The long and tortuous path towards improving photosynthesis by engineering elevated mesophyll conductance

The growing demand for global food production is likely to be a deﬁning issue facing humanity over the next 50 years. In order to tackle this challenge, there is a desire to bioengineer crops with higher photosynthetic eﬃciencies, to increase yields. Recently, there has been a growing interest in engineering leaves with higher mesophyll conductance ( g m ), which would allow CO 2 to move more eﬃciently from the substomatal cavities to the chloroplast stroma. However, if crop yield gains are to be realised through this approach, it is essential that the methodological limitations associated with estimating gm are fully appreciated. In this review, we summarise these limitations, and outline the uncertainties and assumptions that can aﬀect the ﬁnal estimation of g m . Furthermore, we critically assess the predicted quantitative eﬀect that elevating g m will have on assimilation rates in crop species. We highlight the need for more theoretical modelling to determine whether altering g m is truly a viable route to improve crop performance. Finally, we oﬀer suggestions to guide future research on g m , which will help


Introduction
The global demand for food is projected to increase by as much as 2 quadrillion calories per year by 2050, meaning it will be necessary to produce approximately 50 -100 % more food, compared with 2010 (van Dijk et al., 2021).Whilst yields have gone up considerably over the last 70 years, this has been partially driven by changes in management practices, such as higher fertiliser use (Long et al., 2006).Beyond changing management practices, genetic improvements to crops have also contributed to increased yields, although this has been largely due to the development of genotypes with greater harvest indices, which partition a greater proportion of their biomass to the harvested product (e.g.grain).Based on these strategies, yields have seen an approximate doubling over the second half of the 20 th century.However, harvest indices of most staple crops are thought to be near their maxima and further gains from fertiliser use minimal, and hence alternative approaches must be considered, to meet the requirements of a growing global population.To this end, increasing photosynthetic efficiency of crops has been proposed as a viable route to elevate future yields (Smith et al., 2023;Zhu et al., 2010).
Several proof-of-principle studies have shown that bioengineering changes to photosynthesis can increase yields in C3 species.For example, introducing photorespiratory bypass pathways, speeding up the relaxation of photoprotection under fluctuating light, and increasing the catalytic flux through the Calvin-Benson-Bassham (CBB) cycle have all been shown to increase plant growth (De Souza et al., 2022.;Kromdijk et al., 2016;López-Calcagno et al., 2020;South et al., 2019;Yoon et al., 2020).However, these examples all involve changing the underlying biochemistry of leaves.Beyond changing biochemistry, an alternative route that has been proposed to increase photosynthetic rates is to reduce the diffusive limitations as CO2 moves from the atmosphere to the site of carboxylation (Gago et al., 2019;Salesse-Smith et al., 2023;Xiong, 2023).Of this diffusive limitation to photosynthesis, about half is the result of stomatal conductance, which confers some restriction to the rate at which CO2 can enter the leaf.Engineering higher stomatal conductance is likely to provide benefits to CO2 fixation, but would also result in greater water loss via evapotranspiration which is likely to be problematic as global temperatures rise (Leakey et al., 2019;Li et al., 2023).In contrast, reducing the diffusive resistance to CO2 within the leaf (i.e. from the substomatal cavities to the sites of carboxylation) may have the potential to increase photosynthetic rates without concurrent water losses (Zhu et al., 2010).As such, there is a growing interest in developing crops in which CO2 moves more efficiently within the mesophyll, as this may result in increased growth rates (Salesse-Smith et al., 2023;Wu et al., 2019).
The internal diffusive limitation to photosynthesis is most commonly considered using a parameter known as mesophyll conductance (gm is the reciprocal of resistance).This onedimensional value is often used to describe the efficiency with which CO2 moves from the substomatal cavities to the active site of the enzyme ribulose bisphosphate carboxylase oxygenase (Rubisco).It is worth noting that for the purpose of this review, a distinction is being drawn between gm and internal diffusive limitations to photosynthesis, as the former is a parameter that is used to describe the latter.The reason for this distinction is that gm is specifically describes the diffusive conductance to CO2 transfer within mesophyll tissue in the context of the Farquhar-von Caemmerer-Berry (FvCB) model of photosynthesis (Farquhar et al., 1980;von Caemmerer, 2000).Within this model, gm can be represented using Fick's 1 st law of diffusion as Equation 1 where An is the rate of CO2 assimilation, on a leaf area basis, Ci is the CO2 concentration in the substomatal cavity and Cc is the CO2 concentration at the site of carboxylation in the chloroplast (Fig. 1A).Whilst this model has seen a few adjustments since its initial publication, it remains by far the most used framework for describing the photosynthetic physiology of leaves (Yin et al., 2021).However, despite the huge benefits the FvCB model offers for assessing photosynthetic physiology, there are significant ambiguities that arise from using gm to describe the internal diffusive limitations to photosynthesis.Here we outline these and critically assess the hurdles that must be overcome if photosynthetic rates are to be increased by transgenically elevating gm.

How is mesophyll conductance (g m ) estimated?
One major limitation of using gm to represent the diffusive limitation to photosynthesis arises from the fact that there is no way to directly measure Cc, the CO2 concentration at the site of carboxylation.Therefore, whilst it is possible to estimate An and Ci (although see caveats to this in section 4), there is no simple way to solve Equation 1.Some elegant solutions have been used to estimate Cc indirectly, with the two most common methods combining gas exchange with either isotopic signals or pulse-amplitude-modulated chlorophyll fluorescence to make these inferences.Here we outline the theoretical basis of these approaches, but readers are referred to Pons et al., (2009) and Warren, (2006) for more detail and methodological considerations.

Combined gas exchange and isotope analysis
The isotope method leverages the fact that C3 plants discriminate against 13 CO2, which is naturally occurring as roughly 1.1 % of total atmospheric CO2, but is heavier and thus reacts and diffuses slower than 12 CO2, which makes up the remaining 98.9 %.In the atmosphere, the slower-and faster-moving isotopes will remain mixed, as there is no directionality to net diffusion.However, during photosynthesis CO2 moves into the leaf from the atmosphere, at a rate that is proportional to Ca-Ci.Hence, just by diffusion alone, leaves will discriminate against the slower moving 13 CO2, by a fractionation factor (a) of 4.4 ‰.Furthermore, the enzyme Rubisco preferentially fixes 12 CO2, with a fractionation factor (b) of 29 ‰.Finally, there will be discrimination due to diffusion through the boundary layer (ab), due to the dissolution of CO2 into water (am), and as a result of respiration (e) and photorespiration (f).In a scenario where gm is ignored (i.e.gm = ∞), overall 13 CO2 discrimination (D 13 C) can be predicted using these fractionation factors, alongside An, Ci, Ca and Cs (the CO2 concentration at the surface of the leaf) using Equation 2 (Farquhar & Cernusak, 2012) Equation 2 where t is the ternary correction factor due to transpiration, RL is day-time respiration and G* is the Cc at which CO2 assimilation within the chloroplasts is equal to CO2 release from the mitochondria due to photorespiration.However, note that Equation 2 assumes that Ci = Cc.D 13 C can be measured directly (D 13 Cobs) by analysing the gas that has passed over a photosynthesising leaf.D 13 Cobs is typically less than D 13 C, as a consequence of Cc being lower than Ci.This difference is represented in Fig. 2, which depicts modelled D 13 C (assuming Ci = Cc) and D 13 Cobs values that would occur from two different gm values.The difference between D 13 Cobs and D 13 C can be used to infer Cc and hence solve Equation 1 using:

Combined gas exchange and fluorescence
Another way to estimate Cc leverages the relationship between whole-chain electron transport rate (J) and An.Within the FvCB model, An can be predicted from Equation 4 when electron transport rate is limiting photosynthetic rates, where JA is used to specify the value of the electron transport rate approximated from gas exchange (Farquhar et al., 1980;von Caemmerer, 2000).Because Cc will relate to gm according to Equation 1, Equation 4 is typically rearranged as: . * /0 2 12(  14 4 )6 0 2 78(  14 4 ) .However, it is not possible to estimate J from gas exchange alone, without prior knowledge of gm.Instead, PAM chlorophyll fluorescence measurements can be used to estimate J, which can be substituted into Equation 5, thereby determining Cc, which can in turn be used to solve Equation 1 (Harley et al., 1992).Chloroplast electron transport based on fluorescence (JF) can be calculated as Equation 6 9 =  :;< × ) 9 5 6 79 6 9 5 6 1 ×  =>?? , where Iabs is the fraction of light absorbed by a leaf, F' is steady state fluorescence, Fm' is maximal fluorescence and fPSII is the relative absorption of light by photosystem II.However, substituting JA with JF assumes that all electron transport associated with JF is functioning to support photosynthesis and photorespiration, and no other ATP demands are present in the leaf.To account for alternative ATP sinks as well as measurement imperfections, a 'calibration curve' is often constructed, where JF and An are measured under 2 % O2, to minimise the contribution of photorespiration.By measuring under non-photorespiratory conditions, JF can be compared to JA from Equation 5, thereby determining a correction factor that can be applied under 21 % O2.

Unmeasurable components
Within the FvCB model, gm represents a composite trait that combines all anatomical and biochemical phenomena that affect the diffusive limitation to photosynthesis.This means that gm will be determined by the conductance of gaseous CO2 through the internal air space (gIAS), as well as the conductance to CO2 after it dissolves into the liquid phase (gcell) (Fig. 1B).Recently, a new methodological approach to quantify the CO2 concentration at the surface of cells (Cw) allowed the direct estimation of gcell, which was 15 % lower than bulk gm in sunflower leaves at an atmospheric CO2 concentration of 400 ppm (Márquez et al., 2023).However, despite being able to experimentally dissect gIAS from gcell, the underlying biological traits that determine these conductances remain uncertain.Conceptually, gIAS is more straightforward, as it is likely determined by the porosity, tortuosity and lateral path length of the IAS within leaves, which can all be measured using X-ray micro-CT scanning and other emerging techniques for 3D anatomical imaging (Earles et al., 2018;Harwood, 2023;Harwood et al., 2020;Lundgren et al., 2019;Théroux-Rancourt et al., 2017, 2021).In contrast, gcell will be determined by the conductance associated with CO2 transfer through the cell wall (gcw), plasma membrane (gpm), cytoplasm (gcyt) and chloroplast envelope (gchl) (Fig. 1B) (Lawson et al., 2022).Unfortunately, no methodology exist to experimentally estimate any of these fine resolution conductances in vivo.Furthermore, modelling efforts to dissect gcell into constituent conductances, are highly dependent on the assumed permeability of membranes to CO2, for which there is no satisfactory consensus (Evans, 2021;Gutknecht et al., 1977;Sarkar et al., 2023).Consequently, the relative contribution that different components of the CO2 transfer pathway have on the overall estimate of gm remains unknown.
The lack of experimental methods available to directly measure fine resolution conductances (gcw, gpm, gcyt, etc) limits researchers' ability to move beyond correlative studies to generate a true mechanistic understanding of which part of the leaf has the biggest impact on gm.Due to the composite nature of gm, interspecific comparisons are potentially confounded by both the allometric scaling rules that govern leaf development and the biomechanical interactions between different parts of the leaf.For example, if cell size, cell packing and cell wall thickness correlate, it becomes extremely difficult to determine which trait is governing intraspecific differences in gcell and thence gm (John et al., 2013;Théroux-Rancourt et al., 2021;Wilson et al., 2021).Furthermore, there may be cryptic allometric trait relationships that are undetectable using current imaging techniques; if cell wall thickness correlates with cell wall porosity or tortuosity, then this may further obscure relationships between anatomy and gm.In addition, the different components of a leaf may biomechanically interact with each other, in ways that can further complicate interpretations.For example, if cell wall thickness impacts turgor pressure, this may cause changes to vesicular exocytosis (and hence membrane protein composition) and plasma membrane thickness, both of which could impact gpm and make it extremely difficult to appreciate the causes of interspecific differences in gm (Bacete et al., 2022;Coster et al., 1977;Fricke et al., 2000).Likewise, evidence is emerging that cell walls may, at times, experience substantially lower water potentials than the cells they surround, suggesting that plasma membrane channels may be acting to regulate and restrict hydraulic conductance (Buckley & Sack, 2019;Cernusak et al., 2018;Wong et al., 2022).Low apoplastic water potentials would result in the aqueous meniscus within the cell walls becoming more concave, due to the Kelvin effect.This concavity would increase the solubility of CO2, thereby causing an increase to gcw that is mechanistically driven primarily by the plasma membrane, rather than cell wall properties themselves (Vesala et al., 2017).Whilst the aforementioned considerations are speculative, they stress the point that without the ability to directly measure gcw and gpm, it is extremely difficult to generate robust interpretations of what biological phenomena drive interspecific differences in gm.
In addition to interspecific comparisons, studies of transgenic plants suffer from similar limitations, as any genetic manipulation can affect multiple traits, making it difficult to draw robust conclusions.For example, a study into rice plants with perturbed mixed linkage glucans found that Cs/Fs knockout lines had reduced gm, compared to WT.These knockout lines had reduced cell wall thickness and chloroplast area exposed to IAS (Sc), and may have lower effective cell wall porosity (i.e.porosity divided by tortuosity).Whilst this study is extremely thorough, and makes efforts to consider multiple aspects of leaf physiology, it is difficult to determine cause and effect leading to the observed decreases in gm.Likewise, the growing literature on aquaporin knockout lines suffer from their inability to distinguish between the putative role that these membrane proteins play in transporting CO2, from pleiotropic effects that aquaporin manipulations may have on anatomy and the water status of leaves, which could both contribute to gm (Ding et al., 2019;Postaire et al., 2010;Prado et al., 2013).It is possible that such indirect effects have driven the inconsistent conclusions drawn from studies exploring gm in plants with manipulated aquaporin expression (Clarke et al., 2022;Heckwolf et al., 2011;Huang et al., 2021;Kromdijk et al., 2020;Xu et al., 2019).However, without the ability to directly measure gpm, it is very difficult to verify this.
The difficulties in determining which parts of the leaf limit gm, outlined above, are a direct consequence of this parameter being a composite trait, for which there are very few ways to analyse the constituent components.This is a major hurdle for bioengineering efforts, as this prevents researchers' ability to identify unambiguous phenotypic targets to transform.Therefore, whilst it is conceptually appealing to direct efforts towards bioengineering plants with elevated gm to increase photosynthesis or intrinsic water use efficiency, reducing this concept to practice has proven difficult.
Finally, of all the unmeasurable components mentioned thus far, an inability to directly determine conductance across the chloroplast envelope (gch) results in unique issues for the final estimation of gm.The reason for this is that Equation 1 assumes all CO2 assimilated by Rubisco is moving from the substomatal cavities to the stroma and can therefore be represented by a single conductance value.However, CO2 produced from respiration and photorespiration will originate in the mitochondria, and subsequently move to the chloroplasts without passing through the IAS, cell wall, plasma membrane, and most of the cytoplasm (Tholen et al., 2012;Tholen & Zhu, 2011).Consequently, the gchl:gm ratio and the rate of (photo)respiration have an impact on the final estimations of mesophyll conductance.This can be represented as Equation 7 , where gm' is used here to denote the 'apparent' mesophyll conductance (i.e. the value determined from the methodologies outlined in Section 2 of this paper), rm is the true total resistance from the substomatal cavity to the stroma (i.e. the reciprocal of gm), w is the ratio of rchl to rm, F is the rate of photorespiration and s is the fraction of (photo)respired CO2 that is not reassimilated (Yin & Struik, 2017).Under this scenario, a finite value of gchl results in a biased gm estimation (i.e.gm' ≠ gm), if any CO2 originating in the mitochondria is not reassimilated by chloroplasts.Whilst it is probable that a large proportion of (photo)respired CO2 is reassimilated, it is unlikely that s = 0 because a small fraction of mitochondria are located externally to chloroplasts within cells in C3 species (Harwood et al., 2020;Hatakeyama & Ueno, 2017;Sage & Sage, 2009).Furthermore, a recent study analysing transgenic tobacco plants with larger chloroplasts found that gm was lower in FTSZ1-16 lines than WT, but that this difference was less pronounced when photorespiration was inhibited (Głowacka et al., 2023).This observation indicates that photorespiratory CO2 fluxes are contributing to the final estimation of gm', and thus gchl must be non-negligible.As a result, the final estimation of gm will be offset from the true value, but without the ability to directly measure gchl the extent that this happens remains unknown (Gu & Sun, 2014).

Accumulation of uncertainty
Both isotope-and fluorescence-based methods for estimating gm are highly derived, often requiring several inputs, each of which themselves are associated with considerable ambiguity.As a result, the final calculated value of gm incorporates multiple uncertainties, which limits the ability to draw robust conclusions.Here, we outline the various uncertainties that go into the estimation of gm using the 13 C isotope or fluorescence-based techniques.It is important to note that we do not cover the curve-fitting method, which is based on gas exchange alone (Ethier & Livingston, 2004).Although this method can result in reasonable gm estimates, the available information in gas exchange alone is often insufficient to arrive at unique solutions and is therefore considered inferior to methods that incorporate additional measurements to better constrain the model equations (Pons et al., 2009).

Respiration in the light (RL)
Both methods to estimate gm employ gas exchange, and consequently share a number of parameter inputs, which are each associated with their own estimation error.One example is respiration rate in the light, RL.Measuring RL is somewhat problematic, because the CO2 produced from this process is masked by photosynthetic assimilation.Some studies approximate RL as half of the respiratory rate in the dark (RD), although this assumption is unlikely to provide a precise estimate.Of the techniques that exist to estimate RL in vivo, the most commonly used is the Laisk method, which measures An vs Ci, at a range of subsaturating light intensities (Brooks & Farquhar, 1985;Laisk, 1977;Schmiege et al., 2023).Assuming that RL does not change with light intensity, the A/Ci slopes will theoretically intersect where An = -RL.However, in reality the regression lines do not intersect at a single point, because the relationship between An and Ci is not perfectly linear (Gu & Sun, 2014).Gu and Sun demonstrated that even when A/Ci relationships could be approximated well via linear regressions (i.e.R 2 > 0.95), the non-linearity of these slopes would result in an underestimation of RL.This issue has been largely resolved by the implementation of a slopeintercept regression approach, but it remains critical that the Laisk method is performed only on Ci values less than 10 Pa, and that the distance between slopes is roughly equal (Walker & Ort, 2015).Furthermore, it is worth noting that whilst the slope-intercept regression method increases the reliability of estimations of RL, Walker and Ort show that this parameter is vulnerable to noise in gas exchange data.This is problematic, because ideally RL for every replicate leaf should be measured and subsequently used to estimate gm, rather than inputting the average for each treatment/species in an experiment.However, the Laisk method's sensitivity to noise makes it difficult to generate precise estimates of RL for each individual leaf, which may introduce error into the final estimation of gm.One potential way to overcome the issues associated with estimating RL via the Laisk method is to employ the combined gas exchange and chlorophyll fluorescence technique described by Yin et al., (2009).This method involves finding the slope between An and  × )  (Yin et al., 2011).Thus, going forward, the Yin method should receive greater attention in attempts to parameterise models to estimate gm.

The photorespiratory CO2 compensation point (G*)
Another parameter that is important for both isotope-and fluorescence-based techniques is the photorespiratory CO2 compensation point, G*: the Cc at which photosynthetic CO2 uptake is equal in magnitude to CO2 lost from photorespiration.G* is usually estimated from the Laisk method based on the Ci at which An = -RL (von Caemmerer, 2000).As mentioned above, the A/Ci curves should intersect where An = -RL, and hence the Ci value at this point is representative of the photorespiratory compensation point.Thus, the Laisk method does not actually provide the true G*, but instead estimates the photorespiratory compensation point on a Ci basis (Ci*).G* and Ci* relate according to Equation 8: Solving Equation 8 requires pre-existing knowledge of gm which, in turn, requires G* to calculate.A few approaches can be employed to work around this circularity, but each has its own limitations.For example, G* can be estimated from in vitro measurements of the specificity of Rubisco to CO2 and O2 (SC/O) (Xiong, 2023).However, it remains unclear if in vitro biochemical estimates will truly match the kinetics of Rubisco in vivo (Walker et al., 2017).Another work-around involves using an initial value of gm (usually taken from a literature source) to iteratively solve Equation 8 (Weise et al., 2015).While this in itself will also generate an estimate of gm, it is not clear if published values of gm under ambient conditions will be equivalent to those at the photorespiratory compensation point, because for the latter, most of the CO2 being fixed in the chloroplasts will originate in the mitochondria and will not be subject to resistance from the cell walls and plasma membrane.Finally, many studies simply assume G* = Ci*, but this will inevitably result in G* being underestimated (Du et al., 2019;Lanigan et al., 2008;Liu et al., 2023;Meng et al., 2023;Mizokami et al., 2019).CO2 concentration in the substomatal cavities (Ci) Finally, there are errors associated with the estimation of Ci, the CO2 concentration in the substomatal cavities.Ci cannot be directly measured, so it is instead estimated based on the stomatal conductance to water.If the ternary effect of transpiration is ignored, for simplicity, Ci can be estimated as Equation 9 # =  : − 1.6 ) 1, where gsw is the stomatal conductance to water, and 1.6 is the ratio of diffusivity between H2O and CO2 (Lamour et al., 2022).Equation 9 assumes all water is exiting the leaf via the stomata.However, in many leaves, small fluxes of water will exit the leaf via the cuticle.Taking this into account, Ci is calculated as Equation 10 # = I < H :; 1I < H =>?.; 7A.K  L A.KH =>?.; 1 H :; L , where gcut.w is the cuticular conductance to water, and ζ is the ratio of diffusivity between H2O and CO2 across the cuticle.Because ζ is much higher than 1.6 (measurements on a limited number of species are in the range of 20-40), Ci calculated from Equation 9 will be an overestimation (Márquez et al., 2021).Methods to measure gcut.w and ζ do exist, but these are time-consuming and have not yet been routinely adopted in experiments addressing gm (Márquez et al., 2022).Furthermore, gcut.wappears to vary intra-and interspecifically, and depending on the water status of a leaf, meaning correcting gas exchange data based on species averages is unlikely to prove a viable solution (Boyer, 2015b(Boyer, , 2015a;;Márquez et al., 2022).Consequently, most estimates of gm are likely to incorporate error, due to an incorrect value of Ci.It is also worth noting that the Laisk method, described above, plots An against Ci, and thus using Equation 9to calculate Ci will also result in further error in the estimation of Ci*.Finally, it is important to mention that the estimation of Ci is also vulnerable to inaccurate leaf temperature measurements.Both Equations 9 and 10 rely on an accurate determination of gsw, which in turn is calculated based on the total conductance to water (gtw).Within a gas exchange cuvette, gtw is estimated by, Equation 11 # −  $ where E is the evapotranspiration rate, WS is the molar concentration of water in gas that has passed over the leaf and Wl is the molar concentration of water in the substomatal cavities.
Wl is assumed to be saturated, and hence this value is dependent on the temperature of the leaf, which will impact the holding capacity of the air.If the temperature of the leaf is not measured accurately, gtw will be incorrectly estimated, which will have a knock-on effect on the value of Ci, and ultimately gm.Inaccurate determination of leaf temperature arises primarily due to the influence of cuvette air temperature on leaf thermocouple measurements in off-the-shelf instruments and were still a significant issue in the widely used LI-6400XT IRGA platform (Tyree & Wilmot, 1990;Zhang & Zhang, 2019).However, recently a comparison of LI-6400XT and LI-6800 platforms indicated that the latter introduces fewer errors from inaccurate temperature estimates (Garen et al., 2022).Nevertheless, even the newer LI-6800 instruments will introduce a degree of inaccuracy in their reported air-leaf temperature differences.Despite achieving a good degree of accuracy for most measurements, some estimates of Ci can be misestimated by more than 25 % due to measurement bias in leaf temperature (Garen et al., 2022).Inaccurate measurements of leaf temperature in gas exchange cuvettes therefore introduce another source of uncertainty in the determination of Ci.In combination with the aforementioned issue surrounding cuticular conductance, Ci has the potential to introduce significant error into the final estimation of gm.

Uncertainty specific to the chlorophyll fluorescence method Mismatch between chloroplast populations probed by fluorescence and gas exchange
In addition to considerations regarding G*, RL and Ci, a major source of uncertainty when estimating gm via combined fluorescence and gas exchange comes from the fact that these two techniques probe different populations of chloroplasts.If gs is sufficiently homogenous across the leaf surface, gas exchange techniques will determine a rate of CO2 assimilation based on all the photosynthetically active mesophyll cells within a given area of leaf.On the other hand, fluorescence is biased towards cells closest to the measuring light source.If an adaxial light source is applied to a leaf, a greater proportion of light will be absorbed by the adaxial tissue, compared to the abaxial tissue (Slattery et al., 2016;Vogelmann & Evans, 2002).This is problematic when calculating gm, if Ci and Cc terms in Equation 1 are based on different populations of chloroplasts.In fact, Evans et al., (2017) point out that whilst fluorescence can be used to estimate JF, Equation 6 will only be able to determine the true linear electron transport rate when the light absorbance profile in a leaf is the same as the adaxial-abaxial profile of photosynthetic capacity (Evans et al., 2017).
However, this condition is rarely met.Efforts to assess the distribution of CO2 assimilation in spinach have suggested that more carbon is fixed on the adaxial side of the leaf (Evans & Vogelmann, 2003).However, the C fixation profile, determined from C 14 pulse-labelling did not match the light absorption profile determined from chlorophyll fluorescence.This issue may be exaggerated depending on the light source used, as light absorption profiles within leaves are wavelength dependent.For example, blue light is absorbed more readily, whereas red light penetrates deeper into leaves.This results in JF going up as the ratio of blue to red light increases, despite the fact that estimations based on gas exchange suggest linear electron transport rate remains relatively constant under these varying light regimes (Evans et al., 2017).Such discrepancies between fluorescence-and gas exchange-based estimates highlight that, whilst these methods both assess the photosynthetic physiology of leaves, care must be taken and errors can be introduced when both techniques are combined.

Uncertainty specific to the isotope method Fractionation factor associated with carboxylation (b)
While the isotope method does not suffer from mismatched populations of chloroplasts probed by the two techniques, the precise values of several fractionation factors used in the Δ 13 C model can be hard to pin-point.First of all, estimation of gm using combined gas exchange and isotope discrimination analysis requires knowledge of the fractionation factor associated with carboxylation (b).Most studies employ a b of 29 ‰ in their models: a value based on biochemical analyses of Rubisco extracted from spinach leaves (Roeske & O'Leary, 1984).Whilst the kinetic properties of Rubisco are very conserved across C3 land plants, there is still some variability, and it is not clear if these differences will result in different b values.One attempt to quantify b, in vivo, used transgenic tobacco plants expressing Rubisco large subunits (RbcL) from Flaveria (Von Caemmerer et al., 2014).This study concluded that b values for transgenic plants were also 29 ‰.However, the kinetic properties of Rubisco appear to be phylogenetically constrained, due to the slow rate of evolution of RbcL (Bouvier et al., 2021(Bouvier et al., , 2022)).As Nicotiana and Flaveria both fall within the Core Asterid clade, a comparison of these genera may not reflect the full diversity of Rubisco kinetics across the angiosperms (Zhang et al., 2020).This is particularly important when considering that many staple crop species are in the monocot family, Poaceae, and hence quite distantly related to the Asterids.Furthermore, von Caemmerer et al., (2014) point out that their calculation of b assumes equal gm between transgenic and WT plants.However, a 35 % difference in gm between lines would equate to b being underestimated by 5 ‰, and this bias becomes substantially greater if gm differs by more than 50 %.Consequently, it remains unclear if using a b value of 29 ‰ for all species is a valid approach.
It is important to mention that C3 plants possess another enzymatic reaction capable of fixing CO2.Carbonic anhydrase can convert CO2 to H2CO3, which can then be fixed via the enzyme phosphoenolpyruvate carboxylase (PEPC) into oxaloacetate.The value of b in Equation 2 is the fractionation that occurs during carboxylation, and hence it is determined by both the Rubisco plus the dual action of carbonic anhydrase and PEPC.It is often assumed that PEPC activity is negligible in C3 leaves, and so b can be approximated entirely on in vitro Rubisco values.However, recent carbon labelling experiments have indicated that PEPC may play a greater role in diurnal assimilation: accounting for 2 % of total assimilatory C uptake under ambient conditions and as much as 40 % when photorespiration is high, in sunflower leaves (Abadie & Tcherkez, 2019;You et al., 2020).It is unclear how PEPC-based assimilation rates vary between species which makes it unclear if results based on sunflower can be extrapolated to all crops (Abadie & Tcherkez, 2019).
It may still be tempting to conclude from the aforementioned discussion that b = 29 ‰ is still a good approximation.One might argue that a 2 -5 % error in b is not large enough to cause real issues to the final estimation of gm.However, sensitivity analyses have indicated that b has a particularly large effect on the final estimation of gm, and so small errors may be important (Gu & Sun, 2014;Mizokami et al., 2019).In fact, even the original determination of b, from extracted spinach Rubisco held at pH 8 and 25 °C, ranged from 26.6 to 30.3 ‰, which represents -10 % and +4.4% differences in b, respectively (Roeske & O'Leary, 1984).These differences could result in gm being miscalculated by as much as 25 %, and thus pose a real issue (Gu & Sun, 2014).

Fractionation associated with photorespiration (f)
The fractionation associated with photorespiration, f, is another source of uncertainty in models that estimate gm from combined gas exchange and isotope analysis.Analysis of three species in the genus Senecio, and subsequently of tobacco suggested that f may be > 10 ‰ (Evans & Von Caemmerer, 2013;Lanigan et al., 2008).As is the case with b, most estimations of gm must assume a value of f that remains constant across species, genotypes or experimental conditions.However, this assumption has not been tested, and in most cases a value calculated from tobacco is used (16.6 ‰) (Lanigan et al., 2008).It is worth noting that, unlike b, f is the fractionation that occurs during several reactions, which constitute the photorespiratory pathway (Gillon et al., 1998).The carbon fluxes through photorespiratory pathway may vary, as there have been suggestions that the amino acids, glycine and serine, may be exported from this pathway (Busch et al., 2018;Fu et al., 2022).If the conversion of glycine to serine represents a significant fractionation step in the photorespiratory pathway, then glycine export could have a meaningful impact on f, which would depend on the nitrogen source available to the plant (Busch et al., 2018;Schmiege et al., 2023;Tcherkez, 2006).There is still a real uncertainty surrounding the true value of f, and whether this value remains constant between species or under different environmental conditions.This issue is difficult to resolve, especially because estimation of f is highly dependent on the assumed values for b and G*.Evans and von Caemmerer (2013) showed that the estimation of f was linearly dependent on the assumed b value used; f = 16.6 ‰ corresponds to a situation where b = 29 ‰.This co-dependency means it is not truly possible to solve for f, but instead only for the relationship between f and b.For example, a recent comparison of tobacco and Rhazya stricta (Apocynaceae) found that f ranged from 10 to 30 ‰ but did not significantly differ between species (Gregory et al., 2023).However, this statistical comparison assumed b was constant.Rather than comparing f, it would be interesting to assess whether the gradient between f and b varies significantly between these species.Nevertheless, such an analysis cannot yield a single f value that can be input into Equation 2. Similarly, f was estimated in tobacco lines with reduced glycine decarboxylase complex H-subunit expression (gdch-KD), showing significantly lower f fractionation, compared with WT plants (Giuliani et al., 2019).This difference is likely to represent a real biological phenomenon, but it is important to note that the estimation of f is influenced by the assumed G*, which may be higher in gdch-KD plants due to their altered photorespiratory fluxes.Hence, this represents another case where deriving an unambiguous and precise estimate of f remains elusive.Whilst sensitivity analyses suggest that the final estimation of gm is less vulnerable to differences in f, than is the case for b (Gu & Sun, 2014), the arguments presented above show that these sensitivity analyses fail to capture the inter-dependencies in estimation of the parameters in the isotope discrimination model.

Mesophyll conductance frameworks don't capture the 3D nature of diffusion within leaves
A major shortcoming of using gm to describe the diffusive resistance to internal CO2 movement is that this parameter cannot account for the three-dimensional structure of leaves.After moving through the stomata, CO2 will move within the 3D geometry of a leaf mesophyll, and hence is not well characterised by a single one-dimensional value.One issue that arises from this has already been described in section 3; a finite gchl can lead to miscalculation of gm if some CO2 originates from the mitochondria.However, the issues that occur from using a one-dimensional value to represent a three-dimensional process go beyond the specific considerations surrounding gchl.Namely, there are multiple routes that a given CO2 molecule can take from the substomatal cavity to the site of carboxylation.Whilst the CO2 concentration at the surface of cells (Cw) may be uniform within the mesophyll tissue, the distance each CO2 molecule must travel before dissolving into the liquid phase is highly heterogenous (Márquez et al., 2023).Likewise, within a cell, the pathway a given CO2 molecule must travel will depend on the proximity between the site of dissolution and the chloroplasts.If a chloroplast is ovoid shaped, then the location halfway along the length of this organelle will be closest to the cell wall, and will require the shortest path length for CO2 to reach it (Tomás et al., 2013).In contrast, CO2 moving through the cell wall at a position adjacent to the chloroplast tips, or a position that does not have a chloroplast directly adjacent to it, will have further to travel through the cytoplasm before reaching the chloroplast.The variable path lengths for CO2 are problematic when considering the diffusive resistance in terms of a one-dimensional conductance value, because Equation 1 implicitly assumes all CO2 fixation occurs in a single location, and as a result the stromal CO2 concentration can be approximated by one value, Cc.However, if the path length for CO2 movement within leaves is variable, the value of gm becomes dependent on the assimilation rate (Parkhurst, 1994).Consequently, An limits gm, rather than the other way round, making it problematic to confidently compare gm in any two species/genotypes that exhibit different assimilation rates.This is particularly problematic when considering the goal of engineering higher photosynthetic rates by manipulating gm as it becomes difficult to dissect cause and effect in experimental studies.

Have the potential benefits of increasing g m to photosynthesis been tested with sufficient rigour?
The sections above have focused on the various technical and conceptual issues that exist when using gm as a parameter to describe the internal diffusive limitations to photosynthesis.Despite these methodological challenges, one might argue that the desire to manipulate the diffusive path for CO2 within leaves is still a worthwhile endeavour, especially if this has the potential to increase crop yields (Lundgren & Fleming, 2020).However, the theoretical benefits of enhancing gm in crops must be quantitatively assessed, to predict whether this approach is likely to result in worthwhile increases in assimilation.To this end, many studies have explored the relative limitations that gm, stomatal conductance to CO2 (gsc), and biochemistry impose on assimilation.These limitations, which sum to 100 %, are denoted as Lm, Ls and Lb, respectively, and can be calculated by (Grassi & Magnani, 2005) Equation 12 , where the total conductance (gt) is calculated by Equation 15 N = A A/H : 1A/H 5 .Crop species tend to exhibit Lm values between 20 -40 %, leading many to conclude that elevating gm is likely to confer a substantial benefit to assimilation rates.However, it is important to note that calculating Lm using Equation 12does not truly determine the extent to which assimilation is limited by gm, but rather estimates how much the limitation imposed by gm compares to limitations imposed by gsc and biochemistry.Importantly, this means that if Lm were reduced in a plant from 30 to 0 %, this would not necessarily result in a 30 % increase in assimilation.In fact, it is possible that such a change could have only a negligible impact on An, if gm, gsc and Jmax were sufficiently high.In contrast, an alternative calculation for the limitation imposed by gm can be applied (Warren et al., 2003), where Equation 16 !@ = P AB 7P A P AB × 100.L'm is used here to differentiate from Lm calculated according to Grassi and Magnani (2005).Anp is the assimilation rate where Cc = Ci (i.e.assuming gm is infinite), and An is assimilation under ambient conditions.In contrast to Lm, the estimation of L'm directly calculates the extent to which a finite gm reduces assimilation.L'm was calculated as a part of a metaanalysis, which sought to compare plant functional types.This analysis found that all annual herbaceous species (a plant functional type to which most crops belong) had L'm values < 32 %, with approximately half being < 10 %.These numbers match well with a reanalysis of recently published data for 10 major crop species (Xiong, 2023).Using gm values derived from the isotopic method and assuming Jmax was double Vcmax we estimated L'm to range from 7.7 to 16.2 % (Fig. 3B).This indicates that even if it were possible to engineer an infinite gm, a 30 % increase in steady-state assimilation would not be realised.In fact, using these published data to model steady state photosynthetic rates we predict that a 125 % increase in gm would only lead to a 5.7 -10.2 % higher An, depending of the species (Fig. 3D).Likewise, recent crop productivity models have predicted that increasing gm will result in minimal increases to crop yields, and that the benefits of increasing biochemical capacity far outstrip any benefits derived from elevating gm (Harbinson & Yin, 2023;Wu et al., 2019).Consequently, it remains unclear if altering gm can truly be considered a viable route to producing meaningful elevations to assimilation and yield in crops.

Future Directions
In this review, we have summarised 4 conceptual drawbacks that limit attempts to engineer higher crop yields by elevating gm.Here, we offer suggestions for how these issues can be addressed by the scientific community going forward.

Check for pleiotropic effects
Section 3 of this paper highlights that many of the small-scale conductances (e.g., gcw, gpm, gch -see Fig. 1B) that contribute to the overall gm cannot be directly measured or reliably estimated.This makes it difficult to pinpoint the exact effect a given trait is having, and hence makes comparative analyses vulnerable to confounding variables.In the absence of establishing methods to directly measure small-scale conductances, it is essential that we devise ways to minimise the impact that confounding variables have on the interpretation of experimental data.To this end, greater emphasis should be applied to identify transgenic manipulations that can alter gm in the absence of pleiotropic changes.Focus should, therefore, be directed to identify plants where a transgenic manipulation directly effects gm via a single alteration to leaf anatomy/physiology.For example, changing the abundance of a cell wall polysaccharide or a plasma membrane aquaporin should only be interpreted as driving an alteration in gm if said transgenic manipulation did not inadvertently alter leaf anatomy or physiology otherwise.Furthermore, the link between gm and assimilation rates may also be vulnerable to confounding variables if transgenic lines have different biochemical capacities for photosynthesis than WT plants.Put simply, it is difficult to confidently conclude that gm is affecting An, if Vcmax and Jmax also vary.Therefore, future work should ensure that Vcmax and Jmax are always reported alongside gm, as this information is integral to understanding whether elevated assimilation rates can be interpreted as the direct result of changing gm.Taken together, the 'holy grail' is a scenario where a genetic manipulation alters gm without any anatomical pleiotropy, and where the altered gm results in higher An without any observable differences in Vcmax or Jmax.To date, no such genetic manipulation has been identified, but if such a discovery were to be made it would provide critical proof of concept that changing gm is a viable route to improving photosynthetic performance of crops.

Employ Sensitivity Analyses
In section 4, we outlined the fact that gm is highly derived, and therefore suffers from the accumulation of measurement errors.One way to circumvent this issue is for sensitivity analyses to become a routine part of the statistical analyses conducted on any experimental data set.Conceptually, this involves varying input parameters (e.g., b, f, G*), within a reasonable range, to ensure that a statistical comparison remains robust.The idea of employing sensitivity analyses after the estimation of gm is not new (Pons et al., 2009;Warren, 2006); however, such approaches are rarely adopted.In cases where sensitivity analyses have been conducted, each input parameter is often independently varied, to assess the impact that this has on a given statistical comparison (Giuliani et al., 2019;Mizokami et al., 2019;Weise et al., 2015).However, a more robust approach would be to employ routine multiparameter sensitivity analysis, to reconstruct confidence intervals for each estimated gm value.Such an approach would account for the interdependency of input parameters that are required for the models that estimate gm.

Reaction Diffusion Models to capture 3D movement of CO2 within leaves
As discussed in section 5, there are substantial limitations associated with using a onedimensional value, gm, to describe the three-dimensional movement of CO2 within leaves.One way to overcome these issues is through the employment of reaction-diffusion models, which can be integrated into 3D descriptions of leaf anatomy (Berghuijs et al., 2016).Early reaction-diffusion models applied somewhat simplified geometries to represent leaf and organelle anatomy (Aalto & Juurola, 2002;Tholen & Zhu, 2011).However, recent advances in 3D image acquisition have allowed a more nuanced anatomical arrangements to be described.For example, recently, X-ray micro-CT scanning was combined with confocal and electron microscopy to analyse the arrangement of cells and chloroplasts within rice leaves (Xiao et al., 2023).These data were then used to model a 'virtual leaf' which was scrutinised with a sensitivity analysis, to predict how changing a variety of anatomical traits would impact assimilation rates.Going forward, construction of these models in a greater range of crop species, with increasing levels of anatomical and biochemical detail, should be prioritised, to complement research estimating gm (Harwood, 2023).It is worth noting that whilst reactiondiffusion models can be integrated with the 3D arrangement of leaves, these models are only able to simulate leaf physiology, and therefore should not replace traditional data-driven estimations of gm.In fact, a combination of both approaches has the potential to considerably push the field forwards.For example, conducting sensitivity analyses on these reaction diffusion-models may help to distinguish anatomical traits that have causal effects on gm from those that are merely indirectly correlated.Such an approach has been applied elsewhere: in the study of outside-xylem leaf hydraulic conductance, modelled predictions do not always align with the correlations observed in interspecific comparisons (Buckley et al., 2015).It would be interesting to assess whether this is also the case for estimates of gm.

Develop robust predictions of how much gm limits An in crop species
Finally, section 6 outlines the uncertainty that exists surrounding the theoretical benefits that may be achieved from altering gm.It is worth noting that our reanalysis of data from Xiong (2023) contrasts considerably from earlier predictive calculations, which suggested that doubling gm could enhance An by as much as 20 % (Zhu et al., 2010).This inconsistency points to the importance of parameterising such model predictions with high precision, in order to ensure that accurate conclusions can be drawn.The vulnerability of such predictions to error is explained by the meta-analysis conducted by Knauer et al., (2022), in which a negative exponential regression was fit between gm and L'm; this exponential relationship leads to vastly different L'm values, depending on whether gm is more or less than 0.4 mol m -2 s -1 .Consequently, going forward it is important that L'm is estimated in a wide range of crops, grown under different conditions.Likewise, more work is needed to determine if Vcmax and Jmax (calculated on a Cc-basis) are coordinated with gm across species and/or cultivars.This is important because Vcmax and/or Jmax influence Anp, and hence the final estimate of L'm (Equation 16) is determined by these biochemical parameters as well as by gm.As a result, L'm is highest when Vcmax and Jmax are high, and gm is low.If gm naturally positively correlates with Vcmax and Jmax, this will have a negative impact on how much benefit can be realised from transgenically elevating the former.However, the degree to which gm correlates with Vcmax and Jmax has not been satisfactorily resolved.Some evidence suggests that Vcmax and gm may positively correlate across species, although this trend unfortunately seems to depend on the method used to estimate gm (Knauer et al., 2022;Xiong, 2023).In contrast, no such corelation was observed across 13 African cultivars of cassava (De Souza et al., 2020).Caution is required when interpreting these results; as outlined in Section 5, estimates of gm are dependent on An, which will in turn be affected by Vcmax and Jmax.Nevertheless, looking forward, more studies should focus on measuring L'm and developing a deeper understanding of the relationships between gm, Vcmax and Jmax.Only by doing so, will it be possible to begin to critically assess whether transgenically altering gm is a worthwhile route to improving photosynthesis and yield.

Conclusion
There has been considerable interest in bioengineering leaves with higher gm as a means to enhance assimilation rates.However, if the scientific community is to realise this goal, it is essential that we understand the methodological and conceptual limitations that are everpresent when estimating gm.Greater stringency is needed when interpreting results: there is a need to more critically address pleiotropy; employ sensitivity analyses; and complement estimates of gm with reaction-diffusion models.Only by doing so will it be possible to confidently identify transgenic manipulations that enhance An by elevating gm.Finally, it is important that the theoretical potential benefits of enhancing gm be thoroughly assessed, to ensure that this bioengineering goal is worthwhile.Acknowledgements This work was funded by the Novo Nordisk Foundation Challenge grant 'Data science driven leaf architecture optimization' (DIRECTION, NNF 21OC0068884).For the purpose of open access, the authors have applied a Creative Commons Attribution (CC BY) licence to any Author Accepted Manuscript version arising from this submission.Fig. 1) Schematic depicting the conductances within leaves.(A) Major CO2 conductances within a leaf.A finite stomatal conductance to CO2 (gsc) results in the CO2 concentration in the substomatal cavities (Ci) being lower than atmospheric levels (Ca).Likewise, a finite mesophyll conductance results in the CO2 concentration in the chloroplasts being lower than Ci.CO2 conductance across the leaf cuticle is also shown.(B) Small-scale conductances that contribute to the total gm.Conductance of the internal air space gIAS determines the efficiency with which CO2 in the substomatal cavity (Ci) moves to the cell walls (Cw).The pathway from the cell surface to the stroma is characterised by conductance of the cell walls (gcw), plasma membranes (gpm), cytoplasm (gcyt) and chloroplasts (gchl).Subcellular compartments are not drawn to scale.

A) B)
C) D) and extrapolating to the y-intercept to estimate -RL.A comparison of the Yin and Laisk methods yielded comparable mean RL values, although the former had substantially lower standard deviations