The Péclet effect on leaf water enrichment correlates with leaf hydraulic conductance and mesophyll conductance for CO2



    Corresponding author
    1. Department of Crop and Forest Science, Universitat de Lleida, E-25198, Lleida, Spain
    2. Institute of Forest Botany and Tree Physiology, University of Freiburg, D-79110, Freiburg im Breisgau, Germany
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    • JPF and AP contributed equally to this work.


    1. Plant Physiology Lab, Department of Biology, Universitat de les Illes Balears, E-07122, Palma de Mallorca, Spain
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    • JPF and AP contributed equally to this work.


    1. Plant Physiology Lab, Department of Biology, Universitat de les Illes Balears, E-07122, Palma de Mallorca, Spain
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    1. Institute for Landscape Biogeochemistry, Leibniz-Zentrum für Agrarlandschaftsforschung (ZALF) e.V., D-15374 Müncheberg, Germany
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    1. Agro-meterology Division, National Institute for Agro-Environmental Sciences (NIAES), 305-8604, Tsukuba, Japan
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    1. Plant Physiology Lab, Department of Biology, Universitat de les Illes Balears, E-07122, Palma de Mallorca, Spain
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    1. Plant Physiology Lab, Department of Biology, Universitat de les Illes Balears, E-07122, Palma de Mallorca, Spain
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J. P. Ferrio. Fax: +34 973 702924; e-mail:


Leaf water gets isotopically enriched through transpiration, and diffusion of enriched water through the leaf depends on transpiration flow and the effective path length (L). The aim of this work was to relate L with physiological variables likely to respond to similar processes. We studied the response to drought and vein severing of leaf lamina hydraulic conductance (Klamina), mesophyll conductance for CO2 (gm) and leaf water isotope enrichment in Vitis vinifera L cv. Grenache. We hypothesized that restrictions in water pathways would reduce Klamina and increase L. As a secondary hypothesis, we proposed that, given the common pathways for water and CO2 involved, a similar response should be found in gm. Our results showed that L was strongly related to mesophyll variables, such as Klamina or gm across experimental drought and vein-cutting treatments, showing stronger relationships than with variables included as input parameters for the models, such as transpiration. Our findings were further supported by a literature survey showing a close link between L and leaf hydraulic conductance (Kleaf = 31.5 × L−0.43, r2 = 0.60, n = 24). The strong correlation found between L, Klamina and gm supports the idea that water and CO2 share an important part of their diffusion pathways through the mesophyll.


Evaporative enrichment of leaf water and its effect on newly produced assimilates are well characterized and can be described with mechanistic models (Barbour & Farquhar 2003; Farquhar & Cernusak 2005; Cuntz et al. 2007). Briefly, the isotopic composition of mean lamina leaf water reflects variations in (1) source water isotope signature (i.e. xylem water) and (2) the evaporative enrichment during transpiration (Yakir 1992a; Farquhar & Lloyd 1993). The isotopic enrichment at the site of evaporation can be described using the Craig & Gordon (1965) model for evaporation in water surfaces, adapted for plants by Dongmann et al. (1974). However, this model overestimates mean lamina leaf water enrichment during the day, as the diffusion of enriched water from the sites of evaporation to the rest of the leaf is counteracted by the input of unenriched water through the transpiration flow, what is known as the Péclet effect (Farquhar & Lloyd 1993). The Péclet effect is mainly determined by the magnitude of the transpiration flow, modulated by the ‘scaled effective path length’ (L) (Farquhar & Lloyd 1993). L is defined as the product of two components: the actual distance of the water pathway (l) from the xylem to the evaporative surface, and a scaling factor (k) that accounts for tortuous path of water through a porous media (Farquhar & Lloyd 1993; Barbour et al. 2000b; Cuntz et al. 2007). Hence, L is theoretically related to mesophyll hydraulic resistance to water flow, which in turn has a strong influence on whole leaf hydraulic resistance (Steudle & Frensch 1996; Nardini & Salleo 2005; Sack & Holbrook 2006). In this regard, interspecific differences in anatomical features associated with l, such as vein density or the maximum mesophyll path length, have shown to be closely related to variations in leaf hydraulic resistance (Sack & Frole 2006; Brodribb, Feild & Jordan 2007). However, although some attempts have been made to relate L and the Péclet effect with measurable leaf parameters (Wang, Yakir & Avishai 1998; Barbour & Farquhar 2003; Kahmen et al. 2008, 2009), the mechanistic reasons underlying observed L differences are still unclear. Besides anatomical differences, short-term variations in mesophyll hydraulic properties in response to environmental conditions might cause changes in L, as has been already suggested elsewhere (Barbour & Farquhar 2003; Keitel et al. 2006), and recently confirmed by experimental studies (Ripullone et al. 2008; Ferrio et al. 2009).

When leaving the xylem, water can move through three main water pathways (Steudle & Frensch 1996): the apoplastic pathway, that is, around the protoplasts; the symplastic pathway, travelling along the cytoplasmic continuum through plasmodesmata; and the transcellular or vacuolar pathway, which takes place across membranes and is dominated by transmembrane water channels (aquaporins). Evidence so far has shown that due to changes in aquaporin expression and activity, leaf hydraulic conductivity can be highly dynamic and respond rapidly and reversibly to changes in temperature, irradiance and water supply (Kaldenhoff & Eckert 1999; Martre et al. 2002; Sack & Holbrook 2006; Cochard et al. 2007; Katsuhara et al. 2008; Mahdieh et al. 2008). Similarly, the regulation of the transcellular pathway by aquaporins would modify the proportion between the different water pathways, thus affecting not only the length of the water path (l), but also the magnitude of the scaling factor k, due to differences in porosity among alternative water pathways (Yakir 1992b; Farquhar & Lloyd 1993; Barbour et al. 2000b; Barbour & Farquhar 2003; Ferrio et al. 2009). In summary, leaf hydraulic conductivity is expected to be inversely related to variations in the two components of L (k and l), either due to anatomical differences (e.g. among species or in response to treatments affecting leaf development) or to short-term regulatory mechanisms. Surprisingly, in the only work comparing L with leaf hydraulic conductivity, Kahmen et al. (2009) did not find a clear relationship between them. In this study, however, both variables showed little variation in response to the treatments applied. Therefore, research on potential changes in the scaled effective pathlength L under conditions providing a clear response in leaf hydraulic conductivity is still needed.

Water and CO2 diffusion share at least in part common diffusion pathways in the mesophyll, including the transcellular pathway (Evans et al. 2009; Terashima et al. 2011), in which the transport of both water and CO2 is facilitated by aquaporins (Uehlein et al. 2003; Flexas et al. 2006; Kaldenhoff et al. 2008; Heinen, Ye & Chaumont 2009; Otto et al. 2010). For this reason, assessing to what extent the regulation of water transport pathways in the mesophyll also affects mesophyll diffusion conductance to CO2 (gm) has been recently highlighted as a research priority (Flexas et al. 2008). We are not aware of any attempt to relate mesophyll conductance for CO2 (also mediated by aquaporins) with leaf hydraulic conductivity and leaf water enrichment. Nevertheless, a strong relationship between leaf anatomical features associated with l, hydraulic conductance and assimilation rates has been reported, further supporting the existence of a close link between water and CO2 mesophyll pathways (Brodribb et al. 2007).

In this work, we studied simultaneously the response of leaf lamina hydraulic conductivity, mesophyll conductance for CO2, and leaf water isotope enrichment to drought and vein severing in grapevine. We hypothesized that changes in mesophyll water pathways caused by drought and/or vein severing would result in a concomitant increase in leaf lamina hydraulic resistance and L. As a secondary hypothesis, we propose that, provided that these changes involve variations in common pathways for water and CO2, the transport of the latter should also be affected, resulting in a decrease in mesophyll conductance for CO2. Additional comparisons between values of L and hydraulic conductance were performed using data from a literature survey with further enhancement of our central hypothesis.


Plant material and treatments

The experiment was carried out in July 2008 on 2-year-old grapevine plants (Vitis vinifera L cv. Grenache) grafted on Richter-110. Plants were grown outdoors at the experimental field of University of the Balearic Islands (Mallorca, Spain) in 15 L pots filled with a mixture of soil and organic substrate and were irrigated daily from April to mid-July. Supplemental Hoagland's solution at 50% was given once per week. From 15 July, half of the plants were irrigated daily to field capacity (control), and in the other half (drought exposed), irrigation was limited to one half of daily water loss (determined gravimetrically). Before water withholding was applied, two leaves per plant in both control and drought treatments were subjected to in vivo severing treatments. The treatment consisted of parallel incisions on both sides of each primary vein, 5 mm from primary veins, beginning 5 mm from the petiole-leaf junction, and for each vein finishing 1 cm from the margin, that is, nearly eliminating water transport through the xylem (Sack, Streeter & Holbrook 2004). Cuts were made by using a scalpel while supporting the leaf on a cardboard. Abaxial and adaxial cuts of the leaf were taped over with a 1.9 mm transparent waterproof tape. Every treated leaf was paired with a nearby control leaf (uncut leaf) on the same branch matched approximately in same size and light exposure. Plants were protected from direct sunlight until wounds healed (approximately after 3–4 days), then returned to their position and left to re-acclimate for 1–2 d. Approximately one fourth of the severed leaves died before being included in the experiment.

Experimental schedule

Sampling and gas-exchange measurements in intact leaves were performed daily, starting the day after the beginning of drought treatment. Fully expanded leaves were chosen to avoid any development effect of the treatments. Two sampling/measurement rounds were performed each day, one in the morning (ca. 10–12 h) and one in the afternoon (ca. 13–15 h). For each treatment and measurement round, three leaves from three plants (one leaf per plant) were sampled for stable isotope determinations. Just before harvesting, leaf temperature, gas exchange and chlorophyll fluorescence measurements were performed as detailed in the next section. Main veins were removed, and the petiole and two thirds of the leaf lamina were stored separately in glass tubes and frozen for subsequent water distillation. The remaining third of the leaf was kept to determine water concentration (% in weight of water divided by fresh weight) per leaf area (m−2). Simultaneously, one severed leaf per treatment and day was measured and harvested as described previously. Only healthy leaves were selected, discarding those with clear symptoms of desiccation or providing negative assimilation rates.

Additionally, three to five leaves per treatment (including both intact and severed leaves) were excised under water for hydraulic conductivity determinations (see next). Due to time-consuming measurements, it was not possible to determine hydraulic conductivity for all treatments in the same day, and thus leaves from different treatments were sampled consecutively throughout the experiment, between 1000 and 1400 h, when transpiration rates were maximal, to minimize the potential impact of diurnal periodicity on leaf hydraulic conductivity.

Instantaneous gas exchange and chlorophyll fluorescence measurements, and estimation of gm

Instantaneous gas-exchange and chlorophyll fluorescence measurements were taken using an open gas-exchange system (Li-6400; Li-Cor, Inc., Lincoln, NE, USA) with an integrated fluorescence chamber head (Li-6400–40; Li-Cor Inc.). All measurements were made on young, fully expanded leaves, at 1500 µmol m−2 s−1 to ensure light saturation, with a CO2 concentration in the cuvette of 400 µmol COmol−1 air, and using the 2-cm2 leaf chamber. From instantaneous measurements, net CO2 assimilation rate (AN), stomatal conductance (gs) and sub-stomatal CO2 concentration (Ci) were recorded. Leaf temperature under ambient conditions was determined just before gas-exchange measurements attaching a leaf thermocouple (Li-6400-04; Li-Cor Inc.) coupled to a digital thermometer (model 51 II; Fluke Corporation, Everett, WA, USA) to the abaxial surface of the leaf.

Photochemical efficiency of photosystem II (φPSII) was determined by measuring steady-state fluorescence (Fs) and maximum fluorescence during a light-saturating pulse of ca. 8000 µmol m−2 s−1 (Fm′) following the procedures of Genty, Briantais & Baker (1989):


The electron transport rate (Jflu) was then calculated as:


where PPFD is the photosynthetically active photon flux density, α is leaf absorptance and β reflects the partitioning of absorbed quanta between photosystems II and I. The products α and β were determined, following Valentini et al. (1995), from the relationship between φPSII and φCO2 obtained by varying light intensity under non-photorespiratory conditions in an atmosphere containing less than 1% O2. Leakage of CO2 into and out the leaf cuvette was determined with photosynthetically inactive leaves (obtained by heating the leaves until no variable chlorophyll fluorescence was observed) enclosed in the leaf chamber (Flexas et al. 2007). The method by Harley et al. (1992) was then used to make estimations of gm. In essence, this method is based in comparing fluorescence estimates of electron transport (Jflu) with gas exchange estimates (J) based on the Farquhar, Von-Caemmerer & Berry (1980) model of photosynthesis:


where Rd is the rate of mitochondrial respiration in the light and is the CO2 photocompensation point in the absence of Rd.

The mismatches between the two estimates are ascribed to differences between Ci and the actual CO2 concentration in the chloroplasts (Cc), as the estimate of J is based on Ci while the obtained Jflu is determined by the prevailing Cc. As, from Fick's law of diffusion, AN = gm · (Ci – Cc), replacing Ci by Cc in Eqn 3 allows estimating gm as:


where AN and Ci are taken from gas exchange measurements at saturating light.

Ci* was used as a proxy for Γ* following Warren & Dreyer (2006). Ci* and Rd were determined according to the method by Laisk (1977). Briefly, ANCi curves were measured at three different PPFDs (50, 150 and 750 µmol m−2 s−1) at six different CO2 levels ranging from 400 to 50 µmol CO2 mol−1 air. The intersection point of the three ANCi curves was used to determine Ci* (x-axis) and Rd (y-axis). Further details on this method and required precautions that were followed in the present study can be found in Pons et al. (2009).

Measuring lamina hydraulic conductance (K)

Maximum leaf K was determined using a high pressure flow meter (HPFM; Dynamax Inc., Houston TX, USA), as described in Tyree et al. (1995). Detached leaves were excised under water and allowed to reach a steady-state flow while attached to a flow meter through the petiole using compression fittings. KCl solution (15 mm) filtered at 0.1 µm was forced into the leaves at a pressure (P; MPa) up to 0.4 MPa, while measuring the instantaneous flow (F; mmol s−1) every 8 s. Leaves showing leaks from the cut veins were immediately discarded. Corresponding hydraulic conductances (K; mmol s−1 MPa) were computed as K = F / P. During measurements, leaf temperature was monitored by a thermocouple, and maintained between 20 and 25 °C by adding water uniformly over the leaf blade. The leaf conductance values were then corrected for eventual temperature changes to account for changes in water viscosity, according to manufacturer's instructions:


where K is the uncorrected conductance, T is the temperature at which K was measured and T* is the temperature at which the HPFM was calibrated.

K decreased during the early phases of measurements as the likely effect of progressive infiltration of leaf air spaces, and reached stable values after 25–30 min. After K was recorded, leaf blades were removed using a fresh razor blade. The hydraulic conductance of the petiole (Kpetiole) was measured and the lamina hydraulic conductance (Klamina) (Klamina = 1/R) was calculated as:


After each experiment, projected leaf areas (LA; m2) were measured with a leaf area meter (AM-100 Area Meter, Analytical Development Co., Hoddesdon, UK), and leaf and lamina maximum K on a surface area basis were calculated (mmol s−1 MPa−1 m−2).

Water vapour collection, water distillation and mass spectrometry measurements

During each sampling/measuring round, atmospheric water vapour was collected by cryogenic condensation (Roden & Ehleringer 1999). Briefly, air was pumped at 1 L min−1 for about 2 h through a trap filled with ethanol and dry ice (ca. −70 °C). Petiole and leaf lamina water were extracted by cryogenic vacuum distillation (Ehleringer & Dawson 1992). For both, water vapour and distilled water, cryogenically trapped water was transferred immediately into sealed 2 mL crimp cap vials (Infochroma, Zug, Switzerland) and kept cooled until isotope analysis. An aliquot of 0.6 µL of each water sample was then injected in a High Temperature Combustion Elemental Analyzer (TC/EA, Thermo Finnigan, Bremen, Germany), pyrolized at 1450 °C on glassy carbon to CO, the oxygen isotope ratio of which was determined by isotope ratio mass spectrometry (Delta plus XP, Thermo Finnigan) and the values expressed as deviations in per mil (‰) from the international standard VSMOW (δ18O). Overall precision was better than 0.2‰.

Leaf water models and determination of effective pathlength L

Isotopic enrichment of mean lamina leaf water above source water (ΔL, in‰) was calculated as ΔL = (δL − δS) / (1 + δS), where δL and δS stand for the isotopic composition of leaf lamina (after removing main veins) and source water, respectively. Petiole water (δ18OP) was considered here to be representative for source water. Steady-state isotopic enrichment at the site of evaporation (Δe) was modelled according to Craig & Gordon (1965) and Dongmann et al. (1974):


where ε+ is the equilibrium fractionation between liquid water and vapour (Majoube 1971); εk is the kinetic fractionation of vapour diffusion from the leaf to the atmosphere (Farquhar et al. 1989); Δv is the isotopic enrichment of atmospheric water vapour; and ea / ei is the ratio of ambient to intercellular vapour pressures.

The steady-state isotopic enrichment of mean leaf lamina mesophyll water (ΔLss) was calculated by correcting for the gradient from xylem source water to enriched water at the evaporating sites, the so-called Péclet effect (Farquhar & Lloyd 1993):


where ℘ is the Péclet number, E the leaf transpiration rate (mol m−2 s−1), L the scaled effective path length (m) for water movement from the veins to the site of evaporation, C the molar concentration of water (55.56 103 mol m−3) and D the tracer-diffusivity (ms−1) of the heavy water isotopologue (H218O) in ‘normal’ water. The effective pathlength L under the steady-state assumption (Lss) was determined by fitting Eqn 2 to measured ΔL. Lss values were fitted independently for each leaf.

Non-steady-state effects in leaf lamina mesophyll water enrichment (inline image) were tested using the simplified non-steady-state Péclet description (Farquhar & Cernusak 2005):


where α = 1 + ε (α+ and αk are corresponding to ε+ and εk, respectively), Vm is lamina leaf water molar concentration (mol m−2), t is time (s), gt is the total conductance for water vapour of stomata and boundary layer (mol m−2 s−1), and wi is the mole fraction of water vapour in the leaf intercellular air spaces (mol mol−1). The term inline image stands for the rate of change in ‘isostorage’ (inline image) between a given measuring time-point (t0) and a previous measurement, used as reference (t−1), and is applied to estimate the ‘net isoflux’ during transpiration (Farquhar & Cernusak 2005). According to previous studies on Grenache grapevines (Schultz 2003; Soar et al. 2006; Vandeleur et al. 2009; Lovisolo et al. 2010), leaves were considered to behave isohydrically, and no changes in Vm were included in the non-steady state model. Indeed, we did not find any significant effect of the treatments for this parameter, so we took it as a constant throughout the experiment (Vm = 10.9 ± 0.02 mol H2O m−2). To prevent artefacts due to differences between the individual leaves sampled at each time-point, we calculated inline image using average values for each time-point and treatment (n = 3). Sensu stricto, the model could only be applied to the values from intact leaves in the afternoon, using morning data as reference values (t−1). Nevertheless, we also applied the non-steady state model to severed leaves, and to morning values in intact leaves. In these cases, in which measured values for t−1 were not available, the rate of changes in ΔL was estimated from the average and the 95% confidence interval for the differences in ΔL between morning and afternoon values (2.60 and 1.66–3.53‰, respectively), and the average dt (8324 s). Although the non-steady state model under these assumptions may have lost its predictive value, the comparison between Lss and Lnss, as well as the sensitivity of Lnss to ΔL changes, provided a qualitative test of the potential risks associated with assuming steady-state conditions.

Equilibrium fractionation ε+ was calculated after Majoube (1971), and kinetic fractionation εk was calculated after Farquhar et al. (1989) with the diffusional fractionation factors of Cappa et al. (2003). Tracer-diffusivity D as depending on temperature was estimated after Cuntz et al. (2007):


with a1 = 100·10−9, a2 = 577, a3 = 145 and aD = 1/1.026 for H218O.

Effective pathlength L under non-steady state conditions (Lnss) was calculated by fitting iteratively Eqn 3 until ΔLnP values at both sides of equation differed by less than 0.01‰.

Literature survey

To further assess the link between leaf K and L, we compiled published data from both variables for different species and growing conditions (see details in Supporting Information Table S1). We are only aware of one additional work reporting both variables determined in the same experiment (Kahmen et al. 2009). In the rest of species, data for L and Kleaf were derived from independent sources. An attempt was made to select the most comparable species and/or growing conditions, taking gs, when available, as the main reference criterion for the water stress severity endured by the plants under study (Medrano et al. 2002). In other cases, other indicators of plant water status were used (e.g. transpiration rate, water potential, reported environmental conditions). As a first choice, we looked for data from the same species, but when such data were not available, or environmental conditions for L and Kleaf were not fully comparable, data from closely related species were included to obtain a more robust value. When possible, data were divided in two groups, ‘dry’ and ‘wet’, according to plant water status, rather than to habitat preferences (e.g. a species from semi-arid environments may be included as wet, if showing high gs, whereas a mesic species growing under water stress would appear as ‘dry’). Compiled Kleaf values were determined by different methods: either high pressure flow (Tyree et al. 1995), evaporative flux (Boyer 1977; Brodribb & Holbrook 2003), rehydration kinetics (Brodribb & Holbrook 2003), vacuum pump (Kolb, Sperry & Lamont 1996; Nardini, Tyree & Salleo 2001) or the Ohm's Law (Van den Honert 1948). We selected Kleaf instead of Klamina because the former is the most commonly found in literature.

Statistical analysis

The effect of treatment on physiological variables and isotopes was first assessed by means of analyses of variance (anovas), including water status (control, drought) and leaf treatment (non-severed veins, severed veins) as fixed factors. Additionally, the effect of day and measuring time were considered by adding them as fixed factors to the model, but due to the lack of replicates this was only possible for non-severed plants. All the anovas were performed using standard SAS–STAT procedures (SAS 1988). The relationship between pairs of variables was assessed by means of linear regressions and simple correlation analyses, indicating determination coefficients and P values as main statistics. Unless otherwise stated, averages are reported together with the standard errors of the mean.


Experimental conditions and physiological response to drought and vein severing

Conditions close to steady state were kept during the measurement time (ca. 10–15 h) in all measurement days. Nevertheless, environmental conditions varied slightly from one day to another (Supporting Information Fig. S1). From 18 to 20 July (2008), relative air humidity decreased, recovering again from 21 July until the end of the experiment. July 22 was a cloudy day and thus gas exchange and sampling for isotopes were not performed. As expected, water availability (expressed as % of field capacity) decreased steadily throughout the experiment in drought-exposed plants, from 90 ± 1.0 to 66 ± 1.5% (data plotted in Supporting Information Fig. S1). δ18O of water vapour (δ18Ov) also varied from day to day, following fluctuations in relative humidity.

The combination of drought and leaf severing treatments resulted in a wide range of leaf water status, and this was reflected in ΔL and the effective pathlengh Lss (Tables 1 & 2, Fig. 1). Similarly, we obtained a wide range of values for Kleaf and Klamina (Table 3, Fig. 1). According to the general anova (Table 4), both drought and leaf severing treatments affected significantly the main gas exchange variables (AN, gs, E), as well as gm. However, although leaf temperature was affected by both treatments, and a subsequent effect on Δe was predicted, ΔL was only significantly affected by drought, whereas for Kleaf and Klamina only leaf severing showed a significant effect (Table 4). More detailed anova, including day and time effects in the model, confirmed these trends for non-severed leaves. AN, gs and E showed again a strongly significant response to drought, responding to day and measuring time at different levels (Table 4). The direct effect of drought on gm was weak, but showed a stronger interaction with day. Looking in depth at non-severed leaves, the anovas including day and time in the model showed a strongly significant effect of drought (P < 0.001), day and time on δ18OL, ΔL and Δe, whereas Lss was only significantly affected by the drought treatment (P < 0.001).

Table 1.  Main physiological variables and isotope values in intact leaves (average and standard error of three replicates)
TreatmentDateTimeAN (µmol CO2 m−2 s−1)gs (mmol H2O m−2 s−1)E (mmol H2O m−2 s−1)gm (mmol CO2 m−2 s−1)Tleaf (°C)δ18OP(‰)ΔL(‰)Δe(‰)Lss (mm)
  1. AN, net photosynthesis; gs, stomatal conductance; E, transpiration rate; gm, mesophyll conductance for CO2; Tleaf, leaf temperature; δ18OP, petiol water isotope composition; ΔL, measured isotopic enrichment in leaf lamina water; Δe, modelled isotopic enrichment at the site of evaporation assuming steady-state conditions; Lss, scaled effective pathlength assuming steady-state conditions. (Average and standard error of three replicates.)

Control18/0710:16–11:0316.80 ± 0.71205 ± 14.04.00 ± 0.13229 ± 14.130.2 ± 0.54−7.5 ± 1.6615.0 ± 2.0920.7 ± 0.1226 ± 8.7
 13:56–14:1915.48 ± 0.86216 ± 13.64.70 ± 0.31176 ± 12.730.4 ± 1.07−7.9 ± 0.1419.1 ± 0.8521.5 ± 0.137 ± 0.3
19/0710:59–12:3013.33 ± 0.16253 ± 20.15.69 ± 0.56190 ± 9.632.5 ± 0.20−8.2 ± 0.5919.6 ± 1.2523.1 ± 0.1110 ± 3.7
 13:20–13:5211.58 ± 0.31206 ± 18.05.36 ± 0.47173 ± 11.534.4 ± 1.06−6.1 ± 1.0421.8 ± 1.7324.5 ± 0.127 ± 2.5
20/0710:50–11:3313.43 ± 1.20227 ± 41.35.39 ± 0.79164 ± 24.632.2 ± 0.65−5.4 ± 0.2917.6 ± 0.8122.2 ± 0.1215 ± 6.0
 13:07–13:3812.57 ± 1.45196 ± 35.35.54 ± 0.79178 ± 12.734.8 ± 0.32−7.4 ± 1.4520.7 ± 0.6825.4 ± 0.1613 ± 3.6
21/0710:44–11:3114.45 ± 1.00204 ± 20.64.30 ± 0.42166 ± 3.728.3 ± 0.72−8.6 ± 0.4317.9 ± 0.2121.0 ± 0.1410 ± 1.7
 12:25–13:2314.67 ± 0.83215 ± 1.95.02 ± 0.04154 ± 21.929.7 ± 0.60−8.3 ± 0.5518.3 ± 0.4022.1 ± 0.1611 ± 1.6
23/0711:20–12:0216.34 ± 0.22274 ± 14.46.31 ± 0.25207 ± 33.229.6 ± 0.28−5.9 ± 0.4614.4 ± 1.5817.1 ± 0.159 ± 5.0
 13:43–15:0815.48 ± 0.97239 ± 19.65.68 ± 0.63162 ± 28.131.5 ± 0.49−7.0 ± 0.8015.3 ± 0.6719.8 ± 0.0315 ± 3.0
24/0711:07–11:4315.42 ± 0.92274 ± 12.05.31 ± 0.38142 ± 15.128.6 ± 0.12−9.5 ± 0.0213.4 ± 0.7818.2 ± 0.0017 ± 2.0
 13:18–13:3416.25 ± 0.25260 ± 11.05.74 ± 0.22158 ± 7.230.8 ± 0.20−8.7 ± 0.4417.0 ± 1.6020.9 ± 0.0612 ± 5.5
Mean ± SE  14.58 ± 0.34229 ± 7.05.24 ± 0.16175 ± 6.231.2 ± 0.38−7.5 ± 0.2917.7 ± 0.5121.5 ± 0.4413 ± 1.4
Drought18/0710:27–11:126.96 ± 0.8854 ± 15.11.30 ± 0.35197 ± 58.432.2 ± 0.20−6.1 ± 0.7019.8 ± 0.6422.8 ± 0.0241 ± 16.2
 13:48–13:564.51 ± 2.4935 ± 19.01.02 ± 0.55114 ± 50.336.5 ± 0.00−7.9 ± 0.7025.2 ± 0.7227.3 ± 0.0433 ± 9.8
19/0711:27–12:1412.42 ± 0.52117 ± 3.53.09 ± 0.02270 ± 3.435.8 ± 2.20−6.4 ± 0.3622.6 ± 0.1825.5 ± 0.0313 ± 5.7
 13:12–13:355.21 ± 3.7141 ± 26.91.31 ± 0.84167 ± 104.037.9 ± 0.29−7.5 ± 1.8825.3 ± 1.4528.2 ± 0.0770 ± 50.7
20/0710:36–11:276.64 ± 2.7770 ± 30.22.03 ± 0.7492 ± 32.235.7 ± 1.18−6.8 ± 0.3520.2 ± 0.7626.6 ± 0.0362 ± 21.5
 13:00–13:314.48 ± 1.4345 ± 15.21.60 ± 0.4969 ± 9.937.3 ± 0.30−5.9 ± 0.6524.1 ± 0.8427.6 ± 0.0735 ± 11.5
21/0710:36–11:1910.63 ± 0.37118 ± 8.12.75 ± 0.20191 ± 38.330.0 ± 0.29−7.0 ± 0.3120.0 ± 1.5322.2 ± 0.0412 ± 10.8
 12:34–13:346.45 ± 0.4551 ± 5.61.50 ± 0.19239 ± 12.733.4 ± 0.49−8.3 ± 0.4723.2 ± 0.9525.9 ± 0.0222 ± 6.9
23/0710:52–11:409.09 ± 1.46114 ± 41.82.81 ± 0.93168 ± 33.034.2 ± 1.33−4.5 ± 0.7317.3 ± 1.3821.7 ± 0.0222 ± 2.6
 14:01–14:566.72 ± 1.7270 ± 21.11.99 ± 0.55121 ± 22.033.5 ± 1.39−6.9 ± 0.5919.0 ± 0.7822.3 ± 0.0133 ± 14.7
24/0710:50–11:533.09 ± 1.1831 ± 12.30.84 ± 0.2856 ± 21.334.2 ± 0.28−8.0 ± 1.5320.6 ± 1.2424.2 ± 0.0175 ± 25.8
 13:02–13:073.46 ± 0.4027 ± 4.90.88 ± 0.16101 ± 18.233.7 ± 2.61−7.2 ± 0.5420.7 ± 1.7123.9 ± 0.0253 ± 0.5
Mean ± SE  6.67 ± 0.6066 ± 7.61.78 ± 0.18149 ± 14.534.3 ± 0.47−6.8 ± 0.2721.3 ± 0.4924.7 ± 0.4439 ± 5.6
Table 2.  Main physiological variables and isotope values in vein-severed leaves (individual leaf values)
TreatmentDateTimeAN (µmol CO2 m−2 s−1)gs (mmol H2O m−2 s−1)E (mmol H2O m−2 s−1)gm (mmol CO2 m−2 s−1)Tleaf (°C)δ18OP(‰)ΔL(‰)Δe(‰)Lss (mm)
  • a

    Discarded as outliers in all calculations.

  • b

    Discarded as outlier only for Lnss calculations (see Fig. 3). In both cases, the particular variables in which the samples were recognized as outliers are highlighted.

  • AN, net photosynthesis; gs, stomatal conductance; E, transpiration rate; gm, mesophyll conductance for CO2; Tleaf, leaf temperature; δ18OP, petiol water isotope composition; ΔL, measured isotopic enrichment in leaf lamina water; Δe, modelled isotopic enrichment at the site of evaporation assuming steady-state conditions; Lss, scaled effective pathlenght assuming steady-state conditions.

Mean ± SE  5.0 ± 1.8249 ± 17.11.30 ± 0.39137 ± 52.333.1 ± 0.63−7.4 ± 0.2420.4 ± 0.7225.1 ± 0.2669 ± 22.0
Mean ± SE  2.8 ± 0.4823 ± 3.60.78 ± 0.1360 ± 20.935.4 ± 1.03−8.2 ± 0.6422.0 ± 0.4926.1 ± 0.8176 ± 7.1
Figure 1.

Treatment means for leaf and leaf lamina hydraulic conductance (Kleaf and Klam, respectively), effective pathlength calculated with the steady-state model (Lss), and transpiration rates (E). For simplicity, the axis for Lss has been inverted. C and D, intact leaves from control and drought-exposed plants; C-VS and D-VS, vein-severed leaves from control and drought-exposed plants. Replication: for Lss and E, n = 12(×3) for C and D, n = 4–6 for C-VS and D-VS; for Kleaf and Klam, n = 4–5 for C and D, n = 3–5 for C-VS and D-VS. See Tables 1–3 for details.

Table 3.  Individual leaf values of leaf hydraulic conductance
TreatmentDateMax. conductance (K)(mmol H2O s−1 MPa−1 m−2)
  1. C-severed, D-severed: vein-severed leaves in control and drought-exposed plants, respectively.

Mean ± SE 7.0 ± 1.777.7 ± 1.77
Mean ± SE 4.1 ± 0.394.4 ± 0.42
Mean ± SE 4.8 ± 1.276.4 ± 1.50
Mean ± SE 3.5 ± 1.363.8 ± 1.28
Table 4.  Summary of the results of anovas for the most relevant variables studied
  1. ***P < 0.001; **P < 0.01; *P < 0.05; P < 0.1; n.s., P ≥ 0.1.

  2. anova, analysis of variance; AN, net photosynthesis; gs, stomatal conductance; E, transpiration rate; gm, mesophyll conductance for CO2; Tleaf, leaf temperature; δ18OP and δ18OL, petiol and leaf lamina water isotope composition; ΔL, measured isotopic enrichment in leaf lamina water; Δe, modelled isotopic enrichment at the site of evaporation assuming steady-state conditions; Lss, scaled effective pathlength assuming steady-state conditions; Kleaf and Klamina, leaf and lamina maximum specific hydraulic conductance.

General anova
Vein severing (VS)**********n.s.n.s.n.s.n.s.****
Drought × VS*********n.s.n.s.n.s.n.s.*n.s.n.s.n.s.
anova non-severed
Drought × day**n.s.*n.s.n.s.n.s.n.s.
Drought × timen.s.n.s.n.s.n.s.n.s.n.s.n.s.n.s.
Day × timen.s.n.s.n.s.*n.s.n.s.n.s.n.s.n.s.n.s.

Relationship between K, gas exchange variables and effective pathlength L

Whereas treatment averages of Kleaf showed the strongest correlation with E (r = 0.988, P = 0.012), Klamina was not significantly correlated with this variable. On the other hand, Lss was negatively correlated with leaf and lamina K (r = −0.995, P = 0.005 and r = −0.932, P = 0.034, respectively). In particular, among all the physiological variables studied, the strongest relationship across treatment means was found between Lss and Klamina. Lss showed also a weak negative trend with E (r = −0.924, P = 0.075). Correlations between gs and both K and Lss showed the same pattern found for E, but generally weaker. Treatment averages of gm showed a weak correlation with Klamina and Lss (r = 0.933, P = 0.067 and r = −0.907, P = 0.093, respectively) but were not significantly correlated with leaf Kleaf, E and gs (P = 0.133–0.247).

When individual replicates were plotted, Lss was only correlated with E and gs in their lowest range of values (E < 4 mmol H2O m−2 s−1 and gs < 150 mmol H2O m−2 s−1), which excluded nearly all samples from control plants (r = −0.735 for E; r = −0.716 for gs; see Fig. 2a). Similarly, gm was linearly correlated with Lss in its lowest range of values (gm < 200 mmol H2O m−2 s−1; r = 0.791; P < 0.001; Fig. 2b), although in this case this condition was fulfilled by most of the samples (about 79 and 71% of control and drought plants, respectively). Looking at treatment averages after excluding samples with high apparent gm, we found the strongest correlations between this variable and the other two mesophyll parameters, Klamina (r = 0.976; P = 0.024, Fig. 2b, inset) and Lss (r = −0.989, P = 0.011). After applying this filter to gm, other correlations emerged across treatment averages: with Kleaf (r = 0.952; P = 0.048), E (r = 0.923, P = 0.077) and gs (r = 0.903, P = 0.097), although consistently weaker than among mesophyll parameters.

Figure 2.

Relationship of individual leaf values (no replicates) for (a) transpiration rates (E) and (b) mesophyll conductance for CO2 (gm) with scaled effective pathlength (Lss, determined with the steady-state model). Inset: relationship between treatment averages of gm (excluding samples with gm > 200 mmol COm−2 s−1), and leaf lamina maximum specific hydraulic conductance (Klamina). Circles: control plants; triangles: drought plants. Open symbols: intact leaves. Closed symbols: vein-severed leaves. Grey dots: samples included in regression models.

Divergence between steady-state and non-steady-state models

The application of non-steady-state models to calculate the effective pathlength (Lnss) of the afternoon data confirmed the observations derived from the steady-state models (Lss), showing a strong correlation between Lnss and Lss, as well as a similar positive correlation between Lnss and gm (Fig. 3a,b). Extending non-steady state models to those samples in which the values at t−1 were not available gave comparable results, showing a good correlation between the outputs of steady-state and non-steady-state models, and most samples showed small estimation errors (Fig. 3c,d). The resulting correlation between treatment averages of Lnss and Klamina was comparable with that obtained with the steady-state models (r = 0.980; P = 0.020; see Fig. 3d, inset).

Figure 3.

Relationship between averages per measuring time and treatment (n = 3) for scaled effective pathlength (Lss and Lnss, determined with the steady-state and non-steady-state models, respectively), and mesophyll conductance for CO2 (gm). In (a) and (b) Lnss calculated for intact leaves in the afternoon, using morning data as reference values (see text for details); in (c) and (d) Lnss calculated for all the samples using the average (symbol) and the 95% confidence interval (error bars) for the differences between morning and afternoon values in intact leaves (see text for details). Inset: relationship between treatment averages of leaf lamina maximum specific hydraulic conductance (Klamina) and Lnss. Circles: control plants; triangles: drought plants. Open symbols: intact leaves. Closed symbols: vein-severed leaves. Grey dots: samples included in regression models.

Results from the literature survey

Comparing literature data for effective pathlength L and Kleaf showed a relationship between both variables that was consistent with that found between L and both Kleaf and Klam in the present experiment (Fig. 4). The relationship was steeper in the lowest range of L, and thus the best fit was obtained with a potential model (Kleaf = 31.45 × L−0.4307, r2 = 0.603, n = 24, P < 0.001). Monocot species (wheat and maize) clearly appeared as outliers for the general relationship and thus were excluded from the regression model.

Figure 4.

Relationship between effective pathlength (L) and leaf-specific hydraulic conductance (Kleaf) across different genus and growing conditions. Vitis data correspond to the present study; the rest were derived from literature data (Förstel 1978; Gallardo et al. 1996; Gregory & Eastham 1996; Bond & Kavanagh 1999; Barbour & Farquhar 2000; Barbour et al. 2000a,b, 2004; Sack et al. 2002; Gan et al. 2003; Costa e Silva et al. 2004; Aranda, Gil & Pardos 2005; Cernusak, Farquhar & Pate 2005; Farquhar & Cernusak 2005; Li, Xu & Cohen 2005; Liu et al. 2005; Pendall, Williams & Leavitt 2005; Bunce 2006; Keitel et al. 2006; Barnard et al. 2007; Brandes 2007; Santrucek et al. 2007; Kahmen et al. 2008, 2009; Ripullone et al. 2008; Scoffoni et al. 2008; Sellin, Unapuu & Kupper 2008; Welp et al. 2008; Domec et al. 2009; Ferrio et al. 2009; Johnson et al. 2009a,b; Aasamaa & Söber 2010; Blackman, Brodribb & Jordan 2010; Offermann et al. 2011; Zhou et al. 2011). See Supporting Information Table S1 for details.


Mechanisms explaining observed variability in pathlength L

In agreement with our results, a consistent relationship between L and E has been observed across species (Kahmen et al. 2008, 2009), leaf ontogeny (Barnard et al. 2007) and in response to water status (Ripullone et al. 2008; Ferrio et al. 2009). The mechanisms underlying such relationship are still unclear, but it has been speculated that L may reflect changes in the hydraulic properties of the leaf mesophyll (Keitel et al. 2006; Ripullone et al. 2008; Ferrio et al. 2009; Zhou et al. 2011), which in turn are related with transpiration rates (Sack & Holbrook 2006).

According to theory (Farquhar & Lloyd 1993), an inverse relationship between mesophyll hydraulic conductance and L is expected, as its two components (l and k) are closely related to the same anatomical traits and changes in the water pathway that determine hydraulic resistance (Sack & Frole 2006; Sack & Holbrook 2006; Brodribb et al. 2007; Cochard et al. 2007). Both drought and vein-severing treatments were expected to limit water flow inside the leaf mesophyll, presumably through accumulated embolism (Hüve et al. 2002; Johnson et al. 2009b). Besides the magnitude of water restriction (much higher in the vein-severing treatment), the two treatments differ in the origin of the stress signals: in addition to turgor changes within the leaf, the drought treatment involves the input of a stress signal from the roots in the form of abscisic acid (ABA) (Davies, Tardieu & Trejo 1994). Stress signals such as ABA would enhance the response of aquaporins to turgor loss (Morillon & Chrispeels 2001; Kim & Steudle 2007; Mahdieh et al. 2008), and this in turn would affect both gm and Kleaf (Flexas et al. 2002; Sack & Holbrook 2006; Cochard et al. 2007), and presumably L. This may explain why the response of the three mesophyll variables (gm, Klamina and L) was stronger in leaf-severing treatments (see Table 4). In both cases, however, we would expect an increase in water compartmentalization, which may cause partial uncoupling between evaporation sites and mesophyll water (Yakir 1992b; Yakir et al. 1993), forcing a more tortuous water pathway from the xylem to the sites of evaporation. In our case, however, we did not find significant changes in molar leaf water concentration and thus this effect alone cannot be responsible for the apparent increase in L observed in water-stressed plants. Neglecting changes in water content, a reduction in cell membrane permeability appears as the most likely cause for the observed changes in L. With lower cell membrane permeability, the cell-to-cell flow is restricted, and water flow takes place through the tortuous apoplastic pathway, altogether resulting in higher effective L (Ferrio et al. 2009; Zhou et al. 2011).

The relationship between pathlength L and mesophyll conductance to CO2

Both Klamina and gm show fast responses to environmental conditions, often uncoupled from stomatal responses, and at least partly mediated by aquaporins (Flexas et al. 2002; Sack & Holbrook 2006; Cochard et al. 2007). In the present study, where changes in Klamina were forced by means of drought imposition and/or leaf vein severing, gm generally mimicked the variations in both L and Klamina, suggesting a common effect of aquaporin regulation in the three variables. Our results showed that the linear relationship between gm and both Klamina and L is only valid for values of gm < 200 mmol COm−2 s−1: above this range, apparent variations in gm occur while L remains, nearly without changes, in its lowest range. This is likely to be at least in part a consequence of the assumptions required to perform gm calculations using the method developed by Harley et al. (1992). With this method, calculation uncertainties increase with larger gm values (Harley et al. 1992; Pons et al. 2009). Despite the negative relationship observed here between Klamina and gm and the negative relationship between L and gm, recent studies have shown that even though both leaf hydraulics and CO2 diffusion respond to changes in aquaporin activity, different combinations of aquaporin subunits in aquaporin tetramers may promote either water or CO2 transport, or both, depending on the proportion of PIP1 or PIP2 aquaporins (Otto et al. 2010). Thus, although mesophyll conductance for water and CO2 appeared to respond concomitantly in our study, an uncoupling between water and CO2 pathways is likely to occur in response to other environmental variables, for example, light (Kodama et al., unpublished results). On the other hand, the stronger relationship between L and gm than with gs or E further confirms that there is a direct relationship between mesophyll properties and L, rather than an indirect, artefactual relationship associated with the parametrization method, which included E (and to a lesser extent, gs) as input variables (see Fig. 1).

Pathlength L response to environmental variables: a matter of scale?

Previous attempts to assess the response of L to environmental conditions have given contrasting results. Ripullone et al. (2008) showed only a weak but still significant relationship between L and atmospheric vapour pressure deficit (VPD) in cotton plants, while Ferrio et al. (2009) found a threefold increase in L from control to drought plants in beech seedlings, in agreement with our results in grapevine. Similarly, Zhou et al. (2011) interpreted divergences from the theoretical response of ΔL to changes in temperature as a consequence of changes in L. In the first study trying to test the assumption that variations in L were reflecting changes in leaf hydraulic resistance, Kahmen et al. (2009) did not find significant differences between humidity treatments for either L or Kleaf. In addition, although they observed significant differences among species in both parameters, they were not correlated, concluding that L was a species-specific constant parameter. This contrasts with our results, showing not only a strong variation in L, but also a good agreement with leaf and lamina Kleaf (see Fig. 1). Such divergent results may indicate that species with little response in terms of Kleaf and strong variations in leaf water content also show little effects on L, whereas more isohydric species, such as beech or grapevine, show greater variations in both parameters. Thus, the magnitude of L response to environmental changes may depend on the species, but the different treatments applied may also play a role. The works from Ripullone et al. (2008) and Kahmen et al. (2009) show relatively small (if any) response of L to changes in relative humidity. Other studies, although not focused on determining L changes, suggest little response of this parameter to changes in relative humidity (Barbour & Farquhar 2000; Gan et al. 2003; Barbour et al. 2004). At least for some species, the main response to changes in relative humidity takes place in the epidermis, leading to local stomatal closure but with little effect on the whole leaf water relations (Mott 2007). In such cases, the effect of increasing leaf temperature due to stomatal closure is likely to be much higher than the changes in water pathways and thus L variations can be neglected. In contrast, water stress generally induces not only stomatal response but also aquaporin-mediated changes in Kleaf (Costa e Silva et al. 2004; Johnson et al. 2009b), which in turn affect L. Similarly, a stronger response to plant water availability than to water vapour deficit has been reported for gm (Flexas et al. 2004, 2008), further supporting the role of aquaporin-mediated responses in the differential response of L to water availability and humidity.

Alternatively, it may be argued that non-steady-state effects are behind observed deviations under drought stress, due to changes over time in both water concentration and isotopic composition of leaf water (Farquhar & Cernusak 2005). However, in our case, changes in volumetric water content (Vm) were negligible, and the rate of variation in ΔL was generally small, resulting in little deviations between steady-state and non-steady-state estimates for effective pathlength (see Fig. 3). In addition, we observed in most cases a weak sensitivity to varying the rate of change in ‘isostorage’ (VmΔLnss), as shown by the small variations in Lnss estimates along the 95% confidence interval for this value (Fig. 3c). This finding indicates that leaf water enrichment was relatively insensitive to non-steady-state effects in most of the samples. Indeed, the only exceptions were the four samples with extremely low E and gs that were originally flagged as outliers (see Table 2), suggesting that they were well beyond steady-state conditions. Altogether, our data exemplify how the risk of potential deviations due to non-steady-state conditions can be detected a priori based on gas exchange variables, and can be further confirmed by applying a rather simple sensitive analysis to changes in isostorage: the greater the deviations obtained, the higher the risk associated with the steady-state assumption. This procedure might not be extensible to all species and growing conditions, but is likely to be suitable for isohydric species, such as grapevine.

Interspecific trends in L and Kleaf

To assess the general validity of our findings, we plotted the data from this work together with that of Kahmen et al. (2009) and a survey of independent data on L and Kleaf, resulting in a consistent relationship across a broad range of species (Fig. 4). Although comparing Kleaf among species with contrasting leaf anatomy (including presumable differences in petiol conductance) introduces an additional source of error, the data confirm that species with low Kleaf tend to show higher L, and that this trend is consistent in most cases when comparing similar growing conditions for the same or closely related species. Interestingly, monocots showed a distinct relationship between Kleaf and L. In long leaves, the radial effective pathlength, as calculated here, is complicated by longitudinal Péclet effects causing an enrichment in xylem water along the leaf xylem (Helliker & Ehleringer 2000; Farquhar & Gan 2003; Kodama et al. 2011).

Overall, the observed trends in our experiment appear to be extensible to most species, confirming the theoretical relationship between L and mesophyll hydraulic resistance (Cuntz et al. 2007). These results suggest that L variations can be potentially used as a faster surrogate to determine changes in Klamina, which is of practical importance due to the time-consuming measurements of hydraulic conductance. Although determining water isotopes in plant tissues is destructive, and requires a costly and time-consuming procedure for water distillation, it is also possible to determine, in a non-destructive way, leaf water enrichment from the analysis of the isotope composition of oxygen in respired CO2 (Farquhar et al. 1993; Wang et al. 1998; Seibt et al. 2006), and this is becoming easier due to recent advances in laser spectroscopy (Barbour et al. 2007).

Concluding remarks

As hypothesized, L was more consistently related to mesophyll variables, such as K or gm, than to other variables that are included as input parameters for the models, such as E or gs. Indeed, the strongest correlation across treatment averages was found between Lss and Klamina, the latter being the closest estimate available for leaf mesophyll conductivity. Thus, L variations can be potentially used as a faster surrogate to determine changes in Klamina. Moreover, the strong correlation found between L and gm largely supports the idea that water and CO2 share an important part of their respective diffusion pathways through the mesophyll, so that any down-regulation of leaf hydraulics may result not only in reduced gs but also in reduced gm, both contributing to reduced photosynthesis. Further research including simultaneous measurements of leaf water enrichment, Klamina and aquaporin activity in response to environmental conditions, may offer not only new avenues to understand leaf water enrichment, but also for the study of short-term changes in leaf hydraulics.


We thank Alex Gallé, Magdalena Tomàs and Sebastià Martorell for their assistance during measurements; Hugo Moragues for providing meteorological data; and Rolf Siegwolf and Matthias Saurer for the water distillation facility. We also thank Lawren Sack, Ansgar Kahmen and Graham Farquhar for their useful comments. This work was funded by the Marie Curie projects MC-IEF-039418 (FP6) and MC-ERG-246725 (FP7), and Spanish projects BFU2008-01072 (MEFORE) and CGL2009-13079-C02-01 (PALEOISOTREE). A.P. and I.F-S. were supported by FPI fellowships (MCINN, Spain). J.P.F. is supported by the Ramón y Cajal programme (RYC-2008-02050). A.G. acknowledges support by the DFG.