Differences between tree stem CO 2 efflux and O 2 influx rates cannot be explained by internal CO 2 transport or storage in large beech trees

Tree stem respiration ( R S ) is a substantial component of the forest carbon balance. The mass balance approach uses stem CO 2 efflux and internal xylem fluxes to sum

capacity highlight its potential relevance as a mechanism of local CO 2 removal, which merits further research.

K E Y W O R D S
carbon dioxide transport, CO 2 /O 2 ratio, mature trees, oxygen consumption, temperate forest, vertical stem gradient
Two main measurement approaches have been applied to estimate R S .The carbon-based mass balance approach (McGuire & Teskey, 2004) not only considers CO 2 efflux (E CO2 ), but also takes into account the dissolution of CO 2 in the xylem (accounting for its equilibrium species H 2 CO 3 , HCO 3 − and CO 3 2− ; hereafter CO 2 *), its vertical transport through the xylem sap (F T ) and the CO 2 storage flux (ΔS), as the accumulation or depletion of CO 2 in the xylem sap over time, to achieve a more precise estimation of R S on a volume basis (μmol m −3 s −1 ): Most studies applying the mass balance approach examined the contribution of CO 2 efflux, CO 2 transport and CO 2 storage to R S in small trees or saplings (e.g., McGuire & Teskey, 2004;R. L. Salomón et al., 2018;Saveyn, Steppe, McGuire, et al., 2008) due to the easiness of constructing custom-made stem cuvettes surrounding the whole stem.However, applying findings from small trees to interpret CO 2 efflux in mature trees could be hampered by the long radial diffusive pathway in thick stems, which could result in significantly limited CO 2 diffusion rates (Steppe et al., 2007).This assumption is supported by findings in yellow poplar, where the relative contribution of CO 2 efflux to R S decreased with stem diameter (up to 60 cm), while CO 2 transport increased with stem size, as could be expected by larger sapwood conductive area, transpiration rates, and potential for CO 2 removal from the point of production (Fan et al., 2017).
Many studies have relied primarily on CO 2 efflux (and CO 2 transport) to estimate R S ; nevertheless, aerobic respiration involves oxygen (O 2 ) consumption, and the influx of O 2 from the atmosphere into the stem (I O2 ) can also serve as a proxy for R S .The second measurement approach to estimate R S is based on simultaneous measurements of O 2 influx and CO 2 efflux.Given the much lower water solubility of O 2 compared with CO 2 (Dejours, 1981), dissolution effects and vertical transport should play a potentially negligible role for O 2. Boosted by technological improvements to register small O 2 fluctuations in an atmosphere with a large O 2 background, emerging interest arises in the coupled measurement of CO 2 efflux and O 2 influx at the stem surface (Angert & Sherer, 2011;Hilman & Angert, 2016).The ratio of CO 2 efflux to O 2 influx is called the respiratory quotient (RQ) at the cell level.The cell-level RQ allows exploring the substrate of respiratory metabolism.In trees, nonstructural carbohydrates (NSC) are assumed to be the primary respiratory substrate, theoretically resulting in a RQ of ~1.More O 2 is needed for the breakdown of lipids compared with carbohydrates, resulting in RQ ~0.7 (Masiello et al., 2008).Organic acids catabolism would yield RQ above one because of the greater O 2 content of those molecules being oxidized (Masiello et al., 2008).At the organ level, as the stem in this case, the ratio of CO 2 efflux to O 2 influx at the surface is named the apparent respiratory quotient (ARQ) (Angert & Sherer, 2011): Therefore, simultaneous measurements of both gases allow for the assessment of potential shifts in respiratory substrate over time and under environmental stresses (Fischer et al., 2015).Furthermore, the ARQ can be affected by postrespiratory processes (Trumbore et al., 2013), providing information about the role of CO 2 dissolution and transport on R S estimates, as CO 2 is highly soluble in xylem sap, while O 2 is less soluble.Hereby, assuming NSC as respiratory substrate, RQ would be ~1, and so would the ARQ as long as CO 2 transport and storage were negligible, as CO 2 efflux versus O 2 influx equalize.However, Hilman et al. (2019) showed the inability of sap flow (and hence CO 2 transport) to account for the variability in the ARQ of Q. ilex trees.Authors suggested CO 2 refixation via the enzyme PEPC as the primary cause of ARQ below the unit, a mechanism of local CO 2 removal commonly overlooked in R S research.However, the role of PEPC capacity in mature stems is still speculative as it has mainly been investigated in C4 plants and only in leaves and young green twigs of C3 plants (Berveiller & Damesin, 2008).
It is essential to reconcile insights gained through the mass balance approach and oxygen-based measurement methods, which disagree on the primary factor causing the mismatch between R S and CO 2 efflux, either CO 2 transport through the xylem and storage or PEPC-mediated CO 2 fixation, respectively.Note that both approaches commonly use opaque stem cuvettes or chambers, precluding photosynthetic reassimilation of locally respired CO 2 (see De Roo et al., 2020).Mathematically, as a first approximation assuming R S and O 2 influx are equivalent, the mass balance could be formulated as follows: (3) where the apparent respiratory difference (ARD), as an alternative metric to interpret the mismatch of CO 2 and O 2 fluxes in absolute terms, should equal the amount of locally respired CO 2 transported and stored if CO 2 refixation (either photosynthetic or nonphotosynthetic) is negligible.If the latter assumption is valid, carbon-and oxygen-based methods could be indistinguishably applied to estimate R S .If not, it would be necessary to revisit underlying assumptions from both approaches to constrain the interpretation of each other and provide a more comprehensive perspective on the fate of respired CO 2 not emitted locally to the atmosphere.This is precisely the main challenge in research on the metabolism of woody tissue respiration.A direct comparison of both approaches is lacking so far.
By combining both approaches with the same individuals and under the same conditions, it would be possible to assess whether discrepancies observed so far vanish or whether assumptions should be revisited.
To do so, we continuously monitored the vertical and temporal variability in CO 2 efflux, O 2 influx and xylem [CO 2 ] along a 3-m stem gradient in beech trees (Fagus sylvatica L.) during 1.5 summer months.
Importantly, the study was performed in large mature trees, in which the contribution of CO 2 transport to R S is expected to be higher (Fan et al., 2017) Stem CO 2 efflux and O 2 influx at the stem surface were measured hourly on every tree at three stem heights (1, 2.5, and 4 m) following the approach described in Helm et al. (2021).Briefly, we installed a custom-made chamber in each stem location that consisted of (i) a closed-porous cell foam and a base plate of 20 cm length, 10 cm width, and 4 cm height, (ii) a waterproof housing for the CO 2 and O 2 sensors with a removable lid for easy exchange of the sensors, and (iii) a transport-case containing an air pump, an Arduino ® unit for data logging and 5 V power bank battery for power supply (800 mAh, Li-ion type, MP-50000; XTPower).See Supporting Information: were attached against the tree stem using three ratchet straps.The measurement principle is based on a closed system with measurement cycles of 45 min followed by 15 min to flush the chamber's headspace with ambient air.were changed after 3 weeks to limit reading drift (Helm et al., 2021).
CO 2 efflux and O 2 influx on a surface basis (μmol m −2 s −1 ) were calculated from the linear CO 2 increase and O 2 decrease of the first 20-min time interval (of the 45 min measurement cycle excluding 3 min after flushing) following Equation ( 4): where ΔC/Δt is the change in gas concentration over time (ppm s −1 ) for CO 2 or O 2 , V is the chamber headspace volume (m 3 ) determined by water displacement, A is the stem surface area (m 2 ), P is the barometric pressure (kPa), R is the molar gas constant (m 3 kPa K −1 mol −1 ), and T is the temperature (K) obtained from the COZIR sensor.
From CO 2 efflux and O 2 influx time series, the ARQ and ARD were calculated following Equation ( 2) and ( 3).
The concentration of xylem [CO 2 ] in the gas phase (%) was measured with NDIR CO 2 sensors (GMP221 and GMP251; Vaisala Inc.) calibrated before installation using reference gases at known [CO 2 ] of 0%, 5%, 10% and 15%.For each sensor, we drilled a 40 mm deep and 25 mm wide hole into the stem and pushed the probe (length: 96 mm) halfway within the hole (~20 mm), leaving a closed headspace in the xylem tissues beyond the cambium layer.Synthetic rubber sealant (Teroson RB IX; Henkel) was used for isolation from the atmospheric gas.Four sensors were installed in each tree along the vertical profile monitored with stem chambers at 1, 2.35, 2.65 and 4 m.We initially envisaged applying the mass balance approach in the 30-cm-length stem segment between 2.35 and 2.65 m probes.
Nevertheless, we eventually decided to average the xylem [CO 2 ] time series from these two probes to survey longer (and more representative) stem segments, from 1 to 2.5 m (lower stem) and from 2.5 to 4 m (upper stem) (Supporting Information: Figure S1).
Probes were placed ca. 10 cm from each chamber on the northwest side of the trees.Readings of the 16 sensors were recorded every 5 min with a datalogger (CR1000x; Campbell Scientific) for the whole experiment period.

| Xylem CO 2 transport and storage
The amount of CO 2 transported upwards through the xylem and stored within the xylem was estimated in the lower and upper stem segments.The concentration of dissolved CO 2 in xylem sap ([CO 2 *], mol CO 2 l −1 ) was calculated using temperature-dependent Henry's Law coefficients (Levy et al., 1999;McGuire & Teskey, 2002), assuming equilibrium between CO 2 in the gaseous and liquid phases.Once sap [CO 2 *] was known, CO 2 transport (F T , µmol CO 2 m -3 s -1 ) for both lower and upper stem segments were estimated according to: where SF is the sap flow rate (l s −1 ), v is the sapwood volume (m 3 ), and Δ[CO 2 *] is the difference in sap [CO 2 *] above and below the corresponding stem segment (μmol l −1 ).The sap flow rate was estimated as the product of sap flux density (l cm −2 h −1 ) and sapwood area (cm −2 ) using the Sap Flow Tool software (Plant AnalytiX).Sap flux density was monitored using sap flow meters SFM1 (ICT International Pty Ltd.) operated by the heat ratio method (Burgess et al., 2001), assuming a stem water content of 400 l m −3 (Gartner et al., 2004).Sap flow probes were installed at breast height on the north side of the trees, and measurements were recorded every 15 min.
A staining method was applied to determine the sapwood area; upon extraction of one wood core per tree at breast height on the northwest side of the tree (until the pith), a blue dye (E131) was injected into the hole, and a second core was extracted one cm above the first one after 1 h.Sapwood depth was determined by the length of the stained region of the core and assuming a cylindrical shape for both heartwood and sapwood (Table 1) (Goldstein et al., 1998).
The stem CO 2 storage flux (ΔS) was estimated as a function of the time derivative of [CO 2 *] in the xylem; that is, the rate of accumulation and depletion of dissolved CO 2 for both lower and upper stem segments according to:

| PEPC capacity and NSC in woody tissues
We took one stem disc (one cm-length, bark to xylem) at three stem heights (1, 2.5, and 4 m) on the south side of each monitored tree on 14 August (DOY 226).Samples were immediately frozen in liquid  July with values close to 30°C (Figure 1a).Volumetric soil water content at 16 cm depth was lowest end of July, reaching minimum values of 15.7 vol% and maximum values of 19.0 vol% afterwards following summer rains (Figure 1b).Sap flow rate showed a typical subdaily pattern with maximum rates of 30 l h −1 during sunny and warm days (Figure 1c).Shoot midday Ψ (shoot water potential) was close to −1.4 MPa on most measurement days, except the one following rains when it relaxed up to −0.5 MPa (Figure 1c).
Likewise, respiratory fluxes had maximum values during the afternoon, following subdaily thermal dynamics.
Stem height did not affect soluble sugar and starch concentrations (p = 0.37 and 0.40, respectively) (Figure 3).Sapwood depth did affect NSC; both soluble sugar and starch concentrations were higher near the cambium (0-2 cm) than deeper into the sapwood (2-4 cm) (p < 0.05).Soluble sugar and starch concentrations were higher on the second sampling date in August (DOY 226) for the 0-2 cm depth (p < 0.001, p < 0.01 for soluble sugar and starch, respectively), while they remained constant deeper into the cambium (p = 0.1, p = 0.6 for soluble sugar and starch, respectively).

| Comparison of carbon-and oxygen-based estimates of R S
We applied the mass balance approach on the lower (1-2.5 m) and upper (2.5-4 m) stem segments to estimate R S and its contributors for comparison with the oxygen-based approach (Figure 4).In the lower stem segment, there was a positive vertical gradient in sap [CO 2 *], and CO 2 transport was, therefore, positive.Averaged across days and trees, the contribution of CO 2 efflux to R S was 64.6 ± 14.5%, and the remaining fraction was attributed to CO 2 transport (35.8 ± 14.3%), as CO 2 storage was negligible (−0.4 ± 0.2%).
The R S daily average (as the sum of E CO2 , F T and ΔS) was greater than O 2 influx, but on a subdaily basis, R S exceeded O 2 influx only during the daytime.During night-time, R S equalled CO 2 efflux, and both were lower than O 2 influx.
The upper stem showed a different pattern where the vertical gradient in sap [CO 2 *] approached zero and even became negative for the last 2 weeks of our study.As a consequence, the relative contributions of CO 2 transport (−1.2 ± 2.2%) and CO 2 storage (0.0 ± 2.2%) to R S were negligible, and apparently, all the respired CO 2 diffused to the atmosphere (E CO2 = 101.1 ± 22.9%).In this stem section, both CO 2 efflux and R S were on average lower than O 2 influx for most of the surveyed period.Notably, the shift from positive towards negative CO 2 transport flux followed the peak in tempera- To further evaluate the potential of the transpiration stream to transport respired CO 2 away from its point of production, we evaluate the subdaily patterns of ARD, sap flow and sap [CO 2 *] (as a proxy of CO 2 solubility).For the comparison, we normalized the values of each variable to their corresponding daily maxima (Figure 6).
Compared with sap flow dynamics, the ARD showed a relatively stable pattern over the 24-h period.It was higher during the daytime, with night-time reductions of ca.30%-35% relative to the daily

| DISCUSSION
We combined a carbon-based mass balance approach and an oxygenbased method to estimate R S and reconcile apparent discrepancies regarding the fate of respired CO 2 not locally emitted to the atmosphere.O 2 influx was consistently higher than CO 2 efflux across trees, locations and time, with ARQ fluctuating around 0.7 (Figures 2c   and 5a), as similarly observed in several species applying the same methodological approach (Angert et al., 2012;Hilman & Angert, 2016;Hilman et al., 2019).Assuming the beech trees use carbohydrates for respiration, the measured ARQ suggests that 30% of the respired CO 2 is retained in the stem.et al., 2008;Lavigne et al., 1996;Maier et al., 2010;Rodríguez-Calcerrada et al., 2014;Ryan et al., 1995).Interestingly, during and after the peak in temperature and respiratory fluxes at the end of July, xylem [CO 2 ] did increase along the lower stem segment (from 1 to 2.5 m height) but remained relatively stable along the upper stem (from 2.5 to 4 m height).This observed difference in the vertical gradient of the xylem [CO 2 ] led to contrasting contributions of CO 2 transport to R S in the lower and upper stem segments, as discussed below.The lack of a significant relation of both CO 2 efflux and O 2 influx with soil water content denotes that the mild drought did not limit respiratory metabolism to a large extent.Interestingly, ARQ remained relatively stable over the 1.5 summer months, where a temperature peak (30°C) occurred, suggesting similar sensitivity to temperature of CO 2 efflux and O 2 influx.
4.1 | CO 2 internal fluxes cannot explain the differences between stem O 2 influx and CO 2 efflux Higher O 2 influx than CO 2 efflux could result from the higher solubility of CO 2 in xylem sap (30 fold) compared with O 2 (Dejours, 1981), hence the possibility of CO 2 dissolving in the sap solution and being transported upwards or stored.If true, this would be evident in our mature beech trees, whose large sapwood conducting area provides room for potentially high transport and storage of respired CO 2 (Fan et al., 2017).We found a Nevertheless, we must be cautious about the specific methodological issues related to the measurement of sap flow and sap pH and their corresponding propagation errors.For instance, sap flow measured with the heat pulse method often underestimates the actual sap flow, on average, by 35% (Steppe et al., 2010).Considering a proportional underestimation of CO 2 transport, its contribution to R S would also increase in parallel, affecting the difference between R S and O 2 influx differently among individuals and heights.Sap pH, especially above 6.5, is another critical factor for calculating CO 2 transport, as the solubility of CO 2 increases exponentially with pH.
Here, we applied a constant pH value across daily and subdaily temporal scales and assumed similar pH between twig sap and stem sap.However, these assumptions can lead to further CO 2 transport misestimation (Aubrey et al., 2011;Erda et al., 2014;R. Salomón et al., 2016)  Regardless of these potential measurement uncertainties, we did not succeed in reconciling differences between the two approaches, which highlights a crucial methodological difference.The carbonbased approach estimates R S based on fluxes measured at the stem surface and internal fluxes measured in the xylem, while the oxygenbased approach relies on O 2 influx at the stem surface.Therefore, the disagreement between approaches might be related to the fact that (i) CO 2 efflux and O 2 influx likely reflect respiration in the outermost tissues of the stem (bark, phloem, cambium and outer xylem) and that (ii) respiration of the inner sapwood in large trees cannot be appropriately detected by measurements taken at the surface.
According to Fick's law of diffusion, the rate of gas (CO 2 or O 2 ) diffusion is inversely related to the length of the diffusive pathway (Nobel, 2009) and, therefore, such decoupling likely increases in large-sized trees.Here, in the mature beech trees with a sapwood depth between 12 and 16.5 cm, the diffusion of respired CO 2 by inner living cells is much lower than in seedlings and saplings, wherein each respiring cell is located nearer to the bark-atmosphere interface.
Decoupling between internal respiratory fluxes and fluxes from the stem surface can be exacerbated by the high water content of the cambium layer (De Schepper et al., 2012), acting as a major diffusion barrier according to the slow gas diffusivity in water (ca. 10 4 times lower than in air; Nobel 2009).
4.2 | PEPC-mediated CO 2 fixation as a relevant driver of the systematic mismatch between CO 2 efflux and O 2 influx Higher O 2 influx than CO 2 efflux could be explained by CO 2 refixation via PEPC, which hinders CO 2 from being locally emitted.
Therefore, the capacity of CO 2 refixation via PEPC measured here was comparable with that observed in younger, greener twigs.
In nonphotosynthetic tissues, PEPC is involved in anaplerotic reactions, compensating for the depletion of C skeletons consumed by the tricarboxylic acid cycle towards other pathways (synthesis of amino acids) or even other organs (export of malate and citrate via the xylem stream).Part of the phosphoenolpyruvate (PEP) produced by glycolysis may be converted to oxaloacetate and further to malate, with a zero net balance of ATP and NADH during the fixation of two molecules of CO 2 .Given the low ARQ values observed here, the resulting malate may not be locally oxidized, but further metabolized to produce, for example, citrate or amino acids.Evidence shows that malate concentration increases in the stem of Acer platanoides trees moving upwards (Schill et al., 1996).Transported malate can increase the malate pool in leaves (Gessler et al., 2009), where it could be metabolized via malic enzymes releasing CO 2 , thus favouring carboxylation via Rubisco (Hibberd and Quick 2002).Alternatively, the products can be transported downwards via the phloem (Hoffland et al., 1992;Shane et al., 2004;Touraine et al., 1992), followed by excretion in the rhizosphere as root exudates.
Alternatively or additionally, PEPC could be involved in pH regulation (Caburatan & Park, 2021), the latter having appeared stable despite fluctuations in xylem CO 2 (see e.g.Erda et al., 2014).Extrapolating PEPC capacity on a volume basis for comparison with CO 2 efflux or O 2 influx (as in Figure 4) resulted in unrealistically high rates of PEPC fixation (up to two orders of magnitude higher than R S estimates).
First, enzyme activity measured in vitro under saturating substrate usually exceeds the in vivo flux (Junker et al., 2007).Second, PEPC capacity likely decreases with xylem depth (Höll, 1974), and PEPC samples were uniquely taken from the outermost stem tissues.
Nevertheless, the high values of PEPC capacity on a volume basis suggest that even low PEPC capacity could be significant for the stem C budget and could help explain the discrepancy between CO 2 efflux and O 2 influx.

| Other potential C sinks
Another potential missing C sink in R S budgets is the CO 2 photosynthetic refixation occurring in chloroplast-containing cells located in peripheral woody tissues (Ávila et al., 2014;De Roo et al., 2020;R. O. Teskey et al., 2008), which can reduce stem CO 2 emissions by half, as observed in young poplar trees (De Roo et al., 2020).However, local photosynthetic fixation can be safely discarded within our experimental set-up, as opaque stem chambers were used to measure CO 2 efflux, precluding photosynthetic light reactions.Nevertheless, we cannot discard the possibility of axial diffusion of CO 2 in the gas phase ascribed to distant woody tissue photosynthesis (De Roo et al., 2019;Saveyn, Steppe, & Lemeur, 2008).In this line, light-driven photosynthesis above and below the (opaque) stem chamber can develop light-induced vertical [CO 2 ] gradients, leading to CO 2 axial diffusion in the gas phase that has been observed to reduce CO 2 efflux by 22% in oak stems (De Roo et al., 2019).Furthermore, we cannot rule out the possibility of O 2 influx measurements overestimating stem respiratory activity.We must critically note that O 2 influx measurements should be considered as additional information that helps disentangle CO 2 sinks and sources, but not as an equivalent to R S as uncertainties remain.First, a shift in the respiratory substrate from NSCs to lipids or proteins, with a lower oxidation state, requires a higher amount of O 2 for respiratory reduction, hence increasing the ARD (and reducing the ARQ; Fischer et al., 2015;Hanf et al., 2015).However, our study extended over 6 weeks during the summer season and measured NSC concentrations at different heights and depths did not indicate a seasonal NSC depletion that would alter the respiratory substrate (Figure 3).Moreover, beech is not known to store lipids (Hoch et al., 2003), further suggesting the limited role of substrate change

Figures
Figures S1 and S2 for a schematic overview and a photograph of the set-up.Chambers were installed on the north side of the trees, and chambers were covered with aluminium foil to avoid direct solar radiation and impede local woody tissue photosynthesis.Chambers

For
this, xylem[CO 2  ] in the gas phase, xylem sap pH, and stem temperature must be known.To monitor sap pH, xylem sap was collected from twigs of low branches of monitored trees (n = 3, as one tree was inaccessible for sampling) using a Scholander pressure chamber at four sampling dates(DOYs 204, 212, 218 and 226).Sap samples were quickly placed in Eppendorf tubes and a cold box for transportation to the laboratory and then stored in a refrigerator until measurement.Xylem sap pH was measured using a pH meter (Five Easy; Mettler Toledo) with a microelectrode (InLab ® , Ultra-Micro-ISM; Mettler Toledo).Preliminary tests confirmed that sap pH did not significantly vary over the sample storage period.Stem temperature (T stem ,°C) was continuously measured and recorded with a datalogger (CR1000x; Campbell Scientific) every 5 min using thermocouples inserted at 2 cm depth next to each stem chamber.
6)2.4 | Soil water content and shoot water potentialSoil water content (%) was continuously measured at the meteorological flux tower with one sensor (ML-2x; DeltaT) inserted at 16 cm depth, 100 m away from our instrumented trees, with a temporal resolution of 10 min.Shoot water potential (MPa) was measured around solar midday (as for sap pH sampling) at four sampling dates(DOYs 204, 212, 218, and 226)  using the Scholander pressure chamber.
nitrogen to stop the metabolic activity and transported to the laboratory.Stem discs were stored at −80°C before grinding into a fine powder in liquid nitrogen with a mortar and pestle.20 mg of woody tissue material was used for the discontinuous assay performed in a 96-well microplate(Bénard & Gibon, 2016).Briefly, aliquots were extracted by shaking with an extraction buffer.After centrifugation (7 min, 3000 g, 4°C), extracts were diluted and incubated for 20 min.The reaction was stopped with HCl.The sealed microplate was then incubated at 95°C for 10 min to destroy NADH.After cooling down, each well was neutralised with NaOH and Tricine-KOH pH 9.0 to adjust the pH to 9.0.The absorbance was read at 570 nm (30°C) until rates were stabilised.Reaction rates (mOD min −1 ) were used to calculate the amount of NAD + formed during the first step of the assay.All pipetting steps were performed using a 96-head robot (Hamilton Star), and absorbances were measured in a filter-based microplate reader (SAFAS MP96).For further details, see Supporting Information: Methods S1 andBénard and Gibon (2016).We measured soluble sugars and starch in stem cores from the instrumented trees following the Landhausser et al. (2018) protocol.One stem core per height (1, 2.5, 4 m, south-side) was collected on 4 July (DOY 185) and 14 August (DOY 226) for NSC measurements.Samples were stored in cooling bags for transportation and then ovendried at 60°C for 72 h.Stem cores were cut into two 2-cm long sections starting at the cambium (wood depth: 0-2 cm and 2-4 cm) and ground into a fine powder (ball mill, MM 400; Retsch).We extracted the soluble sugars glucose, fructose, sucrose, and starch from each sample.Briefly, ~30 mg of dry plant powder was extracted with 80% ethanol.Supernatants were analysed by High-Performance Liquid Chromatography coupled to a Pulsed Amperometric Detection (HPLC-PAD) for soluble sugar determination.We enzymatically converted the starch from the remaining pellet to glucose using α-amylase amyloglucosidase.Glucose hydrolysate was measured by the HPLC.2.6 | Data analysisStatistical analyses were performed using R software (R Development Core Team, 2019).CO 2 efflux and O 2 influx data were discarded when the R 2 of the linear fit for CO 2 and O 2 readings were below 0.96 to ensure good data quality.For gap filling, we used the pad function in padr package.To test whether the average daily values of CO 2 efflux, O 2 influx and xylem [CO 2 ] varied with stem height, linear mixed models were adjusted using the lme function in nlme package(Pinheiro et al., 2017), considering height as a fixed factor and tree as a random factor including an autocorrelation structure to account for repeated measurements.To test whether PEPC capacity varied with stem height, and sap pH among sampling dates, linear mixed models were adjusted likewise, considering the tree as a random factor.The normality of residuals was checked visually.When significant, differences among heights were tested post hoc with Tukey contrasts using the emmeans function (emmeans package).Consistency between carbon-and oxygen-based measurements was tested by evaluating the relationship between R S (E CO2 + F T + ΔS) and O 2 influx, and between CO 2 internal fluxes (F T + ΔS) and ARD, with mixed models considering tree a random factor.Potential deviances from the 1:1 relationship would indicate a lack of consistency between methodological approaches, hence the need to revisit the underlying assumptions of Equation (3).The conditional and marginal R 2 (Nakagawa & Schielzeth, 2013) of these models was estimated using r2_nakagawa function (performance package) to further evaluate the degree of agreement between approaches.Finally, sap flow, sap [CO 2 *] and the ARD were normalized to their daily maxima, and subdaily patterns were compared to evaluate the potential of xylem transport to remove locally respired CO 2 on a subdaily basis.3 | RESULTS 3.1 | Stem temperature, soil water content, sap flow rate and shoot water potential The mean stem temperature during the experiment was 17.7°C, with minimum values of 10°C during early July and peaking at the end of ture and transpiration at the end of July.Daily values of stem CO 2 efflux and O 2 influx showed good agreement (Figure5a) with a slope of 0.65 ± 0.02 (p < 0.0001), a significant intercept of 0.23 ± 0.11 (p < 0.05), and conditional and marginal R 2 of 0.87 and 0.86, respectively.When this relation was forced through the origin (the intercept is zero), the slope increased to 0.69 ± 0.02, which is in better agreement with the mean ARQ of 0.70.Nevertheless, carbon-and oxygen-based estimates of R S showed poor consistency.Although R S and O 2 influx were positively related (Figure5b), the deviation of the mean slope from unity was significant (1.57± 0.18; p < 0.0001), as well as its intercept (−2.08 ± 1.01; p < 0.05).The model conditional and marginal R 2 were 0.52 and 0.31, respectively.The slope of the relation between the ARD and CO 2 internal fluxes (F T + ΔS) (Figure5c) was almost 0 (0.056 ± 0.012; p < 0.0001), and its intercept was again significant (0.84 ± 0.09; p < 0.0001), denoting the limited potential of CO 2 transport and storage to bridge the gap between CO 2 efflux and O 2 influx.The conditional and marginal R 2 of this model were 0.21 and 0.13, respectively.Stem location did not affect the intercept of any of these relations (p > 0.1), according to the lack of consistency in vertical gradients of respiratory-related variables.
One-hour average of stem temperature, (b) volumetric soil water content, and (c) sap flow rate (lines) with shoot water potential (orange dots) from 4 July to 14 August 2019.Shading in (c) indicates average ±1 SE across the beech trees (n = 4).maxima.By contrast, sap flow showed night-time reductions of ca.85%-90% relative to the daily maxima, denoting subdaily decoupling between CO 2 transport and the ARD.Subdaily variation in sap [CO 2 *] was minimal, with the highest values observed during night-time and limited reductions during daytime (<2%) according to the inverse relation between solubility and temperature.
Figure 7 summarises potential sources of discrepancy between CO 2 efflux and O 2 influx.The ARD could be attributed to an underestimation of the respiratory activity by CO 2 efflux measurements, an overestimation by O 2 influx, or a combination of both.In any case, we must be cautious about the specific methodological issues related to the measurement of the numerous variables monitored here (i.e., CO 2 efflux, O 2 influx, xylem [CO 2 ], sap flow, and sap pH), which might affect the magnitude of the mismatch between measurement approaches (see below).No apparent vertical patterns in stem CO 2 efflux, O 2 influx and xylem [CO 2 ] were observed along a 3-m-long stem segment (Figure 2), likely because of the modest vertical gradient in 38-mtall beech trees.The temporal variability of CO 2 efflux, O 2 influx and F I G U R E 2 (a) CO 2 efflux (E CO2 ), (b) O 2 influx (I O2 ), (c) the apparent respiratory quotient (ARQ; E CO2 /I O2 ) and (d) internal xylem [CO 2 ] at 1, 2.5 and 4 m height from 4 July to 14 August 2019.Sap pH (d, black dots) was measured from twigs (n = 3).[Color figure can be viewed at wileyonlinelibrary.com] xylem [CO 2 ] showed that temperature was the dominant environmental driver controlling R S , as similarly observed before (e.g., Acosta

F
I G U R E 3 Starch and soluble sugar concentration (mg g DW -1 ) in stem xylem tissues of beech trees at three stem heights, two wood depths, and two sampling dates (n = 4).Box whisker plots present the median, lower (25th), and upper (75th) percentiles, minimum and maximum values.Colours denote different sapwood depths.[Color figure can be viewed at wileyonlinelibrary.com]COMBINING THE CARBON-AND OXYGEN-BASED METHODS TO ELUCIDATE THE FATE OF CO 2 | 2687 13653040, 2023, 9, Downloaded from https://onlinelibrary.wiley.com/doi/10.1111/pce.14614by MPI 322 Chemical Ecology, Wiley Online Library on [02/01/2024].See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions)on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License nonneglectable contribution of CO 2 transport to R S , up to 1/3 in the lower stem segment, highlighting the potentially significant role of CO 2 xylem transport in diverting root-respired CO 2 from soil measurements(Aubrey & Teskey, 2021).Nevertheless, we found two lines of evidence refuting our hypothesis, as CO 2 internal fluxes could not bridge the gap between stem O 2 influx and CO 2 efflux.First, the relation between O 2 influx and R S diverged from the 1:1 line (Figure5b), as indicated by a slope different from the unit and a significant intercept.Furthermore, the marginal R 2 = 0.31 of this relation denotes that stem O 2 influx accounted for less than onethird of the variability in the carbon-based estimate of R S .Identical reasoning applies to the comparison between CO 2 internal fluxes (F T + ΔS) and ARD (Figure5c), with a marginal R 2 of 0.13, further supporting the limited potential of xylem CO 2 transport and storage to predict the ARD.Second, if the ARD could be primarily ascribed to xylem CO 2 transport, ARD and sap flow subdaily variability should follow similar patterns(Bowman et al., 2005; McGuire &   Teskey, 2004;McGuire et al., 2007).However, the subdaily variation in ARD was limited compared with sap flow (Figure6).Specifically, ARD maintained values above 50% of the daily maxima during nighttime, when sap flow was reduced to a much larger extent, down to 10%-15% of the daily maxima.Moreover, sap [CO 2 *] on a subdaily basis was remarkably stable, with minimal reductions during daytime ascribed to temperature-driven reductions in CO 2 solubility, partly offset by the daytime increase in respiratory activity and xylem [CO 2 ].Therefore, CO 2 solubility in sap could not significantly affect the strength of CO 2 transport as a mechanism to remove respired CO 2 from its production site.Taken together, subdaily patterns of ARD, sap flow and sap [CO 2 *] thus provide further evidence of the limited role of the transpiration stream in filling the gap between CO 2 efflux and O 2 influx in this study.This observation agrees with Hilman et al. (2019), showing the inability of sap flow to account for the variability in ARD of Q. ilex trees.

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I G U R E 4 Seasonal (left-hand-side panels) and subdaily (right-hand-side panels) variation in carbon-and oxygen-based estimates of stem respiration (R S and O 2 influx [I O2 ], respectively) in the lower (from 1 to 2.5 m) and upper (from 2.5 to 4 m) stem segments of four mature beech trees.Carbon-based R S is calculated as the sum of CO 2 efflux to the atmosphere (E CO2 ), CO 2 transport through the xylem (F T ) and CO 2 storage (ΔS).Mean values ± SE are shown with continuous lines and shaded areas.[Color figure can be viewed at wileyonlinelibrary.com] and deviances between carbon-based estimates of R S and O 2 influx.Moreover, if parenchyma cells were damaged upon sap extraction, the sample might be contaminated, resulting in an overestimation of the pH values(Tarvainen et al., 2023) and hence CO 2 transport.Another source of uncertainty in ARQ estimation is the relative humidity correction applied to estimate O 2 influx.The relative humidity sensor integrated into the [CO 2 ] sensor has a slow response time, as shown in Helm et al. (2021).Assuming an underestimation of humidity levels in the measurement chamber F I G U R E 5 (a) Relationship between daily stem CO 2 efflux (E CO2 ) and O 2 influx (I O2 ) denoting apparent respiratory quotients below the unit.(b) The relationship between carbon-based estimates of stem respiration (R S ) and O 2 influx illustrates the deviation from the 1:1 line and, thus, discrepancies between measurement approaches.(c) The relationship between the apparent respiratory difference (ARD) and internal CO 2 transport and storage (F T + ΔS) indicates the limited potential of internal CO 2 transport and storage to predict the difference between CO 2 efflux and O 2 influx.Measurements were performed in four mature beech trees (shown by different colours) in the lower (from 1 to 2.5 m) and upper (from 2.5 to 4 m) stem segments (shown by different point and line types).Dashed black lines show the 1:1 relation.[Color figure can be viewed at wileyonlinelibrary.com]F I G U R E 6 Subdaily variation in normalized values to the daily maxima of the apparent respiratory difference (ARD, as the difference between stem O 2 influx and CO 2 efflux), sap flow, and sap [CO 2 ] in the liquid phase ([CO 2 *]).The night-time reduction in ARD was limited compared with that of sap flow, indicating a limited role of the transpiration stream in filling the gap between CO 2 efflux and O 2 influx.Subdaily patterns were averaged across four beech trees and two stem locations (lower and upper) over the experimental period.[Color figure can be viewed at wileyonlinelibrary.com]F I G U R E 7 Overview of the potential factors contributing to the apparent respiratory difference (ARD), here observed as the difference between stem CO 2 efflux (E CO2 ) and O 2 influx (I O2 ) measurements (cf. Figure 5a).Our results suggest that CO 2 transport and PEPC-mediated fixation of CO 2 may be the main causes for the deviance from the 1:1 line.Nonrespiratory consumption of O 2 and respiratory substrate change can lead to overestimating stem respiration (R S ) by O 2 influx measurements.By contrast, R S underestimation by CO 2 efflux measurements can be driven by CO 2 transport through the xylem (although, if coming from below, it can also lead to R S overestimation [ * ] ), CO 2 storage in xylem sap, woody tissue photosynthesis (here avoided by using opaque stem chambers), light-induced axial CO 2 diffusion above or below the stem chamber, and PEPC-mediated fixation.Investigated processes within this study are shown with a black frame.[Color figure can be viewed at wileyonlinelibrary.com]COMBINING THE CARBON-AND OXYGEN-BASED METHODS TO ELUCIDATE THE FATE OF CO 2 | 2689 13653040, 2023, 9, Downloaded from https://onlinelibrary.wiley.com/doi/10.1111/pce.14614by MPI 322 Chemical Ecology, Wiley Online Library on [02/01/2024].See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions)on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License by, for example, 5%, the dilution correction required for O 2 estimation would increase the ARQ by ~0.001.