 2017;Lombardozzi et al. 2018).However, gas exchange measurements require a sufficient signal-to-noise ratio to obtain high-quality data for inferences.This can be achieved by ensuring stomata are adequately open or by incorporating a model that accounts for cuticular conductance (g cw ) (Márquez et al. 2021).However, many lines of research specifically address either species or conditions that produce low stomatal conductance, including xerophytic species, conditions of water deficit, or high temperatures.A comprehensive understanding of the factors affecting gas exchange measurements, including stomatal conductance (g sw ) and g cw , is crucial for obtaining accurate data and drawing sound conclusions (See Table 1 for a list of abbreviations and equations).
Stomatal conductance is a vital process that has a direct impact on plant growth and productivity, as it constrains photosynthesis and water-use.Plant species present a wide variation in g sw depending on leaf morphology, physiology, ecotype, and environment, with many exhibiting low conductance.Low g sw presents a challenge to the estimation of photosynthesis, particularly in C3 species with maxima below 0.2 mol m −2 s −1 (Körner et al. 1986;Tezara et al. 1998), and rapid stomatal closure whenever conditions are not ideal (Radin et al. 1994) or at a particular time of day (Steppe et al. 2006).For example, in a survey of Citrus x sinensis (L.) and C. reticulata (Blanco), 35% of the mid-morning (9:00 am-11:00 am) gas exchange measurements exhibited total leaf conductance to water (g lw ) below 0.08 mol m −2 s −1 (Vincent et al., unpublished data).When g lw is low, the signal-to-noise ratio in gas exchange measurements is also low.Additionally, it becomes difficult to obtain a sufficient range in intercellular CO 2 concentration (C i ) to characterize the response of net CO 2 assimilation (A) to C i (A/C i curves) (Stinziano et al. 2020).Further compounding the signal-to-noise challenge in the context of A/C i curves, plants respond to elevated CO 2 by stomatal closure on an order of minutes.
Using A/C i curves, we can apply the Farquhar-von Caemmerer-Berry model of photosynthesis (Farquhar et al. 1980) to estimate photosynthetic parameters for comparing plant performance (Way and Sage 2008), understanding photosynthetic acclimation (Kumarathunge et al. 2019), and modelling vegetative carbon uptake (Oleson et al. 2013).In species or conditions with low g sw or stomata that close rapidly at high CO 2 , such as those seen in evergreen broadleaved species, these responses are difficult to characterize (Lin et al. 2023).Stomatal limitations may further lead to incorrect conclusions on what is limiting photosynthesis.For example, it is possible to misinterpret a stomatal limitation as a constraint related to Rubisco carboxylation.The recent development of rapid A/C i response (RACiR) curves (Stinziano et al. 2017(Stinziano et al. , 2019a, b) , b) and subsequently of the dynamic acclimation approach which allows more efficient use of constant-ramping methods (Saathoff and Welles 2021) may be sufficiently fast to circumvent the difficulties of stomatal closure in such species.
Although g lw is often assumed equal to g sw , this is not entirely accurate.Cuticular conductance (g cw ) is a component of g lw and a key factor that impacts gas exchange measurements in plants, as it involves the diffusion of gases across the cuticle layer of leaves (Márquez et al. 2022).Although in practice it is usually not considered, g cw can impact A/C i measurement, because the ratio of conductance to H 2 O and to CO 2 is dramatically different between stomata and cuticles.The diffusivity of H 2 O and CO 2 through the stomata have a ratio of 1.6, which forms the basis of estimates of stomatal conductance to CO 2 .However, the cuticle is a stronger barrier to CO 2 than H 2 O where the diffusivity of H 2 O is much higher than that of CO 2 with a ratio of 1:20-40 (Boyer et al. 1997;Boyer 2015b).In addition, overlooking g cw can be problematic because, in certain cases, it can reach levels as high as 28% of g lw (Holmgren et al. 1965;Boyer et al. 1997).Because estimates of C i are based on total conductance to CO 2 (g tc ), assuming that g lw = g sw can lead to misestimating C i (Table 1; Boyer 2015b).Variations in g cw among plant species can significantly affect the accuracy of gas exchange measurements (Márquez et al. 2021;Boyer et al. 1997), particularly in lowconductance species (Márquez et al. 2022).Previous studies have highlighted the impact of g cw on gas exchange measurements and underscored the need for appropriate correction methods to ensure accurate measurements (Grassi and Magnani 2005;Tominaga et al. 2018).However, estimating g cw separately from g sw , which usually governs gas diffusion through the leaf surface under illuminated conditions, has been a major challenge.Consequently, it is often neglected in gas exchange calculations.In this regard, a recent study by Márquez et al. (2022) has proposed a new approach, called the red-light method, which estimates g cw from gas exchange measurements and a known CO 2 concentration within the leaf during photosynthetic induction under red light.This novel method enables accurate estimation of g cw , the inclusion of which can improve the precision of gas exchange measurements.Lamour et al. (2022) recently provided a theoretical reassessment of the impact of g cw in the measurement of A/C i curves and the parameters calculated from them, using real A/C i curves and applying a range of hypothetical g cw .In practice, many researchers face species or conditions of highly variable g lw .Thus, knowledge of the impact of these factors and how to circumvent the resulting limitations in practice is essential, especially under low g lw conditions.
In this work, our objective was to assess the impact of g cw , g sw , and other sources of error on the validity of estimates of photosynthetic parameters.To test the impacts of g cw and g sw we selected four species that vary in both.We used the red-light method of g cw measurement and steady state and RACiR methods to estimate A/C i -based parameters in these species with varying g cw and g sw .Although the RACiR method has been superseded by a dynamic assimilation technique (DAT; Tejera-Nieves et al. 2024), which eliminated the need for running empty-chamber curves, the utility of both RACiR and DAT in terms of the use of constant-ramping and frequent logging to assess A/C i are interchangeable.We modeled the impact of g lw and g cw on C i estimates and developed criteria to understand the impact of conductance on the reliability of A/C i curves and the resulting parameters and provide this model for future work.

Modeling the impact of stomatal and cuticular conductance on estimates of internal CO 2
To estimate the impact of g lw on the estimation of C i we modeled the estimation of C i in response to varying external CO 2 concentrations (C a ) and g sw .To achieve this we used the Photosyn() command in the {plantecophys} package (Duursma 2015).This model allowed us to fix vapor pressure deficit (1.5 kPa) and C a (100, 400, or 2000 ppm), along with temperature (25 °C) and maximum rates of carboxylation (50 µmol m −2 s −1 ) and electron transport (100 µmol m −2 s −1 ), which are the default values in the model.We considered a range of g lw values from 0.001 to 1 mol m −2 s −1 in increments of 0.001 mol m −2 s −1 to cover the full range of expected values from medium to low conductance species.C i was initially calculated according to the standard calculations of most gas exchange equipment.This calculation is based on von Caemmerer and Farquhar (1981) as: where g tc is total conductance to CO 2 , which was estimated as: where 1.6 and 1.37 are the ratios of diffusivity of CO 2 to H 2 O in air (in stomata) and in the boundary layer.K is the ratio of stomatal resistance of the adaxial to abaxial sides of the leaf.For this consideration, we set K = 0, which is common for low conductance species, and boundary layer conductance to water (g bw ) as 2.23 mol m −2 s −1 .These equations are standard for estimates in gas exchange.If K = 0 and g bw is large enough to be ignored, as is expected in most gas exchange measurement contexts (Márquez et al. 2021), then Eq. 2 can be simplified as: g tc = g sw 1.6 , which assumes that g lw ≈g sw .
At high g lw , this assumption may be roughly correct.However, as g lw decreases relative to g cw , the assumption is likely to become less tenable and increasingly impact estimates of C i , because the cuticular conductance to CO 2 (g cc ) is expected to be approximately 0.05 g cw (Márquez et al. 2022).Thus, we corrected the original g lc by calculating: where 1:20 is the expected proportion of g cw to g cc (Boyer et al. 1997).Because the Photosynth() command assumes g lw = g sw and does not allow explicit parameterization of g tc , but calculates g tc = g lw /1.6 (Duursma 2015), we recalculated a pseudo-g lw to result in the corrected g tc by multiplying the corrected g tc by 1.6.C i was then recalculated based on the (1)

Gas exchange measurements
Response curves were measured using a portable infrared gas analyzer (LI-6800, Li-COR Inc., Lincoln, NE, USA) (Console version: Bluestem v.1.4.02) equipped with a 3 × 3 cm leaf chamber (9 cm 2 ).Leaf chamber settings were as follows: fan speed of 10,000 rpm, flow rate of 300 μmol s −1 and 600 μmol s −1 (for RACiR and SS, respectively), overpressure of 0.1 kPa, 24 mmol mol −1 of H 2 O in the reference cell producing between ~ 63% and 79% relative humidity (RH) in the leaf chamber, and producing a variation of ~ 2 to 3% in RH over the course of measurements, photosynthetically active radiation of 1200 µmol m −2 s −1 [90% red and 10% blue light], and chamber air temperature at 25 °C.We first measured paired standard RACiR and SS to compare parameter estimates from each.Each set of RACiR and SS curves was gathered on adjacent leaves of the same plant (not on the same leaf to avoid the effects of the first curve on the results of the second) on the same day.

Rapid A/C i response (RACiR) curves
RACiR data were gathered beginning at a reference CO 2 concentration of 100 µmol mol −1 with a ramping rate of 100 µmol mol −1 min −1 , ending at 900 µmol mol −1 .After testing paired measurements, we gathered five additional RACiR curves from five plants each for all four species, this time the C a range was 100 µmol mol −1 to 2000 µmol mol −1 (5) with the same 100 µmol mol −1 min −1 ramping rate.Before each curve, the IRGA was matched to allow the system to stabilize in match mode.The empty chamber curves were determined in exactly the same way as the RACiR curves, except that the leaves were not clamped.Moreover, one empty chamber curve was used to calibrate the two leaf runs taken within 1 h.For all measurements, the leaf chamber was clamped on the leaf and allowed to acclimate to set environmental conditions until A reached a steady state before running the CO 2 response curves; however, the acclimation time was variable among species.The 'Autolog' program of LI-6800 was used to record data every 2 s (9 min and 19 min for RACiR when CO 2 concentration was set at 100-900 µmol mol −1 and 100-2000 µmol mol −1 , respectively).

Steady-state A/C i curves
The LI-6800 CO 2 response program was used for the steadystate (SS) A/C i curves.Firstly, all environmental conditions were set the same as the RACiR curves except for the CO 2 .
Secondly, the sample CO 2 was set to 380 µmol mol −1 CO 2 .All leaves were acclimated to set environmental conditions until A reached a steady state before running the CO 2 response curves.SS curves were collected starting at a reference CO 2 concentration of 380 µmol mol −1 , then proceeding through the following progression conditions: 285,190,145,100,50,380,475,570,665,760,960,1160,1460,1760,1960 µmol mol −1 CO 2 with minimum and maximum waiting times of 60 s and 120 s, respectively.The reference and sample IRGAs were matched before each measurement (Stinziano et al. 2017), and the measuring time for each SS A/C i curve was approximately 30 min.

Measurement of cuticular conductance (g cw )
The g cw was estimated using the red-light technique introduced by Márquez et al. (2021).Briefly, the plants were dark-adapted for 12 h.A leaf was then placed in the darkened LI-6800 chamber and allowed to acclimate to 400 µmol mol −1 CO 2 , 25 °C, and 24 mmol mol −1 of H 2 O in the reference before recording dark respiration (R dark ).The dark-acclimated leaf was subsequently exposed to the same environmental conditions as those for R dark measurements, except that 100 µmol m −2 s −1 red light was applied, and measurements were taken every 7 s during the light induction until the maximum A was achieved, and over 5 min at steady state.
To determine the rate of electron transport or the electron transport rate at a given CO 2 concentration (J a ) and gamma star (Γ*, represents the CO 2 photo-compensation point) during the experiment, a RACiR curve was performed under the same conditions as during the red-light induction, with the exception that stomatal opening is promoted using 100 µmol m −2 s −1 red-blue (40 µmol m −2 s −1 blue), and a CO 2 concentration ranging from 100 µmol mol −1 to 1400 µmol mol −1 with a 100 µmol mol −1 min −1 ramping rate.The leaf chamber was clamped onto the leaf and allowed to acclimate to the set environmental conditions until A reached a steady state before running the CO 2 response curves.

Analysis
Raw data obtained for each leaf sample were filtered and corrected using the empty chamber data as per the protocol for RACiR curve correction provided by Coursolle et al. (2019).RACiR data were calibrated using the {racir} R package (Stinziano et al. 2019a;Lawrence et al. 2019;Stinziano 2020).All curves were fit using the fitaci() command from the {plantecophys} package (Duursma 2015;Pilon et al. 2018) in R statistical software (R Core Team 2013), with options selected to fit triose phosphate utilization (TPU) limitation rate and with no temperature correction.We extracted the maximum Rubisco carboxylation capacity (V cmax ), maximum electron transport rate under saturating light (J 1200 ), triose phosphate utilization (TPU), dark respiration (R dark ), the C i at the CO 2 to RuBP transition (C itrans1 ), and the C i at RuBP to TPU transition (C itrans2 ) for analysis.Subsequently, all A/C i curves were fit with uncorrected and corrected g sw values to assess the impact of g cw on parameter estimates.

Statistics
The resulting parameters from the fit curves were subjected to analysis of variance and paired Student's t-tests by using Statistix 8.1® software to test for differences between SS and RACiR curves.These tests were performed on A/C i curves derived with uncorrected and corrected g sw .Multiple comparisons were performed with Tukey's honestly significant difference (Tukey's HSD), and differences were significant when P < 0.05.Data in the figures were processed and analyzed with R (R version 4.1.1,2021 "Kick Things").

Data and code
Data and code are available in supplementary files S1.

At low g sw , C i estimates become unreasonable
There was a strong impact of g lw on C i .C a also impacted the response dynamics, increasing the magnitude of C i reduction in response to reduced g lw (Fig. 1).The impact of g lw at a C a of 100 ppm was negligible, but its impact was strong at both 400 and 2000 ppm.This result indicated limits to the estimation of C i at low g lw , suggesting improvements in the accuracy of conductance estimates and C i impact estimates of C i to a greater degree at high C a .

Cuticular conductance impacts estimation of internal CO 2 as a proportion of total leaf conductance
We modeled the impact of accounting for g cw for a more accurate estimate of g tc (Fig. 2), using 0.0056 mol m −2 s −1 estimate of g cw from papaya as the case, because it fell toward the middle of the range of the four species assessed in this study (See below).As g lw declined, the proportional misestimation of C i increased exponentially (Fig. 1), this can be expressed as a proportion of g cw : g lw , resulting in a much greater alignment of the species tested and that the slope the response of misestimation due to the assumption that g sw = g lw is much slower than in response to g lw alone.These results suggest that including g cw in the calculation of C i will be important in any context where g cw is greater than 10% of g lw .Additionally, even species with relatively high g lw (eg.C. annuum and C. papaya) reached sufficiently high g cw :g lw to cause very large (> 50%) misestimations of C i .The overall response of misestimation of C i can be seen in Supplemental Fig. 1, where increasing g cw :g lw increases the misestimation of C i with moderate impacts from A, E, and C a .

Noise in the measurement of leaf conductance to water impacts estimation of internal CO 2 at low conductance
Noise is the random unexplained error associated with any measurement.Any instrument will have some noise associated with the estimation of any variable.We estimated the impact of noise on the IRGA instrument's estimation of g lw by summarizing the g lw estimates across several emptychamber rapid A/C i curves, which had been gathered to calibrate the leaf-sample curves.Because an empty, sealed chamber with no sample is known to have a conductance of 0, we could then record the conductance to estimate the precision of the estimate of 0. The standard deviation of g lw was 0.00415 mol m −2 s −1 .Given that the true value of g lw may easily be ± one standard deviation of the estimate at any given point, we added and subtracted this instrumental noise value from the g lw estimate to provide a range of possible "true values" and re-calculated A and C i .Instrumental noise in measuring g lw greatly impacts estimates of C i at low g lw values and compounds the possible misestimation of C i when not accounting for g cw (Fig. 3).

Considering cuticular conductance to water and instrumental noise alters A/C i response estimates
We measured the g cw of magnolia, papaya, citrus, and bell pepper, and found a wide range among these species from 0.0045 to 0.0076 mol m −2 s −1 (Table 2).Although the g cw estimates were within the range of the standard deviation of any single measurement of g lw , the standard deviation of the estimates of g cw were between 0.0009 and 0.0024.The greater precision of the estimate of g cw results from the approach to measuring g cw which uses the average of g lw over 5 min with measurements every 7 s Thus, each g cw measurement resulted from the mean of 42 g lw measurements.We considered the g cw of each species, as well as possible instrumental noise, and applied these to the RACiR and SS A/C i curves with the lowest observed conductance for each species (Fig. 4).The impact of accounting for g cw Proportional C i values are proportional to the value when g sw = 1 mol m −2 s −1 .The light green ribbon shows the gap between the corrected and uncorrected C i values, bounded on the bottom by the uncorrected C i estimate (solid black line) and on the top by the corrected estimate (dashed black line).The correction accounts for the differential effect of g cw in the estimation of g cc and thus on C i .The solid green line shows the proportional misestimation of C i due to not accounting for g cw proportional to the corrected value at the same g sw .The dashed blue horizontal line denotes a proportion 0.05 (5% miscalculation or uncertainty).In all cases vapor pressure deficit was 1.5 kPa, temperature was 25 °C, maximum rate of carboxylation was 50 µmol m −2 s −1 , electron transport was 100 µmol m −2 s −1 , and g cw was 0.0056 mol m −2 s. −1 (results for papaya, which fell toward the middle of the distribution among the four species) Fig. 2 Miscalculation in estimates of leaf internal CO 2 (C i ) concentrations over a range of low leaf conductance to water (g lw ) values considering the impact of cuticular conductance to water (g cw ) in the estimation of g sw and the resulting g tc and C i .Proportional C i values are proportional to the value when g sw = 1 mol m −2 s −1 .A shows the impact of accounting for g cw on the estimate of C i , expressed as a proportion of the C i estimate at g lw = 1.0 mol H 2 0 m −2 s −1 .B shows the same values as a proportion of g cw to g lw .The light red, green, or blue ribbons show the gap between the corrected and uncorrected C i values, bounded by the uncorrected C i estimate (solid black line) and the corrected estimate (dashed black line) proportional to the corrected value at the same g sw .The solid lines corresponding to the bands show the proportional misestimation of C i due to not accounting for g cw .The horizontal error bars show ± 1 standard deviation of maximum g cw :g lw in a series of five steady-state A/C i curves for each species.Assumptions, in this case, are V cmax = 50 µmol m −2 s −1 , C a = 400 µmol mol −1 , and VPD = 1.5 kPa and instrumental noise in the estimation of g lw varied by species and by the A/C i curve method, suggesting that in many cases constant-ramping (RACiR) curves are more precise than SS curves, and that under some conditions SS curves produced estimates within 1 standard deviation of g lw of unrealistic A/C i results.

RACiR versus steady-state A/C i curves
Overall, results from SS and RACiR curves were similar (Table 3).Notable differences are the smaller R dark estimates by SS than by RACiR and the small number of TPU estimates produced by RACiR, the latter was not surprising considering the lower pre-set range of C a values for RACiR, which prompted us to gather a new data set to test whether consistent estimation of TPU was possible with RACiR (see below).In addition, for magnolia, V cmax fitted to RACiR curves was lower than SS curves.In citrus, the value of g sw was higher in RACiR than in SS, illustrating that stomatal attenuation in citrus is lesser when using constant ramping than SS methods, because there is less time for stomatal responses to high C a .

Correcting for g cw impacts the estimation of photosynthetic parameters
To illustrate the effect of the g cw on A/C i -derived parameters, both the RACiR and SS A/C i curves were recomputed with corrected g sw .We then estimated the photosynthetic parameters from the recalculated A/C i data (Table 3).For magnolia and citrus, correcting for g cw affected V cmax and J 1200 estimates.In the case of SS curves, correcting for g cw affected V cmax estimates in all species except for magnolia.With corrected g sw , no difference was found for R dark regardless of A/C i curve type, except for citrus, which had a greater R dark value in RACiR with corrected g sw .Interestingly, correcting g sw decreased RACiR-derived C itrans1 for all species.However, for SS, only citrus showed a difference between corrected and uncorrected g sw -derived C itrans1 and C itrans2 .The g cw correction strongly decreased g sw estimate in SS curves.However, for RACiR, only g sw estimates in magnolia were affected by g cw correction.Solid lines represent the proportional error in the C i estimate.The purple line represents the maximum possible combined error from uncertainty in measuring g lw and not accounting for g cw .This scenario considers V cmax = 50 µmol m −2 s −1 , C a = 400 µmol mol −1 , and VPD = 1.5 kPa.ambient CO 2 , g cw = 0.0056 µmol m −2 s −1 , and the standard deviation of g lw = 0.00415 mol m −2 s −1 .The error in the g lw is based on empty chamber measurements using an LI-6800 infrared gas analyzer (LI-COR Biosciences, Lincoln, NE).The dashed horizontal line denotes a proportion of 0.05 (5% miscalculation or uncertainty) Table 2 Mean leaf conductance to water (g lw ) and cuticular conductance to water (g cw ) of magnolia (Magnolia grandiflora), citrus (Citrus sinensis), bell pepper (Capsicum annuum), papaya (Carica papaya) g lw values are the mean and standard deviation of measurements of five leaves during a steady-state A/C i curve.g cw are the mean and standard deviation of five leaves, estimated according to the method of Márquez et al. (2022) Species g lw (mol m −2 s −1 ) g cw (mol m −2 s −1 ) Magnolia (Magnolia grandiflora) 0.09 ± 0.02 0.0053 ± 0.0019 Citrus (Citrus sinensis) 0.12 ± 0.01 0.0045 ± 0.00085 Bell pepper (Capsicum annuum) 0.33 ± 0.11 0.0076 ± 0.0015 Papaya (Carica papaya) 0.17 ± 0.02 0.0056 ± 0.0024

Stomatal limitations to gas exchange
Maximum and minimum g sw and C i differed among species (Fig. 5).Papaya had the greatest g sw followed by bell pepper, citrus, and magnolia.The same trend was found for C i .Each species' g sw responded differently to changing C a in the RACiR curves, with some exhibiting reductions in A due to low g sw .In magnolia, two curves decreased A noticeably as C a exceeded 700 µmol mol −1 (Fig. 5).Moreover, in all the RACiR curves in magnolia, g sw decreased or remained low over time, regardless of C i concentration.In bell pepper, g sw increased from C a of 380 µmol mol −1 to 475 µmol mol −1 , while higher C a values decreased g sw .In citrus, g sw decreased as C a increased above ~ 400 µmol mol −1 .

RACiR curves with wide C a range
To test the range of C i attainable using constant-ramping, we performed separate curves with elevated C a up to 2000 µmol mol −1 (Table 4).Overall, the g sw pattern among species was the same as for previous measurements.
Table 3 Comparison of photosynthetic parameters as measured by steady-state (SS) and rapid A/C i response (RACiR) curves of magnolia (Magnolia grandiflora), citrus (Citrus sinensis), bell pepper (Cap-sicum annuum), papaya (Carica papaya) leaves with uncorrected g sw or corrected g sw , representing the mean value for all measurements of each curve Values are mean ± standard error.V cmax is the maximum rate of Rubisco carboxylase activity, J 1200 is the maximum rate of photosynthetic electron transport under saturating light (photosynthetic photon flux density of 1200 µmol m −2 s −1 ), R dark is the daytime respiration.TPU is a triose phosphate utilization limitation rate.C i is the intercellular concentration of CO 2 .C itrans1 represents C i at which the transition between CO 2 and RuBP limitations (i.e.V cmax and J 1200 ) occurs.C itrans2 is C i at which the transition from RuBP to TPU limitations (i.e.J 1200 and TPU) occurs.g sw represents the stomatal conductance to water vapor.Except where noted n = 5 *Indicates a significant difference (P < 0.05) between RACiR and SS A/C i derived parameters within g sw corrected or uncorrected categories Ω Indicates a significant difference (P < 0.05) between derived parameters of g sw corrected and uncorrected curves within RACiR or SS A/C i curve categories 1 Mean excludes the J 1200 estimate of 1,000,000 µmol m −2 s −1 , as this is considered to be an error 2 At least one replication has missing data, which resulted when the curve fitting did not produce an estimate for that parameter 3 Δ CV is the fold change in the coefficient of variation (standard deviation/mean) due to using RACiR versus using the steady state technique (eg.positive Δ CV means RACiR reduces CV relative to SS) Moreover, TPU fitted by RACiR curves was observed for all species except for one curve in magnolia (Table 4 and Fig. 4).Correcting for g cw increased the V cmax estimate in all species, except citrus.J 1200 was only impacted in magnolia.R dark , TPU, and C itrans2 were decreased in bell pepper and papaya while C itrans1 and g sw were decreased in all species by correcting for g cw .

Species-specific leaf conductance characteristics and their implications for A/C i curves
Leaf conductance and stomatal behavior are known to vary across environmental conditions and species (Jones et al. 2009;Cabrerizo and Marañón 2022).Through the characterization of species-specific leaf conductance, researchers can gain valuable insights into the functional traits and adaptations that contribute to the successful adaptation of plants in diverse environments (Mott and Buckley 2000;Franks et al. 2009).For this study, we selected four plant species with distinct leaf conductance characteristics: bell pepper and papaya, exhibiting high g lw , citrus with intermediate g lw , and magnolia with the lowest g lw .g cw values were 1-2 orders of magnitude less than the g lw (Table 2).g cw :g lw helped make species more comparable in terms of misestimation of C i , and a ratio of only 0.1 was required to exceed 5% misestimation of C i whenever C a was 400 ppm or greater.This ratio could be used to assess the risk of large C i misestimation, because the risk of misestimation could not be assessed using g lw alone.The risk of misestimation of C i increased with C a , however, the 5% misestimation point is exceeded at approximately the same g lw for C a of both 400 and 2,000 ppm.This misestimation has implications for the interpretation of A/C i curves, as demonstrated by the problematic nature of some of the uncorrected SS curves (Fig. 4).Our findings emphasize the necessity of accounting for g cw in accurately estimating C i and highlight the potential impact of misestimation on the interpretation of A/C i responses.

Impact of accounting for g cw on A/C i fitted parameters
The cuticle has been known to impact the estimation of photosynthetic parameters by impacting estimates of C i (Hanson et al. 2016).According to previous reports, g cw influences the calculation of C i (Boyer 2015a;Tominaga et al. 2018).
In the present study, recalculated A/C i curves (both SS and RACiR) using the g cw values obtained from the red-light method (Márquez et al. 2021) indicate that considering g cw does modify C i estimates.The extent of the effect varies among species and is more pronounced when the g cw :g lw ratio is high or the g sw is low, which results in a decrease in C i .Lamour et al. (2022) proposed that the ratio of g cw :g lw could be important in predicting the misestimation of C i .The present results support and extend that hypothesis by demonstrating that even high conductance species may have sufficiently high g cw :g lw ratios to have strong impacts on the misestimations of C i .Papaya was the least affected on average, as it exhibited the highest g sw during measurements, whereas magnolia, with low g sw , showed significant changes in most photosynthetic parameters.These findings underscore the importance of g cw in estimating photosynthetic traits, as ignoring g cw can introduce a bias that incorrectly increases estimates of C i .The data presented in Table 3 and Table 4 indicate a significant increase in V cmax , J max , R dark , and C itrans1 when the g cw :g sw ratio is high, which could occur in any of the species assessed when g sw was low within the range for that species.Thus, plant conditions of water deficit, supra-or suboptimal temperatures, or other adverse growing conditions are likely to induce sufficiently low g sw as to necessitate the estimation of g cw to estimate accurate photosynthetic parameters.

Constant-ramping A/Ci method improves parameter resolution and avoids some stomatal limitations
In previous studies, comparisons between the RACiR and SS methods have indicated that the A/C i fitted parameters, V cmax and J max , show no significant differences in a range of species (Stinziano et al. 2017(Stinziano et al. , 2019b;;Coursolle et al. 2019;Lawrence et al. 2019;Saathoff and Welles 2021;Lin et al. 2023).In our study, the results of A/C i curves obtained using both the SS and RACiR methods were similar, with more precise estimates of C itrans1 observed with the RACiR method, as seen in the smaller standard deviation in C itrans1 in RACiR than SS for all species, with and without correction of C i (Table 3).For example, the reductions in standard deviation represent a 16% decrease in the coefficient of variation (standard deviation/mean) for magnolia (the smallest change) and a 78% decrease in the coefficient of variation for bell pepper (the largest change).However, a notable difference was found in the g sw values, where the SS curves showed a greater decrease in g sw compared to the RACiR curves (Fig. 5).The likely reason for these differences is that the RACiR curves allowed less time for g sw to decrease before reaching the critical threshold.SS curves are measured slowly relative to the time scale of leaf CO 2 attenuation of g sw (Merilo et al. 2015).This leads to the reduction of g sw in some curves below that required for reliable estimates of C i .We do note, however, that the traditional approach to A/C i curves-starting near atmospheric CO 2 , going down, then up such as in Busch (2018) may not be the best option for maximizing g sw during the SS.Starting at low CO 2 and monotonically increasing CO 2 may result in better A/C i estimates (Sharkey 2019), though our initial attempts were not successful with this approach in terms of avoiding the g sw crash in citrus and magnolia.
To assess the A/C i relationship, it is ideal to achieve a wide range of C i values.The RACiR method achieved as wide a range of C i as the SS method, though low conductance magnolia limited the C i range achieved (Fig. 2).These findings align with the results reported by Lin et al. (2023), who found that measuring SS A/C i and RACiR curves in low conductance species posed challenges due to their low g sw values.Consequently, driving C i to a very high level is difficult or even impossible in these species.In the present study, at higher C a values g sw decreased (Fig. 5).In this case, the advantage of constant ramping lies in that its short time "beats" the speed of stomatal attenuation, affording the ability to avoid stomatal impacts on the shape of the A/C i curve, making TPU estimation more feasible in low conductance species.
Stomatal attenuation can particularly affect the estimation of TPU, as it may induce changes in A at high C i that are limited by g sw , rather than by enzymatic limitations, despite the similarity in shape of the curve to the expected shape with TPU limitations, as is seen in Fig. 4 in papaya and bell pepper.Plants are not typically TPU-limited under ambient conditions (Sage and Sharkey 1987;Sharkey 2019;Ellsworth et al. 2015), and TPU limitation is most easily seen by elevating the rate of photosynthesis through increased light or CO 2 or decreased O 2 partial pressure (Sharkey et al. 1986) such that A is increased by 10% or 20% relative to ambient conditions (Kirschbaum 2011).Our initial comparison was between RACiR and SS fitted photosynthetic parameters with C a maxima of 900 and 2000 µmol mol −1 , respectively.In this comparison, SS curves yielded a greater number of TPU estimates than RACiR curves.However, when RACiR was performed with a maximum C a of 2000 µmol mol −1 , TPU estimates were achieved in all species (Table 4).Thus, constant-ramping methods can consistently estimate TPU when a sufficiently high maximum C a are used.
In addition to its increased speed, the utilization of a constant ramping technique, such as RACiR, offers the advantage of improved resolution of parameter estimates.This improvement stems from the reduction in parameter uncertainty that can be achieved by having a larger amount of data available for curve fitting (Saathoff and Welles 2021).It has been observed that the accuracy of parameter estimation is directly influenced by both the number of data points and the accuracy of the gas exchange data used.When working with small and noisy data sets, obtaining robust parameter estimates can be particularly challenging (Sharkey et al. 2007;Wang et al. 2017).In our study, the SS A/C i curve data consisted of only 16 data points, while the RACiR curves comprised significantly higher numbers (270 and 600 data points at 900 and 2000 µmol mol −1 C a , respectively).Our findings indicate the larger data set obtained by the RACiR technique reduced parameter uncertainty in comparison to SS.
The uncertainty of instrumental noise in g lw estimates has the potential to further compound the challenges of low conductance.Accounting for g cw can mitigate misestimation of C i , and if g cw is accounted for, the potential error due to instrumental noise only exceeds 5% at a g cw : g lw ratio of 0.13.However, constant-ramping methods ameliorate the impact of instrumental noise on the estimation of photosynthetic parameters due to the substantial number of measurements collected.While individual measurements of g lw may deviate by approximately ± 0.00415 mol m −2 s −1 from the true value, the cumulative effect of numerous measurements diminishes the impact of the error on the overall results.With an increased number of measurements, the net effect tends toward zero, rendering the influence of instrumental noise inconsequential in the approach that employs the larger dataset.This is reflected in the very small impact of the error of g lw on parameter estimates in RACiR relative to SS curves (Fig. 3).Thus, accounting for g cw and utilizing constantramping methods significantly enhance the accuracy and reliability of A/C i parameter estimates.

Conclusions
Low conductance presents a challenge to the estimation of photosynthetic parameters via gas exchange due to the misestimation of C i .This work demonstrates that not accounting for g cw can lead to a misestimation of C i , which compounds to the estimation of parameters based on C i , leading to underestimation of V cmax and J max .Instrumental noise can further compound errors when using a steady-state approach to A/C i measurement.The ratio of g cw :g lw is useful in assessing the risk of misestimating C i .Although this challenge was expected for low-conductance species, this work showed that high-conductance species, like C. papaya, can also exhibit high risk of overestimating C i .Thus, practices to improve the estimation of C i include using constant-ramping methods and measuring and accounting for g cw on at least a species basis.Using these approaches will improve the accuracy of A/C i -based photosynthetic parameter estimation, especially under conditions that reduce g sw .

Fig. 1
Fig.1C i in response to g lw , where g lw is assumed to equal g sw , under varying g lw and scenarios of C a = 100, 400, or 2000 µmol mol −1 .Proportional C i values are proportional to the value when g sw = 1 mol m −2 s −1 .The light green ribbon shows the gap between the corrected and uncorrected C i values, bounded on the bottom by the uncorrected C i estimate (solid black line) and on the top by the corrected estimate (dashed black line).The correction accounts for the differential effect of g cw in the estimation of g cc and thus on C i .The solid green line shows the proportional misestimation of C i due to not accounting for g cw proportional to the corrected value at the same g sw .The dashed blue horizontal line denotes a proportion 0.05 (5% miscalculation or uncertainty).In all cases vapor pressure deficit was 1.5 kPa, temperature was 25 °C, maximum rate of carboxylation was 50 µmol m −2 s −1 , electron transport was 100 µmol m −2 s −1 , and g cw was 0.0056 mol m −2 s. −1 (results for papaya, which fell toward the middle of the distribution among the four species)

Fig. 3
Fig. 3 Uncertainty due to instrumental noise and miscalculation in estimates of leaf internal CO 2 (C i ) concentrations over a range of low leaf conductance to water (g lw ) values considering the impact of cuticular conductance to water (g cw ) and technical uncertainty in the estimation of g lw .A shows C i estimate and potential proportional miscalculation in response to g lw .B shows the same variables in response to the ratio of g cw to g lw .C i values are expressed as a proportion of the C i estimate at g lw = 1.0 mol H 2 O m −2 s −1 .Proportional error values are the difference between the uncorrected and the corrected values divided by the corrected value.Red indicates uncorrected estimates, and blue indicates corrected estimates.Dashed lines represent the estimate, while the ribbons indicate the range ± std.dev.Solid lines represent the proportional error in the C i estimate.The purple line represents the maximum possible combined error from uncertainty in measuring g lw and not accounting for g cw .This scenario considers V cmax = 50 µmol m −2 s −1 , C a = 400 µmol mol −1 , and VPD = 1.5 kPa.ambient CO 2 , g cw = 0.0056 µmol m −2 s −1 , and the standard deviation of g lw = 0.00415 mol m −2 s −1 .The error in the g lw is based on empty chamber measurements using an LI-6800 infrared gas analyzer (LI-COR Biosciences, Lincoln, NE).The dashed horizontal line denotes a proportion of 0.05 (5% miscalculation or uncertainty)

Fig. 5
Fig. 5 Plots of net CO 2 assimilation (A) and stomatal conductance (g sw ) by intercellular CO 2 concentration (C i ), and distributions of maximum and minimum g sw and C i of leaves of magnolia (Magnolia grandiflora), citrus (Citrus sinensis), bell pepper (Capsicum annuum), papaya (Carica papaya) using RACiR method.P-values indicate the results of Tukey's HSD test

Table 1
Abbreviations, variables, and equations used to calculate conductances and estimate net assimilation and internal CO 2

Table 4
Values are mean ± standard error.V cmax is the maximum rate of Rubisco carboxylase activity, J 1200 is the maximum rate of photosynthetic electron transport under saturating light (photosynthetic photon flux density of 1200 µmol m −2 s −1 ), R d is the daytime respiration.C i is the intercellular concentration of CO 2 .C itrans1 represents C i at which the transition between CO 2 and RuBP limitations (i.e.V cmax and J 1200 ) occurs.C itrans2 is C i at which the transition from RuBP to TPU limitations (i.e.J 1200 and TPU) occurs.g sw represents the stomatal conductance to water vapor