Bundle sheath leakiness and light limitation during C4 leaf and canopy CO2 uptake.

Perennial species with the C(4) pathway hold promise for biomass-based energy sources. We have explored the extent that CO(2) uptake of such species may be limited by light in a temperate climate. One energetic cost of the C(4) pathway is the leakiness () of bundle sheath tissues, whereby a variable proportion of the CO(2), concentrated in bundle sheath cells, retrodiffuses back to the mesophyll. In this study, we scale from leaf to canopy level of a Miscanthus crop (Miscanthus x giganteus hybrid) under field conditions and model the likely limitations to CO(2) fixation. At the leaf level, measurements of photosynthesis coupled to online carbon isotope discrimination showed that leaves within a 3.3-m canopy (leaf area index = 8.3) show a progressive increase in both carbon isotope discrimination and as light decreases. A similar increase was observed at the ecosystem scale when we used eddy covariance net ecosystem CO(2) fluxes, together with isotopic profiles, to partition photosynthetic and respiratory isotopic flux densities (isofluxes) and derive canopy carbon isotope discrimination as an integrated proxy for at the canopy level. Modeled values of canopy CO(2) fixation using leaf-level measurements of suggest that around 32% of potential photosynthetic carbon gain is lost due to light limitation, whereas using determined independently from isofluxes at the canopy level the reduction in canopy CO(2) uptake is estimated at 14%. Based on these results, we identify as an important limitation to CO(2) uptake of crops with the C(4) pathway.

Biomass production by perennial plant species can abate greenhouse gas emissions either by increased carbon sink activity and soil organic carbon sequestrations or by displacing fossil fuel emissions in the production of static energy (U.S. Department of Energy, 2006;Somerville, 2007). Perennial plant species with the C 4 photosynthetic pathway combine high productivity and resource use efficiency with low requirements for agronomic inputs; thus, they seem well equipped for biomass-based energy production (Lobell et al., 2008). For instance, Miscanthus (Miscanthus 3 giganteus hybrid) is a perennial C 4 grass with a recorded annual dry matter production up to 4 kg m 22 (Heaton et al., 2004a(Heaton et al., , 2004b.
Thus, attributes of the C 4 pathway (potentially high productivity coupled with high nitrogen and water use efficiencies; Sage, 2004) can be coupled to the carbon sequestration potential of a rhizomatous perennial (Hansen et al., 2004;Clifton-Brown et al., 2007). Miscanthus has higher productivity than switchgrass (Panicum virgatum; Heaton et al., 2004a) and has sufficient cold tolerance (Beale et al., 1996;Naidu et al., 2003;Wang et al., 2008aWang et al., , 2008b for cultivation in temperate climatic conditions. However, we hypothesized that growth at low temperatures and low light in a temperate climate may reduce the conversion efficiencies of such a crop, and we set out to explore the specific limitations that may occur due to shading in a crop with a high leaf area index. Our study focused on the leakiness (f) of bundle sheath (BS) cells to CO 2 as a potential bottleneck in the photosynthetic performance of a Miscanthus canopy. The carbon-concentrating mechanism inherent to the C 4 pathway relies on spatial separation of carboxylases between mesophyll (M) cells (phosphoenolpyruvate carboxylase) and BS cells (Rubisco). Decarboxylation of organic acids within the BS generates high CO 2 concentrations adjacent to Rubisco, thereby suppressing oxygenase activity, but some of this CO 2 retrodiffuses and is refixed within the M cells. Such ''leakage'' in the system occurs through the BS cell walls, facilitated by the symplastic connections between M and BS, which are required for metabolite exchanges. Estimates for BS f at the leaf level range between 10% and 40% (Osmond and Smith, 1976;Farquhar, 1983;Henderson et al., 1992;Hatch et al., 1995;Fravolini et al., 2002;Cousins et al., 2006Cousins et al., , 2008Tazoe et al., 2006Tazoe et al., , 2008Kubasek et al., 2007). External factors associated with increasing f are low temperature (Henderson et al., 1992;Kubasek et al., 2007), water stress (Farquhar, 1983;Bowman et al., 1989;Buchmann et al., 1996), low nitrogen nutrition (Meinzer and Zhu, 1998), and, most markedly, low light (Henderson et al., 1992;Buchmann et al., 1996;Cousins et al., 2006Cousins et al., , 2008Tazoe et al., 2006Tazoe et al., , 2008Kubasek et al., 2007).
The loss of C 4 efficiency under low photon flux density (PFD) was recently quantified in a series of laboratory measurements and theoretical modeling studies (Von Caemmerer, 2000;Cousins et al., 2006Cousins et al., , 2008Tazoe et al., 2006Tazoe et al., , 2008 using real-time carbon isotope discrimination (D 13 C). However, it is not clear if the increase in f results initially from light limitation of Rubisco activity, relative to phosphoenolpyruvate carboxylase activity, or increased Rubisco oxygenase and photorespiratory costs, or the ATP requirement for phosphoenolpyruvate regeneration (Von Caemmerer and Furbank, 2003), and whether this phenomenon occurs transiently or permanently following the transfer from high-light to low-light conditions.
In this study, we set out to quantify the extent of f during gas exchange at leaf and canopy scale for a 13-year-old Miscanthus stand at Teagasc Oak Park (Carlow, Ireland). Short-term field measurements of gas exchange and D 13 C at leaf level were used to compute f and the corresponding loss of carbon assimilation under field conditions using the model for C 4 photosynthesis by Von Caemmerer and Furbank (1999) and Von Caemmerer (2000). In parallel, canopy isotopic flux densities, or ''isofluxes'' (CO 2 flux multiplied by isotopic signature), were constructed using eddy covariance data combined with [CO 2 ] and d 13 C (carbon isotope composition relative to Vienna Pee Dee Belemnite standard) diurnal vertical profile measurements within the canopy and used to derive canopy D 13 C and f values. We infer that while the effect of f is higher at leaf level when measured in a well-coupled cuvette, potential carbon uptake is still significantly reduced by f when assessed at the canopy scale. We conclude that leakage represents a considerable constraint on C 4 productivity, particularly in temperate climates, which is especially significant when the current and future importance of the C 4 pathway for food production (e.g. maize [Zea mays], sorghum [Sorghum bicolor], sugarcane [Saccharum officinarum]) and bioenergy production and CO 2 mitigation (Miscanthus, switchgrass) is taken into account.

Canopy Development
In Figure 1, we show the vertical distribution of leaf area through the canopy. The total leaf area index for the canopy was 8.3 6 0.51 m 2 m 22 . A large proportion of this leaf area (2.8 6 0.54 m 2 m 22 ) was located between 2 and 3 m height, with a smaller proportion (1.4 6 0.49 m 2 m 22 ) located between 1 and 2 m. The section between 0 and 1 m also had a substantial fraction of the total leaf area (3.2 6 0.80 m 2 m 22 ).

Potential Rate of Photosynthesis
In Figure 2, photosynthetic CO 2 uptake is depicted by electron transport capacity (J; determined using chlorophyll fluorescence; Fig. 2A) and CO 2 response (determined from gas exchange; Fig. 2B) as a function of height within the canopy. Due to the CO 2 -concentrating mechanism of C 4 photosynthesis, light saturation of J (maximum electron transport capacity; J max ) typically occurred only at very high levels of PFD. At 3 m, J max reached 142.4 6 20.5 mequiv m 22 s 21 at PFD of 1,769 6 42 mmol quanta m 22 s 21 , whereas at 2.5 m, J max was 104.1 6 8.7 mequiv m 22 s 21 at PFD of 1,834 6 41 mmol quanta m 22 s 21 . At 2 m, J max and saturating PFD were lower (54.8 6 13.1 mequiv m 22 s 21 at 1,205 6 21.5 mmol quanta m 22 s 21 ), and they were even lower at 1.5 m (26.6 6 9.1 mequiv m 22 s 21 at 919 6 41.6 mmol quanta m 22 s 21 ). At 1 m, J max and saturating PFD were lowest (7.5 6 1.8 mequiv m 22 s 21 at 553 6 64.0 mmol quanta m 22 s 21 ), and there was very little response of J to light intensity. Mitochondrial (dark) respiration was also measured following 5 min in the dark, and averages yielded 0.89 6 0.29 mmol m 22 s 21 for leaves at 3-m height, 0.71 6 0.36 mmol m 22 s 21 for leaves at 2-m height, and 0.40 6 0.25 mmol m 22 s 21 for leaves at 1-m height.
While J max at 2.5 and 2 m was reduced to 73% and 38% of values at 3 m, maximum photosynthetic capacity (A max ; Fig. 2B) values at 2.5 and 2 m were 113% and 74% of those at 3 m. Similarly, carboxylation efficiency (CE), calculated from the initial slopes of the CO 2 response curves (Fig. 2B), was 0.13 mmol CO 2 m 22 s 21 mol mmol 21 at 3 m, 0.15 at 2.5 m, and 0.08 at 2 m. Below 2 m, CE decreased sharply to 0.04 at 1.5 m and 0.007 at 1 m, with a clear separation in CO 2 response between lower and  higher leaf cohorts. Thus, whereas the light response of J had acclimated to a markedly lower capacity above 2 m, the transition in the decline of A max and carboxylation efficiency occurred lower in the canopy.

Realized Rate of Photosynthesis
Vertical profiles of net CO 2 assimilation (A n ; Fig. 3, A-E), transpiration (E; Fig. 3, F-J), and stomatal conductance (g s ; Fig. 3, K-O), measured in situ on leaves throughout the canopy, are shown as a function of incident PFD. The observations reflected a steep light gradient within the canopy, with incident PFD below 2.5 m seldom higher than 50 mmol quanta m 22 s 21 . High in the canopy at 3 m, A n frequently was light saturated (10-12 mmol CO 2 m 22 s 21 ; Fig. 3A). At 2.5 m, most CO 2 fixation (3-8 mmol CO 2 m 22 s 21 ) occurred at PFD lower than 500 mmol quanta m 22 s 21 (Fig. 3B). Leaves at 2 m ( Fig. 3C) were subject to very low light levels (0-75 mmol quanta m 22 s 21 ), but reasonable values of A n were still sustained (0-7 mmol CO 2 m 22 s 21 ). At 1 and 1.5 m, the colimitation of light intensity and photosynthetic capacity clearly reduced A n (0-2 mmol CO 2 m 22 s 21 ; Fig. 3, D and E).
At 2.5 and 3 m, g s ranged between 0.05 and 0.15 mol m 22 s 21 (Fig. 3, K and L), with generally higher conductances at 3 m than at 2.5 m for comparable light levels, which correspondingly led to higher rates of water loss in leaves at 3 m (Fig. 3, F and G). At 1 and 1.5 m, g s remained below 0.03 mol m 22 s 21 (Fig. 3, N and O), and it increased to just above 0.06 mol m 22 s 21 at 2 m (Fig. 3M), but only for light levels above 50 mmol quanta m 22 s 21 . Corresponding transpiration rates were less than 0.4 mmol water m 22 s 21 for leaves at 1 and 1.5 m (Fig. 3, I and J) and increased with light intensity to 1.5 mmol water m 22 s 21 at 2 m (Fig. 3H).
In conclusion, leaves at 2.5 and 3 m receive higher incident PFD than leaves at lower locations and con-sequently exhibit much higher in situ rates of CO 2 fixation and water loss than leaves at 1 and 1.5 m, while leaves at 2 m frequently achieve comparable assimilation and transpiration rates to leaves higher in the canopy.
Leaf D 13 C and f In Figure 4, we show the results for instantaneous D 13 C and corresponding ratios of intercellular CO 2 and ambient CO 2 partial pressures (p i /p a ) from gas exchange. Also, corresponding derived values of f are shown (derived from Eq. 3 below). D 13 C observations for individual leaves covered a wide range of values. D 13 C above 350 mmol quanta m 22 s 21 PFD showed some variation (Fig. 4A), ranging between 2.6& and 6.9&. At lower PFD, D 13 C measurements were much more variable, ranging from 0.5& (1.5 m) to 16.5& (1 m). There was also a wide range of p i /p a values derived from gas exchange during the isotopic determinations, ranging from 0.25 (high PFD, high in the canopy) to 0.8 (shaded leaves, low in the canopy). BS f to CO 2 , derived from p i /p a and D 13 C using Equation 3 below, showed a similar trend (Fig. 4C), with relatively lower values of f above 350 mmol quanta m 22 s 21 PFD higher in the canopy and a wide range of values below this threshold light intensity lower in the canopy. At higher light intensity, f was mostly between 0.2 and 0.5 for leaves at 3 m. Below 350 mmol quanta m 22 s 21 PFD, the range for f increased with values up to 0.8 (specifically found at 1 m and 48 mmol quanta m 22 s 21 ).
Canopy CO 2 Uptake, D 13 C, and f In Figure 5, we present eddy covariance flux measurements of ecosystem CO 2 exchange with corresponding levels of incident PFD as well as canopy D 13 C (derived with the eddy covariance-flask method, as described by Bowling et al. [2003]). Except for Figure 2. A, Electron transport rate (J) at different levels of incident PFD for leaves at 1-, 1.5-, 2-, 2.5-, and 3-m height. Error bars indicate 1 SD. B, Light-saturated photosynthetic assimilation rates at different leaf intercellular CO 2 concentrations for leaves at 1-, 1.5-, 2-, 2.5-, and 3-m height. Measurements were taken at 1,600 mmol m 22 s 21 PFD and 22°C, and vapor pressure deficit was kept below 1 kPa. measurements in the early morning and late afternoon, the canopy was thoroughly mixed and storage flux below the eddy covariance measurements was insignificant (determined by vertical profile measurements of CO 2 concentrations within the canopy), apart from measurements between 6:00 and 7:00 AM and between 6:00 and 7:00 PM, which were not used for canopy D 13 C determinations.
Ecosystem net CO 2 exchange (Fig. 5B) showed a clear diurnal pattern, with nocturnal respiration mainly correlated with temperature (1°C bin-averaged r 2 5 0.887) and net uptake mostly controlled by incident PFD (Fig.  5A). The d 13 C of ecosystem respiration was determined by taking the y intercept of a Keeling plot (linear geometric mean regression of 1/[CO 2 ] versus d 13 C) assuming a two-source mixing model (Keeling, 1958(Keeling, , 1961. For our 13-year-old stand (Table I), d 13 C of respiration was still very much influenced by a C 3 carbon isotope signal from the previous cropping system, which is consistent with the low turnover of soil organic carbon in Miscanthus ecosystems (Hansen et al., 2004;Clifton-Brown et al., 2007). Canopy D 13 C followed a diurnal trend, with lower values around midday and slightly increased values in morning and afternoon (Fig. 5C). Figure 5D shows the canopy D 13 C determinations as a function of incident PFD, revealing a similar pattern as the measurements of leaf D 13 C (Fig. 4A). Except for two outliers, canopy D 13 C remained between 1.3& and 4.3& above 350 mmol m 22 s 21 PFD. Below this light intensity, the range of canopy D 13 C values steadily expanded, with values between 1.5& and 6.3&.
Losses of Potential CO 2 Fixation Due to f Canopy A n was modeled (according to the model by Von Caemmerer and Furbank [1999] and Von Caemmerer [2000], with some adjustments; see Supplemental Appendix S1) for 3 d to show how f would reduce net carbon gain on the basis of either the leaf or canopy data presented above (Figs. 4 and 5, respectively; hereafter referred to as ''leaf level'' and ''canopy level''). Measured vertical canopy profiles of temperature, PFD, and photosynthetic capacity were used to compute a vertical profile of A n , which was then multiplied by leaf area at each height and summed to obtain canopy A n . Expression of individual leaves in canopy A n , therefore, was weighted by their assimilation rate. In order to estimate the impact of f, we calculated theoretical values for canopy A n without leakage (f 5 0) and compared these values with canopy A n obtained with our estimates for f at leaf or canopy level (Fig. 6A).
In Figure 6A, the 100% datum represents canopy A n with f set to zero. Both leaf-and canopy-level modeled values of canopy A n were reduced because of f. When canopy A n was calculated with the use of f based on canopy-level determinations, the reduction due to leakage was lower than when canopy A n was derived from leaf-level measurements. The decrease in canopy A n would be most severe when light was limiting early in the morning or in the evening, when canopy A n was predicted to be only 43% (leaf level) or 62% (canopy level) of canopy A n without leakage of CO 2 . Canopy A n at midday was predicted to range from 85% (leaf level) to 94% (canopy level) of canopy A n without leakage.
In order to assess the cumulative effect of f, A n was also summed over 3 d. Cumulative canopy A n was 68% (leaf level) to 86% (canopy level) of canopy A n without CO 2 leakage (Fig. 6B), indicating that cumulative losses of canopy CO 2 fixation due to f over 3 d were between 14% and 32%.

DISCUSSION
This study makes a major contribution to understanding the constraints to CO 2 uptake within Miscanthus, an important biomass crop. We have evaluated the impact of f, an intriguing physiological correlate of the C 4 pathway, which has previously been investigated largely under laboratory conditions. The data have demonstrated that f provides a significant constraint to carbon assimilation at leaf and canopy level under field conditions when estimated using real-time D 13 C techniques. We now evaluate the implications of our findings for integrating leaf-level and canopy-level gasexchange processes and scaling likely physiological constraints to Miscanthus productivity in a temperate climate.

Gas Exchange and Fluorescence
Measurements of assimilation rate under controlled conditions comply well with previous findings. The high-light saturation points in Figure 2A are consistent with reported values for C 4 photosynthesis (Usuda, 1987;Beale et al., 1996Beale et al., , 1997. Carboxylation efficiency under saturating light (initial slope; Fig. 2B) as well as gas exchange under field conditions (Fig. 3) at 3 and 2.5 m agreed with findings by Beale et al. (1996Beale et al. ( , 1997 for the third leaf of Miscanthus (top down) during the second half of the growing season. Below 2 m, A n decreased rapidly, which can be explained by leaf age and associated lower enzymatic activity (Usuda, 1984) as well as by early stages of leaf senescence at 1-m height. At canopy level, half-hourly averages of net ecosystem exchange were consistent with long-term measurements above Miscanthus (F. Carroll and M.B. Jones, unpublished data).
In the absence of simultaneous measurements of A n and J under field conditions, we are not able to make any direct comparison of how A n responded to changes in light use efficiency caused by f. Also, measurements of the quantum yield of PSII are known to be influenced by quantitative and qualitative light history of the leaf as well as leaf temperature (Edwards and Baker, 1993). Figure 2B was determined under steadystate laboratory conditions, and so interpolating the ratio of J versus A n , which should increase at low PFD based on our f determinations (assuming that cyclic  Table I) to gross CO 2 uptake derived from daytime net CO 2 fluxes (B) and ecosystem respiration based on nighttime regression with soil temperature (y 5 0.5505e 0.0748T ; r 2 5 0.887). D, Canopy D 13 C (C) as a function of incident PFD. electron flow occurs at a constant fraction of J and absence of other significant electron sinks), could only be inferred on a qualitative basis. However, we note that for a fast-growing crop, leaves that were previously fully exposed were subsequently shaded by the developing canopy. For our observations of Miscanthus, it was evident that J max was down-regulated higher in the canopy (2.5 m), while photosynthetic capacity (CE, A max ) was sustained lower in the canopy (2 m). The implications for the effect of f on the ratio between J and A n , therefore, need to be addressed in a more detailed study.
D 13 C At high PFD (above 350 mmol quanta m 22 s 21 ), D 13 C for leaves at different heights matched well with values generally assigned to C 4 photosynthesis (for reviews, see Farquhar, 1983;O'Leary, 1988). D 13 C at lower PFD tended to be much more variable, ranging from 0.5& (1.5 m) to 16.5& (1 m), which is consistent with likely changes in the coupling of C 4 and C 3 cycles, variations in photosynthetic capacity, local microenvironment, and associated enzyme activity between leaves. Also, D 13 C for individual leaves, when calculated using Equation 4 below, becomes increasingly less precise when CO 2 depletion is low relative to the CO 2 concentration in air. The observation that higher values of D 13 C seemed to occur more often at low PFD deep in the canopy is consistent with previously reported values under low PFD for Amaranthus cruentus (Tazoe et al., 2006(Tazoe et al., , 2008 and Flaveria bidentis (Cousins et al., 2006).
Remarkably, the increase in D 13 C at low PFD was also observed when derived independently at canopy level. Canopy D 13 C mostly reflected D 13 C processes by leaves high in the canopy. Since D 13 C at leaf level is weighted in canopy D 13 C according to the rate of CO 2 uptake relative to other leaves, predictably leaves high in the canopy with higher assimilation rates influence canopy A n and D 13 C more than leaves at lower locations.
The method used to determine canopy D 13 C (Bowling et al., 2003) depended on measurements of ecosystem CO 2 exchange together with isotopic compositions of ecosystem respiration and daytime canopy air. A single isotopic respiratory signal had to be assumed for the complete ecosystem, which is likely to be an oversimplification, given the difference between current (C 4 ) and previous (C 3 ) vegetation on soil respiration (Buchmann and Ehleringer, 1998) and light effects on respiration of aboveground biomass (Atkin et al., 1998).
The ecosystem respiratory flux was defined by an exponential regression between soil temperature and nocturnal eddy covariance measurements of CO 2 efflux (Lloyd and Taylor, 1994), which could only be firmly established by bin averaging the ecosystem respiration measurements in 1°C increments. A similar problem was found by Bowling et al. (2003) and appears to be quite common in previous reports of net ecosystem partitioning into gross assimilation and respiration fluxes (Reichstein et al., 2005;Knohl et al., 2008). Bowling et al. (2003) explained part of the variability by spatial variation of soil moisture content, and Knohl et al. (2008) implied nonhomogeneity of the soil profile. Both factors may have contributed in our study, especially since diurnal measurements of soil respiration as well as soil temperature and moisture content were also spatially variable (data not shown).

Increased D 13 C at Low Light Intensity
Our results support previous observations of an increase in D 13 C at low light intensity. The underlying mechanisms have been analyzed extensively. Based on studies of photosynthetic behavior in C 4 plants, Leegood et al. (1989) argued that the energy supply for the assimilatory pathway (production of ATP and NADPH) declines drastically following a transition from high to low PFD. Stimulation of cyclic electron flow and Q-cycle activity (Furbank et al., 1990) might make up for part of the ATP shortage (by cyclic par-  Figure 5C, using Eq. 3). B, Cumulative modeled canopy A n for f 5 0, based on leaf level measurements of D 13 C and on canopy D 13 C. Scenarios are compared with total cumulative canopy A n with f 5 0.
titioning of electrons around the PSI complex and altering the ATP-NADPH production ratio). However, we can find no evidence in the literature for increased activity of these alternative electron cycling processes as a result of lower PFD; so ultimately, photosynthesis remains limited by the energy supply.
Energy limitation could increase measured D 13 C in several ways. First, an increase in the relative contribution from mitochondrial respiration under low light could vary D 13 C (Duranceau et al., 2001), particularly if respiratory CO 2 is enriched in 13 C (Ghashghaie et al., 2003). Alternatively, Henderson et al. (1992) stated that with reduced phosphoenolpyruvate regeneration slowing C 4 cycle activity under low light, a decrease in the BS CO 2 concentration or CO 2 -O 2 ratio would allow the relative contribution of photorespiration to increase. The extra energy needed for the photorespiratory cycle would limit C 3 cycle activity compared with C 4 cycle activity, which would lead to an increase in leakage of CO 2 (Von Caemmerer et al., 1997aCaemmerer et al., , 1997b from BS cells, thereby allowing more of the isotopic fractionation by Rubisco (30&) to be expressed. Recently, Tazoe et al. (2008) may have provided evidence for an increase in f as a result of energy limitation under low PFD, since the increase in D 13 C and, hence, f, following a transfer to low PFD, was lower in Amaranthus cruentus plants grown under low light intensity compared with highlight-grown plants. This may have been caused by a slightly altered relative composition (within the limits of C 4 pathway plasticity) of the photosynthetic apparatus in the plants grown under low PFD, resulting in an improved ability to sustain carboxylation efficiency in BS cells at low light. The relative changes in light use and carboxylation efficiency within the canopy ( Fig. 2; see discussion above) certainly suggest that differing degrees of acclimation occur at reduced light intensity, once fully expanded leaves are overtopped by the newly growing canopy.

BS f
At high light intensity, f was similar to reported values in NADP-malic enzyme C 4 photosynthesis of 0.2 to 0.3 in maize (Henderson et al., 1992) and 0.3 to 0.4 in sugarcane (Meinzer et al., 1994;Meinzer and Saliendra, 1997). The maximum values for f at low light intensity (below a threshold PFD of 350 mmol quanta m 22 s 21 ) were comparable to reported values of 0.65 at 150 mmol quanta m 22 s 21 for F. bidentis by Cousins et al. (2006) and of 0.76 at 40 mmol quanta m 22 s 21 for A. cruentus by Tazoe et al. (2008). Other contributions to the measured leaf-level variability of D 13 C and f could be related to the input parameters (p i /p a , b 4 , b 3 , s, and a) and simplifying assumptions for Equation 3 below. The assigned parameter value of 26& (at 22°C) to b 4 is based on the assumption that carbonic anhydrase (CA) is abundant enough to maintain isotopic equilibrium between CO 2 and HCO 3 2 . However, if CA activity is too low to maintain equilibrium, b 4 becomes less negative and D 13 C increases (leading to an overestimation of f with Eq. 3), which was shown by Cousins et al. (2006) with F. bidentis RNA antisense CA plants. Von Caemmerer et al. (2004) argued that CA activity was too high to maintain steady-state assimilation rates in F. bidentis; however, Yakir (2000, 2001) have reported that CA activity in C 4 monocots could limit photosynthetic rates. Equation 3 requires high CO 2 concentration in BS cells relative to that in M cells. If this requirement was not met, f might have been overestimated by 10% or more for very low BS CO 2 concentrations (Tazoe et al., 2008). Also, the gradient between intercellular and M CO 2 concentrations was assumed to be negligible in Equation 3. Results of a sensitivity analysis with the extended model by Farquhar (1983) showed that a gradient of 30 mmol mol 21 would cause a mean absolute difference in calculated f of 0.026.
Furthermore, there might be additional fractionations associated with photorespiration (Gillon and Griffiths, 1997;Lanigan et al., 2008), variable mitochondrial respiration between old and young leaves (Villar et al., 1995), or different carbon sources for respiration (Ghashghaie et al., 2003). A sensitivity analysis (Table II) was undertaken, using the extended model by Farquhar (1983), with various combinations of values for mitochondrial respiration, the fractionation factor assigned to respiration (e), and carboxylation rate in BS cells (V c ). The results were relatively insensitive to most of the modeled combinations, and only when V c was low (3 mmol m 22 s 21 ) and mitochondrial respiration was high (1.2 mmol m 22 s 21 ) did mean absolute differences in f range from 20.06 to 0.08 (depending on the value of e; Table II). The observed dark respiration rate in leaves at 1, 2, and 3 m in our study (0.40, 0.71, and 0.89 mmol m 22 s 21 , respectively) suggest that such errors would not occur, due to the relative reduction in both assimilation and respiration rates low in the canopy. The extended model by Farquhar (1983) was used to calculate the mean absolute difference of f between the extended model and the simplified version without respiratory fractionation (Eq. 3). Phosphoenolpyruvate carboxylation and photorespiration rates were set at 1.5 and 0.03 times V c , respectively. A value of 11.5& was used for the fractionation factor associated with photorespiration, based on recent estimates by Lanigan et al. (2008).

Implications of Results for Canopy CO 2 Fixation
Assuming that f is the major correlate of variations in leaf and canopy D 13 C, we suggest that f significantly reduces canopy net assimilation rate. Having calculated f from leaf-level D 13 C and simultaneous gas exchange, and also independently from canopy D 13 C and PFD and temperature measurements within the canopy, there were relative reductions in cumulative canopy A n ranging from 14% to 32%. There are implications for losses of carbon-fixing capacity in densely planted C 4 crops. Screening for varieties with low D 13 C under a range of limiting light conditions might be a means to increase the productivity of Miscanthus (or other C 4 crops), especially in the temperate climate conditions of northwestern Europe. Additionally, the observed variations in the canopy profile of J max and A max may provide a mechanistic understanding of the energetic factors controlling f.
In conclusion, our results have established that retrodiffusion or leakage of CO 2 from BS cells is a major limitation to carbon gain at leaf and canopy scales under field conditions. While additional laboratory studies are required to evaluate the exact nature of this energetic inefficiency at low light (perhaps through the analysis of transient responses of f to light in sun-and shadeacclimated plants), there was an agreeable consistency in response to incident PFD measured independently for individual leaves and their cumulative light limitation within the upper part of a full C 4 crop canopy. Second, we have been able to demonstrate how f, as a function of leaf area index and incident PFD within the canopy, can be translated into canopy-scale carbon partitioning and potential productivity. Additional work is required to confirm the consistency of these responses during canopy development and to allow more precise partitioning between respiratory components and canopy net assimilation. However, carbon isotopes have provided a powerful means to analyze instantaneous photosynthetic limitation at leaf and canopy scale and allowed us to derive estimates of the likely reduction due to f in CO 2 uptake for a C 4 crop limited by light and temperature in a northern temperate environment. The good agreement between previous measurements of f versus PFD from controlled environment studies (Henderson et al., 1992;Meinzer et al., 1994;Meinzer and Saliendra, 1997;Cousins et al., 2006;Tazoe et al., 2008) and our observations under field conditions might also suggest that within-canopy measurements of PFD can be used as a rough proxy for f losses due to light limitation arising from self shading.

Potential Rate of Photosynthesis
Five leaves were randomly selected from 1-, 1.5-, 2-, 2.5-, and 3-m height within the canopy to assess electron transport rate (J; mmol m 22 s 21 ) as a function of incident PFD. All measurements were done just above the end of the visible mid rib. First, the quantum yield of PSII (F PSII ) was measured using pulse amplitude-modulated (PAM) chlorophyll fluorescence at a range of light intensities with a mini-PAM photosynthetic yield analyzer (Heinz Walz) according to Genty et al. (1989): where F m # and F t refer to maximum fluorescence at saturating light pulse and steady-state fluorescence immediately prior to the pulse. J could then be calculated at each light level with the use of Equation 2: where PFD represents the absorbed PFD, and 0.5 is a factor that accounts for the partitioning of energy between PSI and PSII. Leaf absorptance was set at 0.84, which has been shown to be valid for a wide range of growth conditions in Miscanthus (Farage et al., 2006). As a control, we also measured the chlorophyll content of different leaves (n 5 5) from each height using the protocol by Lichtenthaler (1987), but no significant differences were found. CO 2 responses of net assimilation rate were analyzed on three leaves that were cut at the ligule, with the cut end placed in water and recut under water, 3 cm from the base (Beale et al., 1996). The leaves were positioned in the leaf cuvette (area 5 6 cm 2 ) of a LI6400 portable, open gas-exchange system (Li-Cor Biosciences) illuminated by a Walz Fiber Illuminator FL440 with controllable intensity, with a model 400-F fiberglass connection and projector to filter heat, and left for 30 min to acclimatize to saturating light (1,600 mmol quanta m 22 s 21 ) at ambient CO 2 . Leaf temperature was set at 22°C, while the vapor pressure deficit was kept below 1 kPa. After reaching steady state, the photosynthetic assimilation rate as a function of internal CO 2 concentration was determined from high to low external CO 2 concentrations (380, 150, 100, 50, and 40 mmol mol 21 ).
Mitochondrial respiration not associated with photorespiration (R d ) was measured on different leaves from 1, 2, and 3 m (n 5 5) by gas exchange with the LI6400 (leaf temperature set at 22°C), with readings taken after 5 min in the darkened cuvette.

Realized Rate of Photosynthesis
Leaves were randomly selected at 1-, 1.5-, 2-, 2.5-, and 3-m height within the canopy, and (still attached) photosynthetic assimilation rate, transpiration rate, and stomatal conductance were measured under natural light and temperature by placing them in the leaf cuvette of the LI6400 portable, open gas-exchange system, while being careful not to change the angle and orientation of the leaf. A reading was taken after steady state was reached (approximately 5 min).
Use of D 13 C to Calculate BS f Hattersley (1976) first suggested that variation in d 13 C of C 4 species may reflect variations in the amount of leakage. An increase in BS f results in higher D 13 C, because fractionation by Rubisco becomes more expressed. This relationship is used in Equation 3, developed by Farquhar (1983) and Henderson et al. (1992), which allows calculation of BS f if D 13 C and p i /p a are known.
D 5 a 1 ðb 4 1 fðb 3 2 sÞ 2 aÞ where a is the fractionation during diffusion of CO 2 in air (4.4&), b 4 is the combined fractionation of phosphoenolpyruvate carboxylation (2.2&) and the isotopic equilibrium during dissolution of CO 2 and conversion to bicarbonate, yielding a net value of 26& (at 22°C; Mook et al., 1974), b 3 is the fractionation by Rubisco (30&), and s (1.8&) is the fractionation during leakage.

D 13 C Measured Concurrently with Gas Exchange
To measure D 13 C during gas exchange, the exhaust tube of a LI6400 portable photosynthesis system was connected to a cryogenic water and CO 2 trapping-purification line as described by Griffiths et al. (1990). CO 2 was trapped and purified for 15 min. The obtained CO 2 samples were stored in sealed glass vials and analyzed afterward with a VG SIRA dual-inlet isotope ratio mass spectrometer (modified and maintained by Pro-Vac Services), and values were corrected for the presence of N 2 O and 17 O. The d 13 C of CO 2 measured before and after photosynthetic depletion yields the net discrimination using the following equation by Evans et al. (1986): where where d e and d o represent the isotopic compositions of CO 2 relative to the PDB standard, and c e and c o represent the CO 2 mole fractions in air entering and leaving the cuvette, respectively. The D 13 C values obtained in this way thus reflect average values for 15 min of continuous photosynthetic discrimination.

Canopy Microclimate Record
A 3.5-m-tall pole with cross bars at 1-, 2-, and 3-m height was erected within the canopy with the cross bars facing north/south. PFD quantum sensors (SKP-215; Skye Instruments) were mounted on the cross bars facing south and thermocouples (Cu-Co) were mounted facing north. Also, a thermocouple and a soil moisture probe (SM200; Delta-T Devices) were inserted 0.02 m below the soil surface. A data-logger (CR21X; Campbell Scientific) was used to record and store average values every 10 min.
Another pole with air inlets on the cross bars was connected to the air inlet of a LI6400 portable, open gas-exchange system via 4-mm-diameter Teflon tubing and a switching manifold to measure and record within-canopy CO 2 concentrations at 1-, 2-, 3-, and 3.5-m height. During the recordings, the exhaust tube of the LI6400 leaf cuvette was connected to the trapping-purification line, and CO 2 was trapped and purified for 5 min and stored in sealed glass vials. The isotopic ratio of purified CO 2 was determined with a VG SIRA dual-inlet isotope ratio mass spectrometer and corrected for the presence of 17 O and N 2 O.

Canopy Characterization
Leaf area index was measured with a Sunscan System SS-1 (Delta-T Devices). Measurements were made with the sunprobe at 0-, 1-, 2-, and 3-m height to analyze the specific leaf area index of vertical sections within the canopy as well as the total leaf area of the stand (0-m measurements).

Ecosystem CO 2 Exchange
Net ecosystem exchange (NEE) of CO 2 was measured using an eddy covariance system consisting of an open-path infrared gas analyzer (Li-Cor LI-7500) coupled to a three-dimensional sonic anemometer (Soluent R3; Gill Instruments). The sonic anemometer and air intake were positioned 1 m above the canopy. CO 2 concentrations were measured with the open-path LI-7500 infrared gas analyzer. Measurements were recorded at 20 Hz on a CR23X datalogger (Campbell Scientific), and 30-min average fluxes were processed using the EdiRe software version 1.4.3.987 (Edinburgh University). Data quality and stability were tested using the methods of Foken and Wichura (1995), and data were discarded based on a lower u* threshold of 0.1 (m s 21 ), high SD in measured CO 2 concentration, and CO 2 concentration and flux values outside of approved bandwidths. The footprint model of Kormann and Meixner (2001) was used to determine the percentage of measured flux originating from within the measurement plot, when less than 70% of the data were discarded.

Canopy CO 2 Uptake and Isotope Discrimination
Data from diurnal measurements (August 28-29 and August 31-September 1, 2007) as well as eddy covariance flux measurements (August 28-September 1, 2007) were used to reconstruct canopy CO 2 uptake and short-term D 13 C using the method described in detail by Bowling et al. (2003).
A regression (exponential, ordinary least squares) was made of nocturnal eddy covariance measurements of ecosystem respiratory fluxes against soil temperature (bin averaged per 1°C). This regression was extrapolated over daytime to partition daytime gross ecosystem respiratory flux. The daytime gross ecosystem respiratory flux was then subtracted from the daytime total net flux, measured with eddy covariance, which yielded the canopy CO 2 uptake gross flux.
We assumed that daytime net ecosystem CO 2 fluxes were composed of gross fluxes of ecosystem respiration (F R ) and canopy uptake (F A ; Eq. 6), and net ecosystem uptake fluxes were assigned a negative sign by micrometeorological convention.
Analogously, net isofluxes were also assumed to consist of gross respiration and photosynthetic isofluxes (Eq. 7).
The isoflux of ecosystem respiration [(d 13 C R )F R ] was determined by multiplying the daytime gross respiratory flux with the intercept of the nocturnal Keeling plot (geometric mean regression of 1/[CO 2 ] versus d 13 C; Keeling, 1958Keeling, , 1961. Net daytime isofluxes (d 13 CNEE) were calculated by multiplying the daytime net ecosystem exchange fluxes with corresponding isotopic signatures using daytime geometric mean regression of CO 2 concentrations versus d 13 C. Since (d 13 C R )F R , d 13 CNEE, ambient isotopic signature of CO 2 (d 13 C a ), and gross fluxes of canopy CO 2 uptake (F A ) were identified, based on mass balance and negligible storage flux in NEE measurements (checked with diurnal vertical CO 2 concentration profiles), the isotopic contribution of canopy CO 2 uptake (d A ) became the only unknown variable and could be solved.

Losses of Potential CO 2 Fixation Due to f
We used the following approach to calculate the implications of f at leaf level on canopy CO 2 uptake (A n ). Based on the leaf-level determinations, a function for hyperbolic decay [f 5 (a 3 b)/(b 1 PFD)] was fitted to define f as a function of incident PFD (Fig. 4C). Measured incident PFD and temperature at 1, 2, and 3 m from August 29 to August 31 were used to represent the range of conditions defining CO 2 fixation. A vertical profile of A n was calculated using the model for C 4 photosynthesis by Von Caemmerer and Furbank (1999) and Von Caemmerer (2000) with some adaptations (see Supplemental Appendix S1), which was multiplied by a profile of leaf area index and summed to yield canopy A n . We calculated potential canopy A n without CO 2 leakage (f 5 0) and compared it with canopy A n computed with f determined by the fitted relationship between f and PFD in Figure 4C.
A similar approach was used in combination with Equation 3 to translate measurements of canopy D 13 C into f for each height. First, leaf-level data were used to derive a regression between incident PFD and p i /p a (Fig. 4B). Based on previous results (Cousins et al., 2006;Tazoe et al., 2006Tazoe et al., , 2008 and the model by Von Caemmerer and Furbank (1999) and Von Caemmerer (2000), we used a descriptive function for hyperbolic decay [f 5 (a 3 b)/(b 1 PFD)] to describe f as a function of incident PFD. The measured incident PFD within the canopy, together with Equation 3, then allowed the calculation of A n and D 13 C for each layer. D 13 C weighted by A n was used to calculate canopy D 13 C, which was compared with measured canopy D 13 C. This comparison allowed fitting parameters a and b by means of nonlinear regression, and the best fit was used to produce results for canopy A n based on canopy-level determinations of f (as described in the previous paragraph).
The Ventana Simulation Environment Vensim DSS for Windows, version 5.6a Double Precision (Ventana Systems), was used for all calculations and nonlinear regression.

Supplemental Data
The following materials are available in the online version of this article.
Supplemental Appendix S1. Modeling A n for C 4 photosynthesis.