Leaf Maximum Photosynthetic Rate and Venation Are Linked by Hydraulics

Hydraulic and Photosynthetic Capacity

Across the diverse range of land plant diversity sampled, an intimate association between light-saturated net CO₂ assimilation rate (A_max) and the hydraulic conductance (K_leaf) of whole leaves was found (Fig. 1A ). A single regression accurately described the dependence of A_max upon K_leaf in all 43 species, including mosses, ferns, lycopods, gymnosperms, and angiosperms. At values of K_leaf < 10 mmol m⁻² s⁻¹ MPa⁻¹ mean A_max was highly sensitive to increasing K_leaf, but this sensitivity decreased as A_max in the tropical angiosperm species approached the upper limits for C3 photosynthesis in woody plants (Larcher, 1995; Santiago et al., 2004). It should be pointed out that according to protocol, K_leaf was normalized at a temperature of 20°C, however, the mean leaf temperature at A_max was 26°C. Due to the effects of viscosity, K_leaf would be 15% higher at the mean temperature at which A_max was measured.

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Figure 1.

A, K_leaf versus A_max in leaves of bryophytes (black), lycopods (white), ferns (green), conifers (red), angiosperms (blue), and gymnosperms with lignified sclereids in the mesophyll (brown). A highly significant quadratic regression (y = 0.259x² + 1.41x − 0.60; r² = 0.94; P < 0.001) indicates a strong linkage between A_max and efficiency of hydraulic supply (data for 16 of the 43 species are from Brodribb and Holbrook, 2006). Symbols denote means with ses (n = 12). B, D_m from the end of the vein xylem to the gas-exchange epidermis plotted against 1/K_leaf. Means for both parameters are shown for single-vein (white circles) and multivein (red triangles) leaves plotted together, excluding the species with lignified sclereids in the mesophyll. A linear regression (r² = 0.95; P < 0.001) is fitted to all data (y = 0.0005x − 0.031). To improve resolution, the two species with D_m > 1,400 μm (Hymenophyton and Tmesipteris) are offscale, but these species did not deviate from the overall trend (see Fig. 1C). C, Raw data showing D_m from the end of the vein xylem to the gas-exchange epidermis plotted against K_leaf (color legend identical to Fig. 1A). Both axes are on a log scale to compress the enormous range in D_m observed in our species sample. Two regression equations are shown, first the same function as fitted in Figure 1B (dotted line), and second an exponential function (y = 12,674x^−1.26; r² = 0.97). Species with lignified mesophyll sclereids are circled and again not included in the regressions.

Anatomical Determinants of Leaf Hydraulics

Leaf vein architecture and xylem anatomy was extremely diverse in our species sample (Supplemental Table S1), yet the response of K_leaf to mean maximum mesophyll path length (D_m) fell into two distinct groups. In the larger group (34 out of 43 species), a single highly significant regression (r² = 0.97; P < 0.001) described the relationship between 1/K_leaf and D_m (Fig. 1B). Regressions fitted independently to each phylogenetic category (mosses, ferns, conifers, and angiosperms) within this group were all highly significant and not different to the regression for the pooled data set. Also, we did not find any significant differences between regressions based upon grouping species as single-vein or multivein leaves (Fig. 1B). The second group of species (circled in Fig. 1C) demonstrated a very different association between D_m and K_leaf. These species included conifers and cycads that were specifically selected because they possessed specialized conductive tissue (accessory transfusion tissue; Griffith, 1957; Hu and Yao, 1981) interspersed throughout the mesophyll (Fig. 2, E and F ). These species all exhibited much higher K_leaf than the main sample group at similar D_m (Fig. 1C).

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Figure 2.

A, Leaf cross section from the angiosperm Curatela americana with red arrows showing what was measured as the y dimension in leaves, i.e. the distance from the veins (highlighted in red) to the stomatal (gas-exchange) epidermis. B, Paradermal view of a cleared and stained (toluidine blue) leaf of the angiosperm Byrsonima crassifolia identifying the center of the areole as the furthest equidistant point from surrounding veins (defined as the x dimension in the leaf). C, Cross section of a moss leaf, Dawsonia superba, showing D_m as the maximum distance from the vein (nerve) to the gas-exchange surface at the leaf margin. D, Paradermal view of a cleared and stained leaf of Tsuga canadiensis showing how the x dimension in single-vein leaves was measured from the vein to the edge of the stomata. E and F, Visualization of the post-venous hydraulic flow path in two species with water-conducting sclereids. E, Cross section of a leaf of the conifer Podocarpus dispermis showing how water-conducting sclereids (stained blue) facilitate water flow (shown by red arrows) from the midrib (V) to the stomata (black asterisks). F, Similarly in a conifer needle from Sciadopitys verticillata, star-shaped sclereids act as a hydraulic shortcut through the mesophyll tissue.

In single-vein leaves, D_m was the product of both the thickness (vein to epidermis) and width (vein to stomata) of leaves (Fig. 2, C and D), while in multivein leaves the vein density and leaf thickness (vein to epidermis) combined to determine the D_m (Fig. 2, A and B). Species mean K_leaf was extremely sensitive to D_m (excepting gymnosperms with leaf sclereids). Increasing D_m led to a decline in K_leaf proportional to D_m^−1.2 (Fig. 1C). The slope of this relationship was slightly higher than that proportionality expected (D_m⁻¹) if path length was independently controlling K_leaf, i.e. if the resistance to hydraulic flow through the leaf was uniquely controlled by the length of the mesophyll pathway. However, for gymnosperms that possessed lignified accessory transfusion tissues in the leaf mesophyll, there was only weak correlation within this group between K_leaf and D_m. Typically the K_leaf values of these gymnosperms were nearly an order of magnitude higher than other species with equivalent D_m (Fig. 1C).

Vein Density, Leaf Width, and Photosynthesis

Combining the observed relationships between D_m, K_leaf, and A_max enabled us to model how the width of single-veined leaves influences leaf photosynthetic capacity (Fig. 3 ). Among single-veined species, only those with narrow scale or needle leaves were able to attain high photosynthetic rates characteristic of sun-adapted species (Fig. 3A), while broader leaves were associated with low photosynthetic rates (and typically shady, low evaporative demand environments). A similar analysis on multiveined leaves illustrates the impact of vein density on K_leaf and A_max (Fig. 3B). With leaf thickness held constant it would be expected that A_max should respond positively to increasing vein density, with a gradual plateau in slope as vein density reached the upper limits for our angiosperm sample (15.8 mm mm⁻²). It should be noted that vein density was not found to be strongly correlated with either K_leaf or A_max in our sample of multivein leaves presumably due to the large range of vein-epidermal thickness in this morphologically diverse species sample (T.J. Brodribb, unpublished data). This is understandable viewed in the context of Figure 3B showing that the modeled effect of increasing leaf thickness was to reduce the impact of vein density upon A_max. In our sample of multiveined leaves, we found little overlap between the vein density of ferns and the higher vein density in angiosperms (Fig. 3B).

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Figure 3.

Modeled relationships showing the impact of leaf width and vein density on assimilation. A, A hydraulic model based on the relationships in Figure 1, A and C shows how in single-vein leaves the sensitivity of A_max to leaf width increases as leaves become narrower. As a result, high assimilation rates can only be achieved in species where the maximum distance from the vein to stomata is less than a few hundred microns. Approximate positions of five representative species are shown. B, The impact of vein density on A_max in leaves using the same hydraulic model as above. The leaf thicknesses from vein to epidermis (y dimension in the leaf) of 70, 100, and 130 μm were used, and arrows indicate the effect of changing the y axis thickness. The range of vein densities in our sample is indicated by bars on the abscissa.

Mechanisms of Coordination between Vein Location, Hydraulics, and Productivity

Previously it has been suggested that vein density was related to photosynthetic function because the vein surface area is thought to limit photosynthate transport away from the leaf (Amiard et al., 2005). Here we demonstrate strong evidence that the relationship between vein placement and leaf productivity is determined by the flow of water through the mesophyll. The mechanisms that culminate in leaf vein arrangement functioning as a governor of both water flow and leaf productivity are 2-fold. Primarily there is the physical control of leaf hydraulic conductance by the length of post-venous hydraulic pathway (from the vein end to the site of evaporation) traversed by the transpiration stream. This links secondarily to leaf productivity because of the strong coordination between K_leaf and A_max (Fig. 1A).

The first of these two processes is explained by the fact that water flow through the leaf is analogous to current flow in an electrical circuit (Cowan, 1972; Sack and Holbrook, 2006). In its passage through the leaf, water must move from the highly conductive medium of the leaf veins into the highly resistive medium of the living mesophyll before it escapes the leaf via stomata. According to the electrical analog, the hydraulic conductance of this low-conductivity mesophyll pathway should be inversely proportional to the path length (Fig. 1B). The length of this pathway is likely to strongly influence the total hydraulic conductance of the leaf because the hydraulic conductivity of living cells in the plant is very low relative to xylem cells (Boyer, 1985; Passioura, 1988; Frensch and Steudle, 1989), leading to a high proportion of extravascular resistance in the leaf (Nardini and Salleo, 2005; Sack et al., 2005). Indeed, we found that the length of this ultimate hydraulic traverse represents a unifying limit to the hydraulic efficiency of leaves (Fig. 1B). Variation between species in the density of leaf veins and leaf thickness leads to considerable diversity in D_m, and in our sample we recorded a range from 90 μm in the tropical angiosperm Curatela americana to 2,200 μm in the single-vein fern Tmesipteris obliqua. The corresponding range of K_leaf expressed by these species varied over 20-fold.

The second mechanism that coordinates leaf vein arrangement and leaf photosynthetic potential is the tendency for the leaves of terrestrial C₃ plants to produce a conservative CO₂/water exchange ratio (Cowan and Farquhar, 1977; Franks and Farquhar, 1999). As a result, the capacity for water delivery to the photosynthetic tissue corresponds with the photosynthetic capacity of the leaf (Brodribb et al., 2005). Here we established that hydraulic mediation of A_max appears to be a uniform feature of all major terrestrial plant groups (Fig. 1, A and B).

Leaf Dimensions, Vein Density, and CO₂ Assimilation

High CO₂ assimilation rates in plants where water is supplied to leaves through internal conducting cells should, according to our data, be associated with either very narrow leaves (in the case of single-vein leaves), or high vein densities (Fig. 3). However, the impact of leaf thickness on K_leaf and A_max is likely to be more complicated due to the interaction of palisade thickness and the proximity of the vein to the stomatal surface of the leaf. We found here that increasing the vertical distance from the vein to the stomatal epidermis should reduce hydraulic and photosynthetic performance (Fig. 3B), but other studies have shown positive correlations between leaf and palisade thickness and K_leaf (Aasamaa et al., 2001; Sack et al., 2003; Sack and Frole, 2006). These observations are entirely compatible because the palisade tissue is rather hydraulically isolated from the bulk of the transpiration stream (Zwieniecki et al., 2007). As a result, relationships between palisade mesophyll thickness, A_max (Terashima et al., 2001), and K_leaf can exist while K_leaf remains fundamentally controlled by the position of the vein relative to the stomatal epidermis (the vein-to-epidermal thickness shown in Fig. 3B). The distinction between leaf thickness and vein-to-epidermal thickness is important, only the latter is expected to unequivocally influence K_leaf according to our hypothesis.

An Alternative to Vein Branching

A fundamental implication of the relationship shown here between K_leaf and vein proximity (Fig. 1B) is that the hydraulic conductivity of the cell matrix comprising the mesophyll tissue of the leaf is consistently low among terrestrial plants. While it is likely that there is variation between species in the hydraulic conductivity of leaf tissue due to cell anatomy and packing (possibly contributing to the variability in the angiosperm data and the fact that K_leaf was not exactly related to D_m⁻¹), this was outweighed by the influence of path length on the hydraulic conductance of the mesophyll pathway. However, many gymnosperms possess obvious modifications to the mesophyll tissue apparently used to increase the post-venous hydraulic conductivity of their leaves. These plants have water-filled lignified cells (Fig. 2, E and F) that are highly pitted and generally elongated in the plane of water movement from the vein to the leaf margin (Brodribb and Holbrook, 2005). The function of these cells is analogous to the tracheids of the xylem, effectively providing a large apoplastic volume and pits by which water moving toward to stomata can bypass the much slower passage through living mesophyll cells. The effectiveness of this adaptation is clearly evident in enabling single-vein leaves to achieve leaf widths that are orders of magnitude wider than predicted if they possessed unmodified mesophyll (Fig. 1B).

Implications for Leaf Evolution

The presence of highly pitted lignified tissue in the mesophyll of gymnosperms leaves has been formally noted in the conifer family Podocarpaceae and the cycad genus Cycas (Griffith, 1957; Hu and Yao, 1981). We found that similar tissues are present in conifers from all families including Sciadopitys and Amentotaxus (T. Brodribb, unpublished data) and in each case they were associated with leaf widths in excess of those achievable with unmodified mesophyll tissue (Fig. 1B). Indeed it appears that terrestrial plants have adopted two different systems to overcome the intrinsically low hydraulic conductivity of the leaf mesophyll. The most common of these is to branch the vein system such that a high volume apoplastic flow pathway (the xylem) is allowed to approach very close to the sites of evaporation. This is the means of water distribution in most angiosperm leaves. The second system, identified here, is to modify the mesophyll by directing the lignification and apoptosis (Griffith, 1957) of a proportion of mesophyll cells, thereby greatly increasing its conductivity to water. This fascinating divergence in leaf water distribution systems appears to have arisen in the gymnosperm clade, as there have been no reports of lignified mesophyll cells in any plant groups basal to gymnosperms.

Plant Material

Measurements of maximum photosynthetic rate, leaf hydraulic conductance, and leaf anatomy were carried out on 43 C₃ species carefully selected to represent the breadth of land plant evolutionary diversity (Table I ). A mixture of tropical and temperate species were sampled primarily from their natural habitats and included representatives from three major phylogenetic categories (angiosperms, gymnosperms, and ferns), while mosses and lycopods were collected only from temperate regions. Species were chosen to represent the range of vein architecture within major groups. Our sampling included eight species of gymnosperms known to possess lignified transfusion tissue or sclereids in the mesophyll (Griffith, 1957; Hu and Yao, 1981). These structures greatly increase the apoplastic volume of the leaf mesophyll and were expected to result in different leaf hydraulic properties as compared with those species that lack such modifications. Where possible, measurements were made on leaves in open habitats or forest gaps so as to avoid complications due to variable light induction of hydraulic conductance and photosynthesis (Pearcy, 1990; Cochard et al., 2007).

Leaf Photosynthetic and Hydraulic Capacity

K_leaf was measured on excised leaves allowed to reach a transpirational steady state while attached to a flowmeter measuring the transpirational flux (Sack et al., 2002; Brodribb and Holbrook, 2006). Leaves were excised under water at 9 am to 10 am and measurements were made between 9 am and 12 pm when transpiration rates were maximal with leaves maintained under natural sun or a halide lamp delivering 1,500 μmol quanta m⁻² s⁻¹. After 3 to 5 min at steady state (less than 10% variation over 180 s), leaves were removed and water potential measured with a pressure chamber (PMS). Leaf temperature was monitored by two thermocouples pressed against the abaxial surface of the leaf, and leaf temperature was maintained between 20°C and 24°C by directing a stream of air (heated if necessary) uniformly across the leaf blade. This small temperature range was sufficient to produce steady-state leaf water potentials spanning the range −0.2 to −0.8 MPa. The leaf hydraulic conductance was calculated as the ratio of transpirational flux to leaf water potential, and standardized to the viscosity of water at 20°C using an empirical function based on data from Korson et al. (1969). Between 10 and 30 leaves from five individuals of each species were measured and the maximum hydraulic conductance for each species calculated as the y intercept of a plot of water potential versus hydraulic conductance (Brodribb and Holbrook, 2006).

A_max was measured on 10 healthy, mature leaves of each species using a portable gas analyzer (Li-COR 6400) to quantify CO₂ uptake under conditions of saturating light and water availability. All species were measured on plants in the field under conditions of high soil water availability. During all measurements a high flow rate (500 mL min⁻¹) through the cuvette was maintained such that conditions in the cuvette approximated ambient temperature, vapor-pressure difference, and CO₂ (which ranged from 364–375 μmol mol⁻¹). The resultant temperature in the leaf chamber remained between 25°C and 33°C and the leaf to air vapor pressure deficit was less than 2 kPa. Leaves were measured from the same plants used for hydraulic measurements, and all measurements were carried out between 8 am and 11 am when CO₂ uptake was maximal. Light intensities of either 1,800 or 1,000 μmol quanta m⁻¹ s⁻¹ were used depending on the saturating photosynthetic photon flux density of the species (as determined by a light response curve made on one individual per species); the lower photosynthetic photon flux density was used in species with low A_max to avoid oversaturation with light.

Leaf Anatomy

The xylem pathway through the leaf mesophyll was quantified by measuring the linear path length from the minor veins to stomata and then calculating the hydraulic path length assuming water moved in the cell apoplast, and that mesophyll cells were uniform capsules of known aspect ratio (measured for each species). Multiple measurements were made on each leaf by dividing leaves into grids of either 200 × 200 μm or 500 × 500 μm depending on leaf thickness and vein density. For each grid cell the maximum distance between neighboring veins and between the vein and the epidermis was recorded. Maximum rather than mean distance was used because it was easily measured and scales with average distance if stomata are distributed relatively homogenously across the leaf. Calculation of a mean (maximum) linear mesophyll path length for each leaf required measurements to be made along two axes; first, the lateral distances between veins were measured (termed the x axis; Fig. 2B) and second, the perpendicular distance from the vein to the epidermis (termed the y axis; Fig. 2A). A mean value for maximum x and y distance was calculated from 30 to 40 subsamples per leaf in each of three to four leaves previously sampled for K_leaf. Paradermal sections were used to visualize the x axis distance between adjacent minor veins, or to the most distant adjacent stomata for single-vein leaves (Fig. 2, B and D), and cross sections allowed determination of the y axis distance from the vein endings to the stomatal gas exchange epidermis (Fig. 2A). Randomly spaced windows in the epidermis were cut with a razor, and then cleared in 1 m KOH. After clearing, veins were stained with toluidine blue to highlight xylem lignin. In the case of bryophytes and some conifers, sulforhodamine-B was infused into the xylem of transpiring leaves and leaves viewed using a fluorescence microscope (Axiophot, Carl Zeiss) to clearly visualize the water-conducting tissue. Thirty images of vein architecture under 10× magnification were captured from three leaves of each species using a digital camera attached to a compound microscope and the largest distance between adjacent veins measured in all veins. In the case of single-vein leaves or parallel venation, measurements were made using a digital ruler in Image-J (National Institutes of Health, available online). In leaves with reticulate venation, the center of the areole was found by tracing the veins in each field of view in Image-J and increasing the pen size until no white space remained in the areole. The last point of white space remaining was the center of the areole, and this maximum pen size was converted back to a linear distance.

Vertical (y axis) distance from the vein to the epidermis was measured from leaf sections cut from the same leaves used for leaf clearing. Ten sections from three to four leaves per species were cut and stained with toluidine blue. Minor veins or vein endings were identified by their distinctive morphology (paradermal sections allowed clear identification of the types of tracheids that characterized vein endings, typically thin-walled large lumen cells) and these were photographed. Ten images of leaf cross sections were used to measure the distance from the vein xylem to the gas-exchange epidermis (the stomata-bearing surface in tracheophytes and the abaxial leaf surface in bryophytes). Only one amphistomatic leaf was included in our sample (Eucalyptus globulus) and in this species leaves were isobilateral, so measurements were made equally on both sides of the leaf. Cross-section images were also used to measure the dimensions of mesophyll cells along the same two axes described above. A sample of 100 cells located between the vein and the site of evaporation were measured for x and y dimensions for each species.

We assumed that the majority of water flowed apoplastically in the mesophyll (Steudle, 1994), and that there was good contact between neighboring cells. Hence the hydraulic pathway from the vein to epidermis was simplified to the shortest route around the perimeter of rounded mesophyll cells. Mesophyll cells were approximated as cylindrical capsules packed closely together such that water could flow directly from cell wall to cell wall. Because cells were typically elongated in one dimension, the distance through the mesophyll corresponding to the longer cell axis was calculated from the number of cells traversed multiplied by the cell length, plus the distance around the tips of the cells (assumed to have a radius of curvature defined by the minor axis of the cells). The mean distance traversed along the minor axis of cells was calculated from the number of cells traversed multiplied by the distance around half the cylindrical cell perimeter. Hence, if cells are elongated so C_x (mean cell x dimension) > C_y (mean cell y dimension) then X = v/C_x [(C_x − C_y) + π C_y/2] and Y = t/C_y (π C_y/2), where X is the horizontal apoplastic path length from the vein to stomata, v is the mean longest distance from veins to stomata, Y is the vertical apoplastic path length from the vein to stomata, and t is the mean leaf thickness from vein to stomata.

Finally, D_m was taken as the hypotenuse of a right-angled triangle produced by these x and y dimensions: D_m = √(X² + Y²).

In leaves where cells were elongated such that C_y > C_x (such as E. globulus), X and Y distances were calculated as follows: X = v/C_x(π C_x/2) and Y = t/C_y[(C_y − C_x) + π C_x/2].

Modeling the Impact of Leaf Morphology on A_max

The effects of leaf width and vein density on A_max were modeled by combining empirical relationships between K_leaf and A_max and D_m and K_leaf (regression equations from Fig. 1, A and C). Combining these two equations allowed A_max to be solved empirically as a function of D_m. In single-vein species the x dimension in leaves is equivalent to the leaf width (from vein to furthest adjacent stomata in single-vein leaves; Fig. 2D), hence the effect of leaf width on A_max was modeled while holding vein-epidermis thickness at a constant value of 70 μm and using a uniform cell aspect ratio of 1:1.4 (the mean value for all species). In multivein leaves it is the vein density that influences the x dimension in leaves (Fig. 2B); hence, we were able to model the effect of increasing vein density on A_max. Vein density was simplified to a square network and vein-epidermal thicknesses of 70, 100, and 130 μm were imposed. This range corresponded to the observed range in the angiosperm sample.

Statistical Analysis

Our a priori hypothesis was that K_leaf should be related to 1/D_m, so the logarithm of K_leaf was regressed on the logarithm of D_m, then tested to see if the slope was equal to −1. Regression analysis was used to test for variation in slopes and intercepts between single- and multiveined leaves, among major phylogenetic groups, and between species with and without sclereids in the mesophyll. All analyses except the latter excluded species with sclereids in the mesophyll. Model fitting for the regression between A_max and K_leaf was empirical and based on a polynomial best fit. All analyses were performed with SAS (SAS Institute).

Supplemental Data

The following materials are available in the online version of this article.

• Supplemental Table S1. Leaf anatomical parameters.