Major diffusion leaks of clamp-on leaf cuvettes still unaccounted: how erroneous are the estimates of Farquhar et al. model parameters?

Authors

  • MIRCO RODEGHIERO,

    1. Centro di Ecologia Alpina, Viote del Monte Bondone, Trento 38070, Italy,
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  • ÜLO NIINEMETS,

    Corresponding author
    1. Institute of Agricultural and Environmental Sciences, Estonian University of Life Sciences, Kreutzwaldi 1, Tartu 51014, Estonia,
    2. Department of Plant Physiology, University of Tartu, Riia 23, Tartu 51010, Estonia,
      Ü. Niinemets. Fax: +372 731 3738; e-mail: ylo.niinemets@emu.ee
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  • ALESSANDRO CESCATTI

    1. European Commission–DG Joint Research Centre, Institute for Environment and Sustainability, Ispra, Varese 21020, Italy
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Ü. Niinemets. Fax: +372 731 3738; e-mail: ylo.niinemets@emu.ee

ABSTRACT

Estimates of leaf gas-exchange characteristics using standard clamp-on leaf chambers are prone to errors because of diffusion leaks. While some consideration has been given to CO2 diffusion leaks, potential water vapour diffusion leaks through chamber gaskets have been neglected. We estimated diffusion leaks of two clamp-on Li-Cor LI-6400 (Li-Cor, Inc., Lincoln, NE, USA) leaf chambers with polymer foam gaskets and enclosing either 2 or 6 cm2 leaf area, and conducted a sensitivity analysis of the diffusion leak effects on Farquhar et al. photosynthesis model parameters – the maximum carboxylase activity of ribulose 1·5-bisphosphate carboxylase/oxygenase (Rubisco) (Vcmax), capacity for photosynthetic electron transport (Jmax) and non-photorespiratory respiration rate in light (Rd). In addition, net assimilation rate (An) versus intercellular CO2 (Ci) responses were measured in leaves of Mediterranean evergreen species Quercus ilex L. enclosing the whole leaf chamber in a polyvinyl fluoride bag flushed with the exhaust air of leaf chamber, thereby effectively reducing the CO2 and water vapour gradients between ambient air and leaf chamber. For the empty chambers, average diffusion leak for CO2, inline image, (molar flow rate corresponding to unit CO2 mole fraction difference) was ca. 0.40 µmol s−1. inline image increased ca. 50% if a dead leaf was clamped between the leaf chamber. Average diffusion leak for H2O was ca. 5- to 10-fold larger than the diffusion leak for CO2. Sensitivity analyses demonstrated that the consequence of a CO2 diffusion leak was apparent enhancement of An at high CO2 mole fraction and reduction at lower CO2 mole fraction, and overall compression of Ci range. As the result of these modifications, Farquhar et al. model parameters were overestimated. The degree of overestimation increased in the order of Vcmax < Jmax < Rd, and was larger for smaller chambers and for leaves with lower photosynthetic capacity, leading to overestimation of all three parameters by 70–290% for 2 cm2, and by 10–60% for 6 cm2 chamber. Significant diffusion corrections (5–36%) were even required for leaves with high photosynthetic capacity measured in largest chamber. Water vapour diffusion leaks further enhanced the overestimation of model parameters. For small chambers and low photosynthetic capacities, apparent Ci was simulated to decrease with increasing An because of simultaneous CO2 and H2O diffusion leaks. Measurements in low photosynthetic capacity Quercus ilex leaves enclosed in 2 cm2 leaf chamber exhibited negative apparent Ci values at highest An. For the same leaves measured with the entire leaf chamber enclosed in the polyvinyl fluoride bag, Ci and An increased monotonically. While the measurements without the bag could be corrected for diffusion leaks, the required correction in An and transpiration rates was 100–500%, and there was large uncertainty in Farquhar et al. model parameters derived from ‘corrected’An/Ci response curves because of uncertainties in true diffusion leaks. These data demonstrate that both CO2 and water vapour diffusion leaks need consideration in measurements with clamp-on leaf cuvettes. As plants in natural environments are often characterized by low photosynthetic capacities, cuvette designs need to be improved for reliable measurements in such species.

INTRODUCTION

Portable gas-exchange systems with miniaturized clamp-on leaf cuvettes have become increasingly popular in plant science. These systems are characterized by virtual ease of controlling flow rate, leaf temperature and CO2 and water vapour mole fractions, and are therefore widely employed to measure net assimilation rate (An) versus intercellular CO2 mole fraction (Ci) responses, and derive the parameters of Farquhar, von Caemmerer & Berry (1980) biochemical photosynthesis model. However, clamp-on cuvettes have important shortcomings. For homobaric leaves with significant lateral gas exchange, partial leaf clamping can result in significant gas exchange between ambient air and leaf chamber laterally through the leaf gas phase (Jahnke 2001;Jahnke & Krewitt 2002; Pieruschka, Schurr & Jahnke 2005). Even without the lateral gas exchange through the leaf, conventional clamp-on cuvettes are prone to diffusion leaks through chamber foam gaskets (Long & Hällgren 1993; McDermitt et al. 2001; Long & Bernacchi 2003) that inevitably occur if there are gas mole fraction differences between ambient air and leaf chamber. Given that a small leaf area, typically 1–6 cm2, is enclosed in the clamp-on leaf chamber, such diffusion fluxes through the gaskets can be of significant magnitude relative to leaf gas-exchange rates, especially in species with low An (Bruhn, Mikkelsen & Atkin 2002; Pons & Welschen 2002).

As leaf chamber CO2 concentration is changing widely during An/Ci curve measurements, significant CO2 diffusion leaks through the gaskets can occur in clamp-on chambers. While the CO2 diffusion leak problems of such cuvettes have been known for some time (Long & Hällgren 1993; McDermitt et al. 2001; Long & Bernacchi 2003) and manufacturers have suggested ways for correction of the CO2 diffusion leaks (e.g. Li-Cor, Inc. 2004, H. Walz GFS-3000 portable system manual), diffusion leaks are more often ignored than considered. Only few studies have estimated the magnitude of the diffusion leaks through the gaskets on leaf gas-exchange rates (McDermitt et al. 2001; Bruhn et al. 2002). In addition, the corrections suggested are developed for empty leaf chamber, but presence of the leaf in the chamber can enhance the diffusion leaks (Long & Bernacchi 2003).

Furthermore, the importance of water vapour diffusion leaks of clamp-on cuvettes has not been considered so far. Given that humidity in leaf chamber inevitably increases because of leaf transpiration, and gas-exchange measurements are commonly conducted at high leaf chamber humidity to keep the stomata open, significant water vapour diffusion gradients commonly occur between leaf chamber air and less humid ambient air. Significant water vapour diffusion leaks alter An/Ci curves in two ways. Firstly, errors in leaf transpiration measurements result in errors in stomatal conductance, and accordingly, in Ci calculations. Secondly, the humidity increase in the leaf chamber because of transpiration increases the bulk flow rate through the leaf chamber, and therefore, both Ci and An calculations include the flow correction term because of leaf transpiration (von Caemmerer & Farquhar 1981). So far, no detailed analyses have been published on the impact of combined CO2 and water vapour leaks on the estimations of assimilation and transpiration rates with clamp-on cuvettes and on subsequent derivation of Farquhar et al. (1980) model parameters.

Our objectives were to estimate CO2 and water vapour diffusion leaks for different-sized clamp-on cuvettes and for different situations (empty leaf chamber versus leaf chamber with simulated leaf, new versus old gaskets), and to quantify the uncertainties in the measurements of An/Ci responses and in derivation of Farquhar et al. (1980) model parameters that are introduced by the diffusion leaks. As the effects of diffusion leaks are expected to be most significant for leaves with low photosynthetic capacities and transpiration rates (McDermitt et al. 2001; Pons & Welschen 2002), the physiological measurements were conducted with leaves of low-capacity Mediterranean evergreen broadleaved species Quercus ilex L. Quercus ilex possesses heterobaric leaves that have large resistance to lateral gaseous transport (Nikolopoulos et al. 2002). In addition, a sensitivity analysis was conducted to explore the influences of diffusion leaks on the An/Ci responses and on the derivation of leaf photosynthetic potentials for leaves with varying photosynthetic capacity. Finally, we evaluated the effectiveness of a simple method for reduction of the diffusion leaks via diminishing the diffusion gradient between the interior of leaf chamber and ambient air. For this, we enclosed the entire leaf chamber in a Tedlar (Du Pont Inc., Wilmington, DE, USA) (fluorinated hydrocarbon with low CO2 and H2O permeabilities) bag supplied with the exhaust air from the leaf chamber. Our results demonstrate major CO2 and water vapour diffusion leaks of clamp-on cuvettes that result in major errors in derivation of photosynthetic potentials in species with low photosynthetic capacity.

MATERIALS AND METHODS

Theory of diffusion leaks

In an empty leaf cuvette without a diffusion leak, reference (incoming) (CR for CO2 and WR for H2O, in mol mol−1) and sample (outgoing) (CS for CO2 and WS for H2O) CO2 and water vapour mole fractions remain constant. However, incoming and outgoing CO2 and water vapour mole fractions are not equal as soon as the seal is not perfect, and there is a diffusion gradient between cuvette and ambient air, i.e. cuvette and outside gas (CA for CO2 and WA for H2O) mole fractions are different. In a steady state, the mass balance equation for H2O of empty cuvette with a diffusion leak is:

image(1)

where ui is the molar flow rate (µmol s−1) into the leaf chamber that is measured by Li-Cor mass flow controller (Li-Cor, Inc., Lincoln, NE, USA) positioned before the leaf chamber, uo (µmol s−1) is the molar flow rate exiting the leaf chamber and inline image characterizes H2O transfer rate as a result of diffusion (Li-Cor, Inc. 2004). Implicit in Eqn 1 is that air mixing in leaf chamber is turbulent. As a fan is installed in all available commercial gas-exchange chambers, this condition is generally satisfied.

As with transpiration from leaves (von Caemmerer & Farquhar 1981), uo and ui can be different if there is a significant net change in water vapour concentration in the chamber, i.e.

image(2)

Substituting uo into Eqn 1 and revealing inline image, we get:

image(3)

When WS is small, 1 − WS approaches unity and this term can be neglected. Ignoring 1 − WS, and normalizing inline image further with respect to ui, Eqn 3 simplifies to:

image(4)

While analogous equation has been derived by Li-Cor for CO2 diffusion (Li-Cor, Inc. 2004), the equation for water vapour is only valid if WS is small. In such a case, inline image gives the slope of (WS − WR)/(WA − WS) versus 1/ui relationship.

The mass balance for CO2 is expressed as:

image(5)

where inline image quantifies CO2 diffusion molar flow rate. Like transpiration can modify the molar flow rate out of the cuvette, uo, and thereby the calculations of net photosynthesis (von Caemmerer & Farquhar 1981), net change of water vapour concentration as a result of diffusion can alter uo, and thereby the apparent diffusion exchange of CO2 with leaf chamber. Substituting Eqn 2 into Eqn 5, and revealing inline image, we get:

image(6)

The second term in Eqn 6 is analogous to ‘transpiration correction’ in net photosynthesis calculations, i.e. the correction needed to account for changes in the outgoing air flow rate because of addition of water vapour by transpiring leaf (von Caemmerer & Farquhar 1981). Again, if the ‘transpiration’ correction can be neglected, and after normalization with respect to ui, we get the equation derived by Li-Cor (Li-Cor, Inc. 2004) for CO2 diffusion leak estimation:

image(7)

Quantifying CO2 and H2O diffusion leaks

Previous studies assessing the magnitude of CO2 correction term on leaf CO2 exchange using Li-Cor LI-6400 portable photosynthesis system have used the manufacturer's recommended value of inline image estimated for an empty chamber (Bruhn et al. 2002). However, no data are available for water vapour transfer rate as a result of diffusion (inline image), and both inline image and inline image depend on leaf cuvette size and shape (area for diffusion) and chamber foam gasket condition (old versus new). In addition, clamping the leaf between the chamber halves can significantly modify the magnitude of the diffusion leaks relative to an empty chamber (Long & Bernacchi 2003).

We conducted three series of experiments to determine the values of inline image and inline image using the portable LI-6400 gas-exchange system. The chamber effect was studied using two different chambers. The standard LI-6400-02B opaque bottom, rectangular leaf chamber encloses 6 cm2 (dimensions: 2 × 3 cm) leaf area, while LI-6400-40 chamber for combined gas-exchange and fluorescence measurements is a small round chamber enclosing 2 cm2 leaf area. The lower gasket of these leaf chambers is made of neoprene (synthetic rubber) foam, while the upper white gasket is either made of low-density polyethylene foam if used with light source (always the case of LI-6400-40) or of neoprene foam if LI-6400-02B is used without the light source (standard set-up that was used in our study for LI-6400-02B) (Li-Cor, Inc. 2004). For both the large and small chambers, the height of the gaskets on both the upper and lower chamber halves is 3 mm, and length of the diffusion pathway through the gasket (gasket width) is 5 mm. The inner gasket area exposed to chamber interior is 6 cm2 for the large and 3 cm2 for the small chamber.

To study the influence of the presence of a leaf in the chamber, the experiments with different-sized chambers were performed both using: (1) the empty chamber; and (2) the chamber enclosing a dead, dried ca. 250 µm thick leaf of evergreen Mediterranean species Quercus ilex (dead leaf). The average (±SE) area of the leaves used was 10.4 ± 0.31 cm2. The latch adjustment knob that determines the degree of compression of the gaskets was set according to the manufacturer's recommendations (Li-Cor, Inc. 2004), i.e. with the empty chamber closed, the latch knob was turned until it became snug, the chamber was opened and the knob was turned one more turn. The latch adjustment was left unchanged between the empty chamber and dead leaf experiments as recommended (Li-Cor, Inc. 2004).

The influence of gasket wear was investigated with the empty small leaf chamber using either new gaskets or the gaskets that had been previously used to measure net assimilation versus CO2 responses for 10 Quercus ilex leaves, i.e. the gaskets had been compressed in total of ca. 15 h over two measurement days. While the height of two brand new uncompressed gaskets is 6 mm, the height of used gaskets was 4 mm. The latch adjustment knob was set separately for new and old gaskets as explained earlier. Using silicone grease between the gasket halves (empty leaf chamber) demonstrated that the latch adjustment was optimal, and calculated CO2 diffusion coefficients for empty chamber were independent of whether or not silicone grease was used to improve the seal between the chamber halves.

All measurements were conducted in the laboratory. Ambient air temperature (without the bag) was 25.0 ± 0.5 °C, CO2 mole fraction was 350–600 µmol mol−1 and H2O mole fraction was 5.7–8.0 mmol mol−1. Leaf chamber block temperature was set to 28 °C, a specific reference CO2 mole fraction was set by LI-6400 CO2 mixer and the molar flow rate of incoming air (ui) was varied in steps (50, 100, 200, 300, 400 and 600 µmol s−1) to achieve a range of (CS − CR)/(CA − CS) values in dependence on the magnitude of diffusion leak relative to the overall flow rate (Eqn 7). At each flow rate, we waited until stable CO2 reference and sample signals were observed (the sum of coefficient of variations for the input variables <0.2%). After stabilization, the reference and sample gas analysers were carefully matched for at least 15 s to remove the offset between the sample and reference analysers, and the sample and reference CO2 and H2O concentrations were manually stored. At every flow rate, two recordings were taken, and averages were calculated.

Ambient air mole fractions of CO2 and H2O were monitored in the immediate vicinity of the leaf chamber every 2 s with a LI-7000 CO2/H2O analyser operating at a flow rate of 1120 µmol s−1. The values of (WS − WR)/[(WA − WS)(1 − WS)] were calculated for every ui value, and inline image was calculated from non-linear relationships of inline image versus (WS − WR)/[(WA − WS)(1 − WS)] (Eqn 3) iteratively minimizing the sum of squares between the measured and estimated function values.

After inline image was determined for the specific experiment, we calculated the values of (CS − CR)/(CA − CS) and the flow correction caused by apparent transpiration (Eqn 6). inline image was then calculated according to Eqn 6 using non-linear regression.

All diffusion coefficient measurements were replicated at reference (incoming) CO2 concentrations of 0, 50, 600, 1200 and 2000 µmol mol−1, and values of inline image were determined for every CO2 concentration. Repeating the experiment using different CO2 concentration sequences (from 2000 to 0 µmol mol−1 and randomly selecting CO2 concentrations) did not demonstrate any hysteresis effects that may potentially result from CO2 sorption and desorption. For different situations (chamber type, with or without dead leaf, old versus new gaskets), the values of inline image were further averaged over all CO2 concentrations used (as in Li-Cor, Inc. 2004).

To replicate inline image estimations, inline image was determined in separate experiments varying the reference water vapour mole fractions between 10 and 30 mmol mol−1. Stable water vapour mole fraction was achieved by adding a small amount of distilled gas-free water to the CO2 scrubber tube and empirically mixing the humid and dry air by the bypass valve of the desiccant tube. Again, an average value of all inline image estimations was calculated.

Reducing the diffusion gradient: the bag technique

To reduce the diffusion leak by minimizing the concentration gradient between the ambient air and the leaf chamber, we enclosed LI-6400-40 leaf chamber fluorometer in a 10 L Tedlar [polyvinyl fluoride (PVF)] bag (Fig. 1). PVF has ca. three orders of lower permeability for CO2 and ca. one order of magnitude lower permeability for H2O than low-density polyethylene and synthetic rubber neoprene (Shah et al. 1998; Nauta 2000; Sturm et al. 2004). To further reduce the diffusion problems, the original Bev-A-Line (polyethylene, lined with ethylenvinyl acetate) LI-6400 hoses connecting the LI-6400 console with the chamber were replaced by Teflon hoses (Du Pont Inc., Wilmington, DE, USA) as recommended by Li-Cor (Li-Cor, Inc. 2004, pp. 4–44).

Figure 1.

Illustration of the set-up of the bag experiment. To reduce the diffusion leaks, Li-Cor LI-6400 leaf chamber was enclosed in a 10 L Tedlar bag. This way, the bag was supplied with the exhaust air from the leaf chamber, minimizing CO2 and H2O gradients between the interior of the leaf chamber and the surrounding ambient air. The mole fractions of the air inside the bag and outside the bag were analysed with a LI-7000 CO2/H2O analyser. To further reduce the diffusion leaks, the original Bev-A-Line (polyethylene, lined with ethylenvinyl acetate) LI-6400 tubing that connects the LI-6400 console with the leaf chamber was replaced by Teflon hoses.

The Tedlar bag was flushed with the exhaust air from the leaf chamber to achieve CO2 and H2O concentrations inside the bag essentially identical to those in the leaf chamber. Li-Cor 7000 gas-exchange analyser was switched in the system in a way that it could measure the CO2 and H2O mole factions either inside or outside the bag (Fig. 1). The data demonstrated that the difference in bag and chamber water vapour mole fractions was generally less than 0.5 mmol mol−1, and the difference in CO2 mole fractions was less than 1 µmol mol−1 at an incoming air CO2 mole fraction of 50 µmol mol−1 and up to 70 µmol mol−1 at an incoming CO2 mole fraction of 2000 µmol mol−1. The differences were two to three orders of magnitude larger without the bag. These data suggest that the bag effectively reduced the diffusion gradients. However, a part of the air circuit of the LI-6400 made of Bev-A-Line hoses is inside the console and so exposed to ambient atmosphere. In addition, although fresh O-rings (butyl rubber) were used in all cases, some minor diffusion leaks may occur through the O-rings at the hose ends and desiccant and CO2 scrubber tubes. Given this, we also determined the values of inline image and inline image by changing the flow rate and chamber concentrations of CO2 and H2O using the same protocols detailed earlier. In the calculation of inline image and inline image (Eqn 2), CA and WA were the mole fractions measured outside the bag. Thus, inline image and inline image determined in the bag experiments are arbitrary estimates that characterize the minimum diffusion leak observed when the diffusion gradient between the exterior and interior of the leaf chamber is minimized.

Effects of diffusion leaks on foliage photosynthetic measurements

To quantify the uncertainty induced by diffusion leaks on gas exchange measurements, CO2 responses of An (µmol m−2 s−1) were measured in 1-year-old Quercus ilex leaves. Quercus ilex was selected as a typical stress-tolerant tree that dominates large areas in Mediterranean forests and is characterized by low An and effective stomatal regulation of water use (Sala & Tenhunen 1994; Niinemets, Tenhunen & Beyschlag 2004).

The 45-year-old stand of Quercus ilex was located at Lago Toblino, Trentino, Italy (46°03′N, 10°58′E, elevation 260 m). The twigs were sampled from the lower crown third. They were cut under water, the cut ends were kept under water and the twigs were immediately transported to the laboratory for the measurements. The twigs were recut under water, and the gas-exchange measurements were conducted according to the protocol described in detail in Niinemets et al. (2005). We used Li-Cor LI-6400 gas-exchange system with LI-6400-40 leaf chamber fluorometer that encloses 2 cm2 of leaf area. As stated earlier, original Bev-A-Line tubing connecting the leaf chamber with the console was replaced by Teflon tubing. Quantum flux density was set at 1000 µmol m−2 s−1 (15% blue LED, 85% red LED), flow rate was set to 400 µmol s−1 and block temperature was set to 28 °C.

To achieve maximum stomatal openness at the beginning of the experiment, each leaf was kept at a CO2 mole fraction of 50 µmol mol−1 until stomatal opening as recommended by Centritto, Loreto & Chartzoulakis (2003). Stomata opened at about 30 min after leaf enclosure. After stomatal opening and stabilization of conductances, An was measured at nine incoming CO2 mole fractions between 50 and 2000 µmol mol−1.

Firstly, the An versus CO2 responses were measured using the Tedlar bag set-up. A minimum waiting time of 8 min was necessary to reach the equilibrium between the sample cell and the bag CO2 concentrations. When the first An/CO2 curve was completed, the bag was removed, and the second An/CO2 response curve was performed with the same leaf and the same chamber conditions and using the same timing, i.e. minimum of 8 min at every CO2 concentration.

Correction of gas-exchange data for diffusion leaks and calculation of Farquhar et al. model parameters

In a steady state, the mass balance for water vapour of a cuvette enclosing the leaf is given as:

image(8)

where S (m2) is leaf area enclosed in the chamber and E is the transpiration rate (mol m−2 s−1). When both diffusion of water vapour and transpiration rate affect uo, the flow correction is given as (cf. Eqn 2):

image(9)

Substituting uo into Eqn 8 and revealing E, we get:

image(10)

where EV is the apparent transpiration rate calculated according to standard transpiration formula implemented in LI-Cor LI-6400 (von Caemmerer & Farquhar 1981). Equation 10 indicates that when the ambient atmosphere is drier than the air inside the leaf chamber (WA − WS < 0), EA underestimates true leaf transpiration rate.

The mass balance for CO2 is given as:

image(11)

where An is the net assimilation rate, and CO2 mole fractions are given in mol mol−1. Substituting Eqn 9 in Eqn 11 and revealing An, we obtain:

image(12)

Replacing E from Eqn 10, the final equation becomes (Li-Cor, Inc. 2004):

image(13)

where An,A is the apparent photosynthesis rate implemented in LI-Cor LI-6400 on-line calculations (von Caemmerer & Farquhar 1981).

The corrected An was computed according to Eqn 13 as the apparent measured photosynthesis rate plus the diffusion correction term, and the corrected transpiration rate was calculated analogously by Eqn 10. The corrected transpiration rate was then used to calculate the total gas-phase conductance to CO2 (sum of stomatal and boundary layer conductances), gtc (mol CO2 m−2 s−1), and the corrected Ci concentration (µmol mol−1) according to von Caemmerer & Farquhar (1981). For the bag experiment, the corrections were done using both the values of inline image and inline image estimated for the ambient (outside bag) CO2 and H2O mole fractions (large H2O and CO2 gradient, low inline image and inline image, mainly reflecting the diffusion through tubing within the LI-Cor LI-6400 console), and the values of inline image and inline image estimated without bag and the CO2 and H2O mole fractions inside the bag (small H2O and CO2 gradient, large values of inline image and inline image).

After correction of An and Ci values, Farquhar et al. (1980) model parameters – maximum carboxylase activity of ribulose 1·5-bisphosphate carboxylase/oxygenase (Rubisco) (Vcmax) (µmol m−2 s−1), maximum capacity for photosynthetic electron transport (Jmax) (µmol m−2 s−1) and rate of non-photorespiratory respiration in the light (Rd) (µmol m−2 s−1) were calculated iteratively. Vcmax scales with the initial slope of An/Ci response curve, and Rd scales with the intercept, while Jmax scales with CO2-saturated values of assimilation rate. In these calculations, we used Michaelis–Menten constants for CO2 and O2 at specific leaf temperatures reported by Bernacchi et al. (2001). For comparison, Farquhar et al. model parameters were also calculated for non-corrected data when possible (Ci > 0).

Error and sensitivity analyses of the diffusion leaks

A certain variability in inline image and inline image was always observed between different experimental estimations (Results), possibly as the result of slight differences in latch adjustment and gasket wear. We assessed the impact of the uncertainty in inline image and inline image on estimates of An, E, gtc, Ci, Vcmax and Jmax using a resampling methodology. Mean values of inline image and inline image and their standard deviations were calculated for both the estimations with and without the Tedlar bag. Twenty values of inline image and inline image were randomly extracted from corresponding Gaussian distributions described by observed mean and SD values of inline image and inline image. The obtained 20 values of inline image and inline image were finally used to correct the An/Ci curve data for both the experiments with and without the Tedlar bag, yielding in total of 20 corrected An/Ci curves for each measured An versus CO2 response. These 20 corrected curves were employed to assess the uncertainty in foliage photosynthetic characteristics because of experiment-to-experiment differences in diffusion leaks, allowing us to estimate the average values of corrected Farquhar et al. model parameters and their standard deviations.

To further analyse the sensitivity of the photosynthesis measurements to diffusion leaks, we constructed two artificial data sets of paired An and Ci values using Farquhar et al. (1980) model. For the low photosynthetic capacity simulation, we fixed Vcmax at 15 µmol m−2 s−1, Jmax at 2.5Vcmax and Rd at 0.8 µmol m−2 s−1, i.e. to typical values observed in forest evergreen species (Medlyn et al. 2002; Niinemets et al. 2004). In the high leaf capacity simulation, Vcmax and Jmax were increased threefold relative to the low capacity simulation, resulting in Vcmax and Jmax values typical of high capacity broadleaved trees. Using these capacity estimates, values of An were predicted by varying Ci from 20 to 1700 µmol mol−1 in both cases. For both simulations, we set leaf temperature at 28 °C, ambient (outside leaf chamber) CO2 mole fraction at 400 µmol mol−1, water vapour mole fraction at 17 mmol mol−1, leaf chamber H2O mole fraction at 25 mmol mol−1 and incoming air flow rate at 500 µmol s−1. The simulations were conducted for three chamber sizes 0.79 cm2 (Li-Cor Arabidopsis chamber), 2 cm2 chamber (Li-Cor leaf chamber fluorometer) and 6 cm2 (Li-Cor standard chamber). While the manufacturer warns of the possible large diffusion problems of Arabidopsis chamber (Li-Cor, Inc. 2004), even with larger chambers, researchers often measure leaves that are not fully covering the gas-exchange chamber opening. Thus, ‘Arabidopsis chamber’ is used as a general case of low leaf area clipped in the leaf chamber.

For these simulations, values of leaf conductance to CO2 (gtc) are also necessary for any Ci. For simplicity, we used empirical asymptotic relationships between Ci and gtc using the measurements conducted in Quercus ilex (diffusion-corrected data). The asymptotic function derived for the low capacity simulation was inline image, i.e. gtc decreased from 0.06 mol m−2 s−1 at a Ci of 20 µmol mol−1 to 0.013 mol m−2 s−1 at Ci = 1700 µmol mol−1. The maximum stomatal conductance used (ca. 0.1 mol m−2 s−1 for water vapour) reflects adequately the maximum conductances observed in Mediterranean evergreen species (Centritto et al. 2003; Niinemets et al. 2006). For high photosynthetic capacity simulation, the Ci-response shape of gtc was preserved and gtc was adjusted to achieve the same Ci to ambient CO2 ratio at ambient CO2 concentration of 400 µmol mol−1. Of course, more complex models of stomatal conductance describing the dependence of stomatal conductance also on humidity can be used (e.g. Leuning 1995). In the current simulations, we decided to use the empirical fits to adhere to the observations as closely as possible.

Using the values of An, Ci and gtc, the defined environmental constraints and standard leaf chamber gas-exchange calculations with flow correction (von Caemmerer & Farquhar 1981), inverse modeling was used to calculate the values of reference (incoming) and sample (exhaust air outgoing from leaf chamber) H2O and CO2 mole fractions without the diffusion leak. These values were then used along with the diffusion correction terms to determine the apparent rates of transpiration (EV), net assimilation (An,A), stomatal conductance (gtc,A) and internal CO2 mole fraction (Ci,A). Simulations were conducted assuming only CO2 diffusion leak (as suggested by Li-Cor, Inc. 2004) and simultaneous CO2 and H2O diffusion leaks. The Farquhar et al. (1980) model was then fitted again to the apparent An/Ci response curves, and apparent values of Vcmax, Jmax and Rd were determined iteratively as described earlier. The model was fitted only over the data exhibiting monotonic increase of Ci with An.

RESULTS

Estimation of diffusion leaks

Revised mass balance equations for H2O (Eqns 1–3) and CO2 diffusion (Eqns 5 & 6) were developed, and water vapour (inline image) (µmol s−1) and CO2 (inline image) (µmol s−1) molar flow leaks caused by diffusion characterized for different conditions. Overall, the data indicated that accounting for the flow correction (1 − WS in Eqn 3) resulted in ca. 2% higher values of inline image than the simplified expression (Eqn 4). The effect of flow correction on inline image estimates (Eqn 6) relative to the simplified expression (Eqn 7) was ca. 0.5% at the input CO2 mole fraction of 50 µmol mol−1, but the influence of flow correction increased with increasing input CO2 mole fraction such that the simplified expression of inline image (Eqn 7) underestimated inline image by 20–60% at chamber CO2 mole fractions 1200–2000 µmol mol−1 (data not shown).

Given that the flow correction was relatively minor for inline image estimations and for inline image estimations at CR of 50 µmol mol−1, for clarity, we show representative experiments in (WS − WR)/(WA − WS) versus 1/ui (Eqn 4), and (CS − CR)/(CA − CS) (CR = 50 µmol mol−1) versus 1/ui (Eqn 5) axes in Figs 2 and 3. The slopes of these linear relationships provide approximate estimates of inline image and inline image, and facilitate direct visual assessment of the chamber, leaf and bag effects on diffusion leaks. In all other cases (Figs 4–7), estimates of inline image and inline image including the flow correction (Eqns 3 & 6) have been used.

Figure 2.

Representative relationships between (a) the normalized CO2 diffusion leak (difference in CO2 mole fractions between the chamber exhaust, CS, and incoming air, CR, relative to the difference in CO2 mole fractions outside the leaf chamber, CA, and CS) and (b) the normalized water vapour diffusion leak, (WS − WR)/(WA − WS) (symbol definitions analogous to CO2 leak) and the inverse of flow rate (ui) observed with empty chamber (filled symbols) and with dried leaf of the Mediterranean evergreen species Quercus ilex. The experiment was conducted at 50 µmol mol−1 CO2 concentration in the cuvette incoming air using the 6 cm2 Li-Cor LI-6400 leaf chamber (‘big’ chamber). The proportionality factors describing the rate of diffusion between the leaf chamber and ambient atmosphere at common mole fraction difference, i.e. potential molar flow rate because of diffusion (Eqns 1 & 5) (inline image for CO2 and inline image for water vapour, both in µmol s−1) are described by Eqns 3 and 6. However, at this low CO2 concentration, the flow correction term resulting from differences in water vapour concentrations between incoming and exhaust air caused by water vapour diffusion leak (Eqn 6) is ca. 0.5% for inline image. For inline image, the flow correction term (Eqn 3) is generally less than 2%. Thus, the slope of linear regression of (CS − CR)/(CA − CS) versus 1/ui provides a close estimate of inline image (Eqn 7), and the slope of (WS − WR)/(WA − WS) versus 1/ui gives an estimate of inline image (Eqn 4). ns, statistically non-significant regression intercepts (P > 0.05).

Figure 3.

Representative relations between the normalized diffusion leaks for CO2, (CS − CR)/(CA − CS) (symbol definitions as in Fig. 2) (a,b), and water vapour (WS − WR)/(WA − WS) (c,d), and the inverse of air molar flow rate (ui) for the empty chamber (a,c) or for a chamber enclosing a dead dried Quercus ilex leaf (b,d) with (open symbols) or without (filled chamber) a Tedlar bag (Fig. 1). The experiments were conducted with the LI-6400-40 leaf chamber fluorometer (2 cm2 cross-section area inside the gaskets, ‘small’ chamber) and measurements at incoming CO2 mole fraction of 50 µmol mol−1 are shown. As the molar flow correction is relatively small at these conditions, the slopes of these relationships provide estimates of the CO2 (inline image, Eqn 7) and H2O (inline image, Eqn 4) diffusion leaks (see also the explanations in Fig. 2 legend and in the text). As the chamber exhaust air enters the Tedlar bag (Fig. 1), the gradients in CO2 and H2O mole fractions between the chamber interior and the ambient air are small. However, diffusion effects can still be significant as part of the tubing connecting the Li-Cor LI-6400 console to the chamber and within the console is still exposed to ambient air. Therefore, for the bag experiment, the values of CA and WA refer to the gas mole fractions in the ambient air outside the bag. ns, non-significant regression intercepts (P > 0.05).

Figure 4.

Average (±SD) CO2 (inline image) (a,b) and H2O (inline image) (c,d) potential molar flow rates caused by diffusion (Eqns 3 & 6) for four different situations: empty chamber, chamber with dead Quercus ilex leaf and with (Fig. 1) or without the leaf chamber enclosed in a Tedlar bag (see Fig. 3 for representative relationships between normalized diffusion leak and the inverse of molar flow rate).inline image and inline image describe the diffusion flux rate of CO2 and water vapour corresponding to a certain gas mole fraction difference between the ambient air and the leaf chamber interior. All measurements were conducted with LI-6400-40 leaf chamber fluorometer (2 cm2, ‘small’ chamber). For the bag experiments, inline image and inline image were calculated using the CO2 and water vapour mole fractions outside the bag. Table 2 provides average permeability coefficients (Eqn 15) corresponding to these estimates of inline image and inline image.

Figure 5.

Sensitivity analysis of the effects of leaf chamber size and the magnitude of CO2 and water vapour diffusion leaks (potential molar flow rates because of diffusion, inline image and inline image, both in µmol s−1) on the apparent values of An and Ci mole fraction. The simulations were conducted for typical commercial leaf chambers offered by Li-Cor, Inc –Arabidopsis chamber (a), leaf-chamber fluorometer (b), and standard chamber (c) – and using the typical values of inline image and inline image measured (Fig. 4). inline image, inline image denotes hypothetical situation with perfect seal (no diffusion leak) and was simulated using the Farquhar et al. (1980) model with Vcmax = 15 µmol m−2 s−1, Jmax = 2.5Vcmax and Rd = 0.8 µmol m−2 s−1. The simulation with inline image and inline image corresponds to low to moderate diffusion leak, while the simulation with inline image and inline image corresponds to relatively high diffusion leak. Simulations with inline image and inline image or inline image denote hypothetical situations with no water vapour diffusion leak. While Arabidopsis leaf chamber is not recommended for An/Ci curve measurements, this simulation is included as it demonstrates general caveats with enclosing small leaf areas.

Figure 6.

Representative net assimilation (An) versus intercellular CO2 mole fraction (Ci) responses for two different Quercus ilex leaves (samples A and B) measured with the LI-6400 gas-exchange system equipped with LI-6400-40 leaf chamber fluorometer (2 cm2 area) (a,b), and corresponding An/Ci responses corrected for diffusion leaks (c–h). The measurements were either conducted with a Tedlar bag (Fig. 1) surrounding the leaf chamber (low CO2 and H2O diffusion gradients between the exterior and interior of the leaf chamber) or without the bag (standard set-up). The data were corrected for diffusion leaks according to Eqns 10 and 13. The corrected data in (c) and (d) refer to the measurements without the bag, and the data in (e–h) to the measurements with the bag. The corrections were done using the average values of inline image and inline image determined with the enclosed dead leaf (Fig. 4). For the bag experiment, the correction was done either using the average inline image and inline image values estimated without the bag and using within-bag CO2 and H2O mole fractions (e,f) or using the inline image and inline image values estimated with the bag and the CO2 and H2O mole fractions outside the bag (g,h). The data in (c–h) were fitted by the Farquhar et al. (1980) model (solid curves). Corresponding maximum ribulose 1·5-bisphosphate carboxylase/oxygenase (Rubisco) carboxylase activities (Vcmax, µmol m−2 s−1) are also reported in all cases. Because of diffusion leaks, apparent Ci may become negative [paired An/Ci values within the rectangles in (a) and (b)].

Figure 7.

Absolute average ± standard deviation (SD) percentage corrections in apparent CO2 and water vapour flux rates because of CO2 and water diffusion leaks for the experiments with bag and without bag [An − Ci data reported in Fig. 5a,c,e (sample A); b,d,f (sample B)]. For the bag experiments, the corrections were done using either the average inline image and inline image values measured without the bag (Fig. 4) and using the CO2 and water vapour mole fractions within the bag (a,b) or with inline image and inline image values measured with the bag (Fig. 4) and CO2 and water vapour mole fractions outside the bag (c,d). The correction applied in (a) and (b) assumes that only diffusion through the chamber gaskets affects the measurement, while actual data demonstrate (Fig. 4) that the correction used in (c) and (d) more realistically describes the true diffusion leak.

Effects of chamber size, gaskets and presence of the leaf on CO2 and H2O diffusion leaks

The relationships between the normalized diffusion leak and 1/ui at a leaf chamber CO2 mole fraction of 50 µmol mol−1 were always linear, and the intercept of these linear regressions was in most cases not significantly different from zero (Figs 2 & 3), indicating that the data agreed with the diffusion model (Eqns 1–7).

For the empty chamber, the potential CO2 diffusion leaks were similar for the 6 cm2 (‘big’ chamber; inline image for the sample relationship inFig. 2a, average ± SE = 0.45 ± 0.04 µmol s−1) and fluorometer chamber (2 cm2, ‘small’ chamber; inline image for the sample relationship in Fig. 3a; see Fig. 4a for average values). These estimates of inline image were also similar to the value of 0.46 µmol s−1 suggested in the LI-6400 manual (Li-Cor, Inc. 2004). The introduction of a dead leaf in the chamber resulted in a rise of inline image to 0.55–0.63 µmol s−1 for the big chamber (Fig. 2a) and 0.43–0.76 µmol s−1 for the small chamber (Fig. 3b), but the variability between different inline image determinations with dead leaf was large (Fig. 4b). Surprisingly, inline image determined for a chamber with worn gaskets (average ± SE = 0.35 ± 0.06 µmol s−1 for the small chamber) was consistently 20–30% lower than the inline image determined for a chamber with fresh gaskets (Fig. 4a for the data with fresh gaskets).

The diffusion leak was 2- to 10-fold larger for water vapour (cf. Figs 2a and 2b; 3a,b and 3c,d; & 4a,b and 4c,d). inline image was lower for 6 cm2 than for 2 cm2 chamber (cf. Figs 2b & 3c). For 6 cm2 leaf chamber, inline image was larger when a dead leaf was clamped between the leaf chamber (Fig. 2b). In contrast, for small chamber, inline image values with and without the dead leaf (cf. Figs 3c and 3d & 4c and 4d) were statistically not different (t-test; P > 0.1), and the variability between different experimental determinations was large (Fig. 4c,d).

The bag experiment

The enclosure of the LI-6400 chamber in a Tedlar bag resulted in a significant reduction of the mole fraction gradient of CO2 and water vapour between the exterior and interior of the leaf chamber (Materials and methods). However, using the CO2 and water vapour mole fractions inside the bag and inline image and inline image values measured without the bag resulted in two- to threefold lower predicted (Eqns 3 & 6) mole fraction differences between the chamber exhaust air and incoming air, CS − CR and WS − WR, than was actually observed. Given that the gas conduits connecting leaf chamber to the LI-6400 console and additional gas tubes within the console are exposed to ambient air outside the bag, we calculated the inline image and inline image estimates using the CO2 and water vapour mole fractions outside the bag.

The values of inline image were three- to fourfold lower (Figs 3a,b & 4a,b), and the values of inline image were 6- to 10-fold lower (Figs 3c,d & 4c,d) with the bag than without the bag. The presence of the dead leaf in the leaf chamber had a minor effect on the inline image and inline image values (cf.Figs 3a,c and b,d & 4a,c and 4b,d). Overall, these data indicate that enclosure of the leaf chamber in the Tedlar bag significantly reduced the diffusion effects on leaf chamber CO2 and water vapour mole fractions.

Sensitivity analysis of the effects of CO2 and H2O diffusion leaks on Farquhar et al. (1980) model parameters

Sensitivity analysis of the influences of diffusion leaks on An versus Ci responses was conducted for situations with low and high CO2 and H2O diffusion leaks, for different leaf areas clamped in the chamber (S) and for different leaf photosynthetic capacities (Table 1; Fig. 5). In all cases, the diffusion leaks resulted in larger apparent initial slopes of An/Ci response curves, reflecting greater apparent values of maximum Rubisco carboxylase activity (Vcmax) and non-photorespiratory respiration rate in the light (Rd) than the true estimates (Fig. 5; Table 1). At higher ambient CO2 mole fraction, An was generally even more strongly enhanced, while Ci was curbed, resulting in enhanced apparentcapacity for photosynthetic electron transport (Jmax) (Fig. 5; Table 1). However, in certain cases, Ci even decreased after a threshold An value had been reached, becoming occasionally negative in extreme situations with low S and high diffusion leaks (Fig. 5a,b).

Table 1.  Sensitivity of apparent parameters of Farquhar et al. (1980) modela to diffusion leaks of CO2 and water vapour for leaf chambers with different size and for leaves with low and moderate to high photosynthetic capacityb
Photosynthetic potentialcMagnitude of diffusion leakd (µmol s−1)CharacteristicLeaf chamber size (cm2)
0.7926
Apparent value/true value
  • a

    Vcmax, maximum carboxylase activity of Rubisco; Jmax, capacity for photosynthetic electron transport; Rd, non-photorespiratory respiration rate in light.

  • b

    In these simulations, CO2 mole fraction outside the chamber was set at 400 µmol mol−1 and water vapour mole fraction at 17 mmol mol−1, leaf chamber H2O mole fraction at 25 mmol mol−1 and incoming air flow rate at 500 µmol s−1.

  • c

    True Vcmax = 15.0 µmol m−2 s−1, Jmax = 37.5 µmol m−2 s−1, Rd = 0.8 µmol m−2 s−1 for leaves with low photosynthetic capacity, while true Vcmax = 45.0 µmol m−2 s−1, Jmax = 112.5 µmol m−2 s−1, Rd = 2.0 µmol m−2 s−1 for leaves with high photosynthetic capacity. The net assimilation rate (An) versus intercellular CO2 (Ci) response curves are shown in Fig. 5.

  • d

    Diffusion leaks for CO2 and water vapour are given by Eqns 3 and 6.

  • e

    na, not available. Farquhar et al. model was fitted only to the data points exhibiting monotonic increase of Ci with An. For some cases, the paired An/Ci values satisfying this criterion were available only for Rubisco-limited photosynthesis (Fig. 5).

  • Rubisco, ribulose 1·5-bisphosphate carboxylase/oxygenase.

Lowinline imageVcmax1.721.171.07
inline imageJmax1.971.481.12
 Rd4.381.991.35
inline imageVcmax2.231.301.07
inline imageJmaxnaena1.13
 Rd5.522.231.35
inline imageVcmax2.601.551.11
inline imageJmax3.331.851.25
 Rd8.673.591.64
inline imageVcmax4.581.711.11
inline imageJmaxnana1.32
 Rd15.93.871.62
Highinline imageVcmax1.221.081.03
inline imageJmax1.471.171.05
 Rd2.271.481.16
inline imageVcmax1.531.131.04
inline imageJmaxna1.181.06
 Rd2.911.551.17
inline imageVcmax1.601.161.06
inline imageJmax1.961.311.10
 Rd4.181.961.33
inline imageVcmax2.201.271.08
inline imageJmaxna1.341.12
 Rd5.592.191.36

Comparison of the scenario with both CO2 and H2O diffusion leaks and the hypothetical scenario with no H2O diffusion leak indicated that H2O diffusion leak significantly enhanced the departure of apparent An/Ci responses from true responses, especially for small enclosed leaf areas andfor leaves with low photosynthetic potentials (Fig. 5; Table 1).

The influence of diffusion leaks was larger for smaller leaf chambers (cf. Fig. 5a,b and 5c) and for leaves with lower photosynthetic capacity, with Vcmax, Jmax and Rd being several-fold larger than the true values in extreme cases (0.79 cm2 Li-Cor Arabidopsis chamber that provides a general case of enclosing a small leaf area in leaf chamber, Table 1). Nevertheless, even for the 6 cm2 chamber, the low diffusion leak scenario for low capacity leaf (inline image and inline image) resulted in 7% increase in apparent Vcmax, 13% increase in apparent Jmax and 35% increase in apparent Rd, with corresponding modifications being 11% for Vcmax, 32% for Jmax and 62% for Rd for high diffusion leak (Table 1).

The diffusion leaks affected An/Ci responses and derived model parameters less for leaves with high photosynthetic capacity. Still, even for the large chamber, Vcmax was overestimated 3–8%, Jmax by 5–12% and Rd by 16–36% depending on the scenario, and much larger effects were observed for 2 cm2 fluorometer chamber and for Arabidopsis leaf chamber (Table 1).

Influences of CO2 and H2O diffusion leaks on measured An/Ci responses

Sample An/Ci responses of two Quercus ilex leaves measured with and without the bag are shown in Fig. 6a,b. While Ci values monotonically increase with increasing An in the experiments with leaf chamber enclosed in the Tedlar bag, negative apparent Ci values were found at higher values of An in both experiments without the bag (Fig. 6a,b). Correcting the data measured without the bag for diffusion leaks resulted in positive Ci values and overall extension of the Ci range with concomitant reduction of An values (Fig. 6c,d). After correction for diffusion leaks, the Farquhar et al. model parameters could be derived for the leaves measured without the bag. However, SD values of these model parameters were large, indicating large uncertainty in parameter estimation. In fact, the average correction for An and transpiration rates as a result of diffusion leak was more than 100%, extending to 450% (Fig. 7e,f).

For the bag experiments, Vcmax, Jmax and Rd values were estimated for three cases: uncorrected data (Fig. 6a,b), corrected using the CO2 and water vapour mole fractions inside the bag and the largeinline image and inline image values estimated without the bag (Figs 4 & 6e,f) and corrected using the CO2 and water vapour mole fractions outside the bag and the low inline image and inline image values estimated without the bag (Figs 4 & 6g,h). Corrections using the CO2 and water vapour mole fractions within the bag resulted in 0.5–1% reduction in Farquhar et al. model parameters (Fig. 6e,f) and in changes of An and transpiration rate in the order of a few percent (Fig. 7a,b). For a more realistic scenario using the corrections with CO2 and water vapour mole fractions outside the bag, for leaf A, both Vcmax and Jmax decreased 23% relative to uncorrected estimates (Fig. 6g). For leaf B, Vcmax decreased 22% and Jmax 42% relative to uncorrected estimates (Fig. 6h), and An and transpiration rate were affected by 20–30% (Fig. 7c,d).

The estimates of Vcmax and Jmax derived from corrected data differed between the experiments with and without bag by 20–40% (cf. Fig. 6c,d and 6g,h), possibly reflecting large uncertainty in the correction of the experiments without the bag. Indeed, the standard deviation of Vcmax and Jmax of the bag experiments were almost an order of magnitude lower than those obtained from the measurements without the bag (cf. Fig. 6c,d and 6g,h).

DISCUSSION

Diffusion leaks for CO2 and water vapour for empty leaf chamber

Leaf gas-exchange studies using miniature clamp-on leaf cuvettes with foam gaskets have become standard in contemporary plant science. CO2 diffusion leaks of such cuvettes have been recognized for some time (McDermitt et al. 2001; Long & Bernacchi 2003), and manufacturers have suggested ways to correct for the CO2 diffusion leaks (Li-Cor, Inc. 2004). In contrast, water vapour diffusion leaks have not been considered, although the possible water vapour sorption and desorption effects have been suggested to be a potential problem because of induction of hysteresis effects in chamber water vapour concentrations after alterations in chamber humidity (Long & Hällgren 1993; Long, Farage & Garcia 1996). As sorption and desorption can take long, even hours for certain chamber materials, to reach steady state, water vapour sorption has been considered the most significant issue in water vapour measurements, especially in closed systems (Long & Hällgren 1993; Long et al. 1996). Our additional experiments using the bag technique and rapidly changing the humidity within the bag demonstrated that chamber water vapour concentration fully responds to modifications in bag humidity within the time-limits of the experimental system (5–8 min, data not shown), implying that water vapour diffusion not necessarily sorption is a major problem during steady-state An/Ci curve measurements.

For an empty leaf chamber, our estimated CO2 diffusion leaks through the chamber gaskets (Fig. 4 and slopes in Figs 2 & 3) were numerically similar to the value (0.46 µmol s−1) derived by Li-Cor (Li-Cor, Inc. 2004). In addition to important CO2 leaks, the observed water vapour diffusion leaks were almost an order of magnitude larger than CO2 diffusion leaks (Figs 2–4).

To what extent can these results be transferred to other portable systems? Diffusion is a basic physical process, and all commercially available portable leaf gas-exchange systems employ clamp-on cuvettes with similar syntheticrubber gaskets as those used by Li-Cor. In addition to the data reported here, we have estimated an average ± SD inline image of 0.56 ± 0.08 µmol s−1 (n = 22) for the standard 8 cm2 clamp-on empty leaf chamber of Walz GFS-3000 portable gas-exchange system (H. Walz GmbH, Effeltrich, Germany) using the same methodology. This suggests that the diffusion leak is a general problem of clamp-on cuvettes.

Li-Cor, Inc. (2004) states that synthetic rubber neoprene was chosen for the chamber gaskets, because neoprene is one of the polymers with lowest CO2 permeability. In addition, the upper gasket can either be made of neoprene (6 cm2 chamber in our set-up) or polyethylene foam (2 cm2 chamber in our set-up). How large are the measured diffusion leaks compared with polymer permeabilities? We expressed the diffusion leaks in flow units (µmol s−1) following Li-Cor, Inc. (2004) as the diffusion leaks expressed this way can be conveniently used to correct leaf net assimilation and transpiration rates for the diffusion leaks (Eqns 10 & 13). However, diffusion leaks expressed this way are chamber specific and not comparable with conventionally published estimates of material CO2 and water vapour permeabilities. In studies analyzing gas permeation through polymers, the diffusion flux through the polymer surface, F (mol m−2 s−1), is expressed as:

image(14)

where Δp (Pa) is the partial pressure difference, l (m) is the length of the diffusion pathway and P (mol m−1 s−1 Pa−1) is the permeation coefficient. Permeation coefficient is the product of compound solubility (partition coefficient) in the polymer and the compound diffusion coefficient, and indicates how many mol gas permeates in 1 s through a sample of 1 m thickness and 1 m2 surface at a partial pressure difference of 1 Pa (Laguna, Guzmán & Riande 2001; Sturm et al. 2004). P for CO2 can be calculated from the values of inline image(mol s−1) as:

image(15)

where WG (m) is the gasket width (length of diffusion pathway), SG (m2) is the gasket surface area exposed to the chamber (product of gasket circumference and gasket height) and pA (Pa) is air pressure. Analogously, P for H2O is expressed.

The foam gasket permeabilities for CO2 and water vapour are ca. two orders of magnitude less than the permeabilities corresponding to free air (Table 2). However, foam gaskets have ca. four orders of magnitude larger CO2 permeability than neoprene or low-density polyethylene themselves, and the water vapour permeability of foam gaskets is ca. three orders of magnitude larger than that of neoprene and ca. four orders of magnitude larger than that of low-density polyethylene (Table 2). Unfortunately, foam characteristics of most of these polymers are not available. The permeability of foam depends on the relative contributions of gas and solid phases (foam density) and the size of the air bubbles in the foam, and is generally determined empirically for specific foam (Zhang, Rodrigue & Ait-Kadi 2003; Ruiz-Herrero, Rodríguez-Pérez & de Saja 2005). While the permeability of solid polymer may be very low, lightweight, highly porous foam permeability is much higher (Koponen, Kataja & Timonen 1997; Ruiz-Herrero et al. 2005). In addition, foam gaskets typically have open and interconnected pores such that most of the diffusion through the gaskets occurs via air-filled pores rather than through the polymer itself, explaining large permeabilities observed in our study. Main diffusion pathway through the gas phase of the gaskets can also explain the puzzling decrease of diffusion leaks in older, partly compressed gaskets that have lower gas phase volume fraction. In general, polymer permeability decreases with the degree of polymer compression (Ruiz-Herrero et al. 2005).

Table 2.  Permeation coefficients for CO2 and water vapour (P, mol m−1 s−1 Pa−1) for Li-Cor LI-6400 leaf chamber gasketsa at 25 °C (a) and various polymers used in plant gas-exchange studies at 25–30 °C (b)
(a) Free air and chamber gaskets
Experimental systemP for CO2P for H2O
Free airb7.90 × 10−91.36 × 10−8
6 cm2 chamberEmpty(3.91–5.86) × 10−11(0.869–2.93) × 10−10
Dead leaf(4.88–7.82) × 10−11(1.82–2.93) × 10−10
2 cm2 chamberEmpty(5.85–11.7) × 10−11(7.79–13.6) × 10−10
Dead leaf(7.79–15.6) × 10−11(7.79–10.7) × 10−10
(b) Typical polymers used for sealing in plant gas-exchange studiesc
PolymerP for CO2P for H2OReferences
  • a

    Calculated according to Eqn 15 (gasket exposed area = 6 × 10−3 m2 for the 6 cm2 leaf chamber and 3.01 × 10−3 m2 for the 2 cm2 chamber, gasket width = 0.005 m for both).

  • b

    Calculated from the values of CO2 and H2O diffusion coefficients of 2.60 × 10−5 and 1.51 × 10−5 m2 s−1 at 25 °C (Nobel 1991).

  • c

    Ranked according to decreasing minimum permeability. Polymers in bold font are used for leaf chamber gaskets in Li-Cor chambers.

Polydimethylsiloxane (silicone)(4.35–11.4) × 10−133.57 × 10−12(Sturm et al. 2004; Tremblay et al. 2006)
Chloroprene (neoprene)(7.30–8.71) × 10−156.25 × 10−13(Sturm et al. 2004)
Polyurethane(5.36–8.93) × 10−152.07 × 10−12(Sturm et al. 2004; Tremblay et al. 2006)
Low-density polyethylene(3.97–9.71) × 10−15(4.45–5.77) × 10−14(Shah et al. 1998; Nauta 2000; Gholizadeh, Razavi & Mousavi 2007)
High-density polyethylene(0.670–2.68) × 10−15(2.25–6.16) × 10−14(Shah et al. 1998; Nauta 2000)
Polychlorotrifluoroethylene (PCTFE)2.32 × 10−169.82 × 10−17(Sturm et al. 2004)
Polytetrafluoroethylene (Teflon)(0.054–3.35) × 10−151.12 × 10−14(Sturm et al. 2004)
Polyvinylchloride (PVC)(0.535–6.70) × 10−168.0 × 10−14(Miguel, Barbari & Iruin 1999; Tiemblo et al. 2001; Marais et al. 2004)
Polyvinyl fluoride (PVF–Tedlar)(2.23–3.13) × 10−171.12 × 10−13Goodfellow Cambridge Ltd, Du Pont, Inc.

As the data in Table 2 demonstrate, neoprene and polyethylene implemented in Li-Cor LI-6400 portable photosynthesis system are not the best among widespread polymers to minimize CO2 and water vapour diffusion leaks. Clearly, gasket permeabilities can be somewhat reduced using alternative materials such as fluorinated hydrocarbon polymers. However, as most of the diffusion flux apparently occurs through the gasket gas phase, the effect of using different polymers on diffusion leaks is likely minor. Nevertheless, fluorinated hydrocarbons are also the choice if one intends to use the portable chambers for measuring the exchange of volatile hydrocarbons such as monoterpenes that strongly adsorb on synthetic rubber foam. Using solid materials such as silicone (as e.g. in Laisk et al. 2001) and improving the seal using silicone grease (as in Jahnke 2001) can reduce diffusion leaks, but may result in significant ‘memory effects’ after changes in CO2 and/or water vapour concentration. Such ‘memory effects’ are caused by relatively strong absorption and adsorption capacity of silicone (Long & Hällgren 1993; Jahnke, personal communication).

Effects of leaf enclosure on diffusion leaks

As small air pathways can be formed between the leaf and gasket, clamping the chamber on the leaf can enhance the diffusion leak. As recommended by Long & Bernacchi (2003), we used a dead Quercus ilex leaf to evaluate the influence of leaf presence on the diffusion leak. Quercus ilex has heterobaric leaves (Nikolopoulos et al. 2002), implying that lateral diffusion flux through the leaf is minor (Pieruschka et al. 2005). We observed important enhancement of CO2 diffusion leak after leaf enclosure, while the effect on water vapour diffusion was not always significant (Fig. 4; Table 2). This may reflect the overall larger variability in water vapour diffusion leak determination (large error bars in Fig. 4) and the circumstance that solid-phase permeability of gaskets is one to two orders of magnitude larger for water vapour than for CO2 (Table 2) such that the relative effect of additional minor gas-phase diffusion pathways is smaller. While separate experiments suggested that water vapour sorption and desorption by the dried leaf is a relatively slow process (data not shown), sorption and desorption of water vapour by the dried leaf can still have partly affected the determinations of the diffusion coefficient.

Overall, these data demonstrate that empty leaf chamber estimates of CO2 diffusion leaks as recommended by Li-Cor (Li-Cor, Inc. 2004) cannot necessarily be used to correct the gas-exchange data for CO2 diffusion leaks. Furthermore, as the variability of diffusion leaks with the dead leaf was large, enhancement of the diffusion leak caused by an enclosed leaf is difficult to predict.

The bag experiment

Enclosing the leaf inside a Tedlar bag that was supplied with the exhaust air from the leaf chamber dramatically reduced the diffusion gradients between the leaf and ambient atmo sphere. Significant diffusion leaks were still observed when ambient air concentration outside the bag was used (Figs 3 & 4). The diffusion leaks were similar with and without the dead leaf (Fig. 4), suggesting that the bag effectively abolished the diffusion gradients between the chamber exterior and interior. This evidence further indicates that major diffusion leak was restricted to the gas-conducting tubes inside the console and between the console and leaf chamber.

These data demonstrate that CO2 diffusion leaks can be dramatically curbed by reducing the diffusion gradients. Instead of enclosing the whole leaf chamber inside a bag, we suggest that clamp-on leaf chambers can be improved using two gasket rings separated by an air space. Measuring leaf gas exchange from the leaf part that is enclosed in the inner gasket ring, and feeding the exhaust air into the air space between the exterior and interior gasket rings should result in similar CO2 and water vapour concentrations within the areas surrounded by the exterior and interior gasket rings, and thus, in significantly reduced diffusion gradients during An/Ci curve measurements.

Sensitivity of gas-exchange rates to diffusion leaks

As the sensitivity analysis (Fig. 5) demonstrated, diffusion leaks can potentially have major effects on An/Ci response curves and derivation of Farquhar et al. (1980) model parameters – maximum carboxylase activity of Rubisco (Vcmax), capacity for photosynthetic electron transport (Jmax) and non-photorespiratory respiration rate (Rd) in light. Previous studies have only considered CO2 diffusion leak (McDermitt et al. 2001; Long & Bernacchi 2003; Li-Cor, Inc. 2004), but as water vapour diffusion leak affects the calculations of stomatal conductance and Ci, and also affects the flow correction term (Eqn 12), water vapour diffusion leak also has major effects on An/Ci response curves (Fig. 5).

The sensitivity to diffusion leaks increased in the order of Vcmax < Jmax < Rd, and was particularly large for smaller chambers and for leaves with low photosynthetic capacity. In fact, because of water vapour diffusion leaks, the sensitivity analysis predicted that estimation of Jmax was not possible for certain chamber/photosynthetic capacity combinations (Fig. 5).

As both Vcmax that scales with the initial slope of An/Ci response curve and Rd that scales with the intercept were modified by diffusion leaks, diffusion leaks also result in major effects on the CO2 compensation points of leaf CO2 exchange (Γ). While the effects of CO2 leaks on Vcmax, Γ and Rd have been mentioned (Amthor 2000; McDermitt et al. 2001; Bruhn et al. 2002; Pons & Welschen 2002), large overestimation of Jmax has not been considered. Given that diffusion leaks differently modify Jmax and Vcmax, they also alter Jmax/Vcmax ratio that is commonly used as a relative measure of the capacities of light and dark reactions of photosynthesis. While Jmax/Vcmax ratio is commonly around 2.5, awkward values of Jmax/Vcmax have been published (for review, see Wullschleger 1993; Ethier & Livingston 2004), possibly partly because of problems with chamber diffusion leaks.

Of course, the chamber air humidity of portable gas-exchange systems can somewhat be controlled by varying the fraction of dry air that is mixed with ambient air and by varying the flow rate. This may suggest that the results of our simulations conducted with constant incoming air flow rate and constant humidity overstate the problems of water vapour diffusion. However, for full stomatal opening that is needed for reliable An/Ci curve measurements, chamber humidity needs to be high, above 50–60%, implying that enhancing the fraction of dry air to compensate for humidity increase caused by transpiration may adversely affect photosynthesis. This may be especially significant if portable systems are used indoors where the air humidity is typically low, but conditions with low humidity are also frequently observed in the field. Furthermore, in these simulations, we used the maximum flow rate provided by LI-6400 of 500 µmol s−1. Whenever flow rate is less, humidity change caused by transpiration will be even larger, resulting in greater water vapour diffusion corrections than highlighted in these simulations.

Can the influence of diffusion leaks be corrected?

Actual measurements in low photosynthetic capacity species Quercus ilex (Figs 6 & 7) demonstrated major effects of the diffusion leaks on An/Ci response curves. Measurements without the bag exhibited negative Ci values at higher values of An as predicted by sensitivity analyses (cf. Figs 5b and 6a,b). It is surprising that such problems have not been mentioned in the literature before. Published field photosynthesis data are often noisy, and possibly, when negative Ci/high An pairs are observed under standard An/Ci curve estimations, such physiologically meaningless data are suppressed as ‘bad data’.

‘Normal’An/Ci response curves were obtained after correction of the measurements without the bag for the diffusion leak effects on An and transpiration rate (Eqns 10 & 13). However, the corrections introduced were large, on average more than 100% (increasing with the increase of CO2 and water vapour diffusion gradient) for An and transpiration rate (Fig. 7e,f). Thus, it is not surprising that the values of Farquhar et al. (1980) model parameters calculated from corrected measurements without bag (large corrections, Fig. 7e,f) and with bag with lower diffusion gradients (smaller corrections, Fig. 7a–d) were still significantly different (cf. Fig. 6c,d and 6e–h). As there is considerable uncertainty in estimation of the exact diffusion leak because of leaf effect, gasket and latch status, etc. (Fig. 4), and overall large corrections required (Fig. 7e,f), we feel that An/Ci curves cannot be reliably corrected for low photosynthetic capacity leaves measured with small chambers and large diffusion gradients between leaf chamber and ambient air. Even after correction, the error in Vcmax, Jmax and Rd can be more than 50% (Fig. 6).

Diminishing diffusion gradients using double-gasket design can be a useful way to reduce the diffusion leaks through the chamber gaskets (Fig. 6). There are still certain diffusion leaks in the system console tubing and in the tubing connecting the leaf chamber to the console. Accounting for these leaks can still mean that corrections on the order of 5–40% may be needed for leaves with low photosynthetic capacity (Fig. 7c,d).

There are further difficulties with clamp-on cuvettes such as the problem of lateral diffusion of CO2 and water vapour through the homobaric leaves (Jahnke & Krewitt 2002; Jahnke & Pieruschka 2006; Pieruschka et al. 2006). Thus, for species with homobaric leaves, clamp-on cuvettes can introduce additional errors that are hard to quantify and may even occasionally exceed the diffusion corrections as outlined here (Jahnke, personal communication). In addition, respiratory release of CO2 from the leaf area that remains under relatively wide gasket, and further diffusion of this released CO2 into the chamber can significantly alter the measured fluxes, especially when chamber CO2 concentration is small (Pons & Welschen 2002). We did not consider the latter effect in our study because in Pons & Welschen (2002), modification of carbon exchange rate was poorly linked to the relative leaf area under the gasket. This was possibly because multiple factors such as the gas exchange under the gasket, lateral diffusion through the leaf (see Pieruschka et al. 2006) for a discussion) and diffusion leaks affected the patterns. In addition, the overall effect of respiration under gaskets on carbon exchange rate was several-fold less than the effect of diffusion leaks observed in our study. In addition, the water vapour diffusion leak is independent of the leaf area under the gasket as stomata close in darkness and the leaf area under gasket negligibly participates in water vapour exchange. Nevertheless, these complicated factors should be considered in improving the leaf chamber designs. For instance, using a double-gasket design with similar CO2 concentrations between the inner and outer gasket rings, the inner gasket can be made narrower, thereby reducing the leaf area under the gasket.

CONCLUSIONS

Evolution of field gas-exchange systems has led from field instruments with large 1–10 L cuvettes often enclosing entire branch (Koch, Klein & Walz 1968; Field, Ball & Berry 1989) to portable systems with miniature clamp-on leaf chambers enclosing a small leaf area (McDermitt et al. 2001; Long & Bernacchi 2003). However, the fundamental limitations of cuvette size reduction arising from significant permeability of foam gaskets have not been widely recognized. Clamp-on leaf cuvettes are characterized by large diffusion leaks for CO2 and water vapour that significantly alter An/Ci response curves, and estimation of Farquhar et al. (1980) model parameters. While previous studies have considered only CO2 diffusion leak, clamp-on chambers are even more leaky for water vapour. Water vapour diffusion leaks influence An/Ci curves at least as much as CO2 diffusion leaks. The effect of leaks is particularly large for species with inherently low photosynthetic capacities and for leaf chambers enclosing small leaf area. As there is also significant uncertainty in estimation of the exact magnitude of the diffusion leaks, correction of data for diffusion leaks is difficult if not impossible for leaves with low photosynthetic capacity measured with small chambers.

Portable gas-exchange systems are used as standard instruments to derive the parameters for stand-scale, ecosystem-scale and even biome-scale carbon gain simulations. Given that many important communities are dominated by low photosynthetic capacity species, we suggest that existing parameterizations may need significant revision. We further suggest that the leaf cuvette design of these portable systems needs radical improvement. While the use of different polymer foams can marginally reduce the gasket permeability because most CO2 and water vapour diffusion occurs through interconnected gas-filled pores as well as through the small pores created between gasket foam and leaf veins, clamp-on leaf chambers can potentially be improved using a double-gasket design that effectively abolishes the diffusion gradient.

ACKNOWLEDGMENTS

We thank Dr. Siegfried Jahnke and an anonymous reviewer for their thoughtful comments. Financial support for this study was provided by the Estonian Science Foundation (grant 5702), the Estonian Ministry of Education and Science (grant SF1090065s07), the Estonian Academy of Sciences and the Province of Trento, Italy (grant DL3402). We further thank H. Walz GmbH for the opportunity to test the GSF-3000 portable gas-exchange system.

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