Biophysical carbon concentrating mechanisms in land plants: insights from reaction-diffusion modeling

Carbon Concentrating Mechanisms (CCMs) have evolved numerous times in photosynthetic organisms. They elevate the concentration of CO2 around the carbon-fixing enzyme rubisco, thereby increasing CO2 assimilatory flux and reducing photorespiration. Biophysical CCMs, like the pyrenoid-based CCM of Chlamydomonas reinhardtii or carboxysome systems of cyanobacteria, are common in aquatic photosynthetic microbes, but in land plants appear only among the hornworts. To predict the likely efficiency of biophysical CCMs in C3 plants, we used spatially resolved reaction-diffusion models to predict rubisco saturation and light use efficiency. We find that the energy efficiency of adding individual CCM components to a C3 land plant is highly dependent on the permeability of lipid membranes to CO2, with values in the range reported in the literature that are higher than used in previous modeling studies resulting in low light use efficiency. Adding a complete pyrenoid-based CCM into the leaf cells of a C3 land plant is predicted to boost net CO2 fixation, but at higher energetic costs than those incurred by photorespiratory losses without a CCM. Two notable exceptions are when substomatal CO2 levels are as low as those found in land plants that already employ biochemical CCMs and when gas exchange is limited such as with hornworts, making the use of a biophysical CCM necessary to achieve net positive CO2 fixation under atmospheric CO2 levels. This provides an explanation for the uniqueness of hornworts’ CCM among land plants and evolution of pyrenoids multiple times.


Introduction
Ribulose-1,5-bisphosphate carboxylase/oxygenase (rubisco) catalyzes the fixation of CO2 as part of the Calvin-Benson Cycle (CBC) but is also capable of fixing O2.The fixation of O2 results in the formation of 2phosphoglycolate (2PG), with the photorespiratory pathway being necessary to detoxify and recover the carbon in 2PG and recycle it back into the CBC.Although rubisco shows selectivity for CO2 relative to O2, significant photorespiratory flux still occurs in photosynthetic systems due to the much higher partial pressure of O2 in the earth's atmosphere relative to CO2.Photorespiratory flux lowers net carbon assimilation and incurs substantial energetic costs, in the form of ATP, redox equivalents, and ultimately photons.Although the costs associated with photorespiration vary between plant species and environmental conditions, it has been estimated that photorespiration accounts for crop yield decreases of 20 and 36% for soybean and wheat respectively under current climate conditions (Walker et al., 2016).
Carbon Concentrating Mechanisms (CCMs) increase the concentration of CO2 around rubisco, competitively inhibiting the oxygenation reaction, suppressing photorespiration, and increasing carboxylation flux (Raven et al., 2017).In biochemical CCMs, such as C4 and CAM photosynthesis, inorganic carbon is fixed into an intermediate form of organic carbon, before eventually being released around rubisco (Ludwig, 2013;Bräutigam et al., 2017).Biophysical or "inorganic" CCMs, on the other hand, do not rely on any additional intermediate organic carbon species, but instead use transportdriven pumps, diffusional barriers, carbonic anhydrases, and pH differences between cellular compartments to increase the CO2 concentration near rubisco (Raven et al., 2008).Such CCMs are common in cyanobacteria and algae (Raven et al., 2008), but are conspicuously absent in C3 plants, including almost all land plants.This has motivated researchers to look into the possibility of introducing a CCM, either in its entirety or individual components, into these plants to improve carbon fixation, reduce photorespiratory CO2 and energy losses, and ultimately boost yields (Ermakova et al., 2020;Hennacy and Jonikas, 2020).
The seemingly substantial benefits of CCMs raise the question of why they are not already more widespread in land plants.Despite their lack of a CCM, C3 plants are still the most abundant group of land plants in terms of vegetation coverage and gross photosynthetic productivity (Still et al., 2003;Raven et al., 2017).In the case of C4 photosynthesis, the large number of anatomical and biochemical features required has been invoked as a reason why, rather than being universally adopted in land plants, it has instead repeatedly evolved only in lineages exposed to the kinds of hot, arid conditions that limit water availability and exacerbate the losses associated with photorespiration (Sage et al., 2018).However, such an explanation is less satisfactory in the case of biophysical CCMs because they are present in the hornworts.It also raises the question of why biophysical CCMs are uniformly absent in all land plant lineages except for the hornworts (Villarreal and Renner, 2012).
Have inefficiencies associated with biophysical CCMs precluded their successful emergence in C3 plants and can we examine the presence and absence of these biophysical CCMs in different groups of organisms using these inefficiencies?The efficiency of intermediate photosynthetic configurations, featuring some but not all of the essential parts of a CCM, may also represent a barrier to the emergence of CCMs in land plant lineages.Anatomical and life history details of hornworts may explain why, among the land plants, only hornworts have evolved pyrenoid-based biophysical CCMs (PCCMs), and have done so repeatedly (Villarreal and Renner, 2012).The poikilohydric life history of hornworts makes it necessary for them to have highly desiccation-tolerant cell walls which, together with bryophytes' generally thicker cell walls (Flexas et al., 2021) and hornworts' simpler tissue architecture, may explain their extremely low gas conductance (Meyer et al., 2008;Carriquí et al., 2019).We hypothesized that the distinct morphologic characteristics and habitat of hornworts may explain why they, uniquely among the land plants, evolved biophysical CCMs.It is possible that the different paths that inorganic carbon has to take from the environment into a C3 land plant cell versus an algal cell can similarly explain why the former never uses pyrenoids to concentrate carbon and the latter frequently does.
A closer examination of the costs of a CCM may also inform the viability and strategy of biotechnological projects focused on introducing them to C3 crops.Prior quantitative modeling work argues that incorporating individual CCM components -in particular, bicarbonate transporters at the chloroplast membrane -and entire CCMs into land plant systems may boost net CO2 fixation as well as improve the efficiency of photosynthetic carbon assimilation by reducing the energetic costs associated with photorespiration (McGrath and Long, 2014;Fei et al., 2022).Similar arguments have been made in favor of engineering biochemical -e.g.C4 -photosynthesis into C3 plants (Walker et al., 2016).These models represent sophisticated, integrative descriptions of photosynthetic carbon assimilation.For the purposes of the questions we are interested in, however, we needed models of both land plant and algal systems that represent photo-assimilatory processes at the whole-cell level.We also needed models that allow us to explore substantial uncertainties in certain key parameters, and that include energy costs associated with carbonic anhydrase (CA) activity in the thylakoid lumen.
Here we developed spatially-resolved reaction-diffusion models of land plants and green algae with and without PCCMs in the Virtual Cell platform (Schaff et al., 1997;Cowan et al., 2012).These models represent, to our knowledge, the first such models of C3 land plants containing pyrenoid-based biophysical CCMs, as well as the first models of algal systems containing biophysical CCMs going beyond the scale of the chloroplast and including the whole cell in an aqueous environment.We highlight the substantial uncertainty in reported or predicted values of the permeability of lipid membranes to CO2 and explore how this uncertainty can give rise to qualitatively different conclusions as to the efficiency and effectiveness of adding chloroplast envelope bicarbonate pumps in particular.Finally, we find that despite the near-ubiquity of biophysical CCMs in algae, modeling suggests that lower levels of external inorganic carbon (DIC) are needed to make CCMs energetically favorable for land plants.

Model details
Spatially-resolved reaction-diffusion models of carbon assimilation were developed in the Virtual Cell platform, a software suite that allows for the creation and analysis of chemical reaction diffusion dynamics in the context of 3D models (Schaff et al., 1997;Cowan et al., 2012).Baseline parameters for simulations can be found in Table 1 and diagrams of two of the models used in this study, showing the representative features of the land plant and algal models, as well as the differences between the withand without-PCCM models, can be seen in Figure 1.
Systems were represented as spatially symmetrical, with spherical concentric compartments that were converted into volumetric pixels (voxels) according to the simulations' spatial resolution.All results presented are from simulations containing either 9,261 voxels or 12,167 voxels.Due to the large parameter explorations done in this study, minor geometrical modifications were made to make efficient numerical simulation feasible.Specifically, the radius of the apoplast water layer in the land plant models was extended out from the 9.41um it should be based on a cell wall thickness of 0.32um plus an apoplast water layer of equivalent thickness to 10um.We also modeled the thylakoid tubules of with-PCCM models as a set of six cylinders of radius 0.5um extending into the pyrenoid, with exchange between the tubules and the pyrenoid occurring at the end of these cylinders, in contrast to the larger number of finer tubules used in (Fei et al., 2022).
Figure 1: Diagrammatic representations of (A) a model of photosynthetic carbon assimilation in a land plant mesophyll cell containing a C. reinhardtii style PCCM, and (B) a model of an algal cell that does not contain a pyrenoid.CA refers to carbonic anhydrase, BLP refers to bestrophin-like proteins that serve as membrane channels for passive bicarbonate transport, and BicA is a cyanobacterial active bicarbonate transporter.In the VCell implementation of the model, some strongly linked steps are combined for the sake of numerical computability.Exact specifications for all flux equations used can be found in the publicly shared model implementations in VCell (see code and data availability statement).Note that for the sake of numerical tractability, the carbonic-anhydrase catalyzed interconversion of CO2 and HCO3 in the thylakoid in models featuring a CCM (v29) is localized to the pyrenoid but uses the pH value of the thylakoid; in the real biological system, the carbonic-anhydrase is inside the thylakoid tubules that penetrate into the pyrenoid.

Reaction equations
Carboxylation flux by rubisco is calculated as in (Farquhar et al., 1980) (E1).The rate of carboxylation by rubisco is normally taken to be the minimum of Vc and J, where J describes the rate of ribulose-1,5bisphosphate regeneration enabled by photosynthetic electron transport and a function of Jmax, a maximum rate of RuBP regeneration, among other parameters (Farquhar et al., 1980).Estimates of the relevant parameters are available for land plants but, to our knowledge, not for algae.We are also specifically examining CO2-limiting conditions where rubisco reaction rate limitations dominate.For these reasons, we calculate the carboxylation and oxygenation rates assuming that the system is not limited by RuBP regeneration as in (Fei et al., 2022).
The ratio of oxygenation to carboxylation Vmax is: Using a value of 0.21 as in (Farquhar et al., 1980), we can thereby calculate the   of our systems.The oxygenation flux by rubisco is then calculated as: Interconversion of CO2 with bicarbonate via carbonic anhydrase is described as in (McGrath and Long, 2014): In the land plant models, the flux density of dissolution of gaseous CO2 or O2 into the water layer is as in (Hemond and Fechner, 2022): Where Dw is the diffusion rate of the dissolving species in water Cw and Ca are the concentrations of that species in the air and in the water layer, H is the dimensionless Henry's Law constant, and   is the length of the unstirred water layer into which the gas is dissolving.In our models, we assume the presence of a thin layer of water on top of the plant's cell wall that is the same thickness as the cell wall itself into which CO2 is dissolving.
Permeation of aqueous species through the cell wall is given by the following equation, as in (McGrath and Long, 2014): Where EffectivePorosity is the porosity of the cell wall divided by the tortuosity of the cell wall.
For computational tractability, we combine the processes of gases dissolving into water and the aqueous species passing through the cell wall.Note that in the above equation Dw /   and Dw *EffectivePorosity /   gives permeability (in units of um/s) of the water layer and the cell wall, respectively.Multiplying these values by surface area gives conductivities (in units of µm 3 /s).The inverses of these values are resistances, which can be summed to give the total resistance of the water layer plus the cell wall.The inverse of this, again, will be the conductivity of the overall system, which can be multiplied by the concentration gradient from the air to the surface of the plasmalemma to give the total flux.
Permeation through lipid membranes is given by: Active transport by bicarbonate transporter BicA is described using Michaelis-Menten kinetics:

Efficiency Calculations
Net CO2 fixation is described as: 2 NADPH equivalents are expended per carboxylation or oxygenation reaction based on the stoichiometry of the CBC cycle and photorespiration.3 ATP and 3.5 ATP are used for a single carboxylation or oxygenation event, respectively (Edwards and Walker, 1983).
In models featuring a PCCM, there is a lumenal carbonic anhydrase that catalyzes the following reaction: Due to the acidic pH of the lumen (Kramer et al., 1999) the net flux of this reaction is overwhelmingly in the direction of CO2 and H2O, so that entry of bicarbonate depletes the proton motive force (pmf) that is maintained by the light reactions of photosynthesis, which imposes an indirect ATP cost on CCM activity by requiring additional proton pumping to maintain the pmf (Mukherjee et al., 2019).Based on a 14:3 ratio of pumped protons to ATP synthesis via the thylakoid membrane ATP synthase, inferred from the number of c-subunits in such ATP synthases (Seelert et al., 2000), we can calculate the indirect ATP cost of this lumen CA activity as: This is added to the other ATP consumption in the model (due to the metabolic costs of carboxylation and oxygenation) to give total ATP use.This can be compared with NADPH use due to carboxylation and oxygenation to get an estimate of the total ATP, NADPH, and the ATP:NADPH ratio needed to support the activity in the model.From the values provided in (Walker et al., 2020) we estimate the amount of either Cyclic Electron Flow (CEF) or Malate Valve activity needed to rebalance the ATP/NADPH ratio needed for a particular model, which we can then convert into an additional demand for photons and, therefore, a the number of photons needed on a per reaction (carboxylation or oxygenation) basis (Figure S1).From this, we can calculate the number of photons needed to support model fluxes and then compare this to the net fixation achieved by a model to get an estimate of light use efficiency.Where Vc and Vo are the modeled rates of carboxylation and oxygenation, Ratio refers to the modeled ATP/NADPH ratio necessary to support the fluxes in the model, and Photonsbase , ATPbase and NADPHbase refer to the photons used and the ATP and NADPH generated in the process of making two NADPH molecules via Linear Electron Flow (LEF) (Walker et al., 2020).

Concentration calculations
All concentrations in the models used in this study are in units of µM.To calculate the µM concentrations of CO2 and O2 in the atmosphere, we used the following conversion:

Validation of compensation point predictions and sensitivity analysis
The land plant and algal carbon assimilation models were validated by comparing a key estimated result (CO2 compensation point) with experimentally measured values from the literature.The CO2 compensation point is the external CO2 level at which net CO2 assimilation by a photosynthesizing organism is zero (i.e.carbon assimilation by rubisco is balanced out by CO2 losses to photorespiration and respiration in the light, denoted as RL).Low compensation points are also a defining feature of organisms with CCMs since they maintain net positive carbon assimilation at lower CO2 concentrations, making this a useful indicator of whether land plant and algal models with and without CCMs reasonably recreate the carbon assimilation dynamics of real systems.
As shown in Figure 2 and Table 2, the models with CCMs have substantially lower compensation points than the models lacking CCMs.Moreover, as shown in Table 2, these estimated compensation point values fall within the ranges of values reported in the literature for angiosperm land plants and algae with and without CCMs (Table 2).Note that the reported compensation points of hornworts with pyrenoids (11-13 ppm) are lower than those of closely related C3 liverworts, but higher than typical estimates for C4 plants and pyrenoid-containing algae (Villarreal and Renner, 2012).(Fladung and Hesselbach, 1987;Tolbert et al., 1995;Peixoto et al., 2021) Algal model with CCM 2.7 0.75 -2.5; 6.0 (Coleman and Colman, 1980;Raven et al., 1982) Algal model without CCM 44.6 43.5 -58; 64.5 (Raven et al., 1982;Steensma et al., 2023) The sensitivity analysis results shown in Figure 3 show that simulated net CO2 assimilation and quantum yield values from the land plant models are relatively robust to local variations in all parameters, providing us with confidence that these results are not merely the result of a very particular selection of parameters.In both the land plant and algal models without PCCMs, rubisco Vmax, cell and chloroplast radii, and membrane permeability to CO2 are the most influential determinants of net CO2 assimilation and quantum yield.In the land plant model, stomatal conductance also stands out.The addition of a PCCM reduces the sensitivity of net CO2 assimilation to changes in any input parameter but increases the sensitivity of the predicted quantum yield to input parameter values.The local stability of our results to perturbations in key parameters is comparable with previous studies, being more variable than the models presented in (Fei et al., 2022), which spatially modeled a smaller system (algal chloroplasts), and significantly less variable than the models presented in (McGrath and Long, 2014), which modeled land plant CO2 assimilation at a similar scale.We also characterized the sensitivity of our modeling results to the spatial resolution of the numerical simulations.Our results (Figure S2-3) show that rubisco saturation -the percentage of maximum rubisco activity achieved -and quantum yield in an algal model lacking a CCM are robust to the simulation resolution.Increasing the resolution all the way down to 0.32um, well beyond what could feasibly be done given the amount of parameter exploration done in this study, does result in noticeable changes in pyrenoid [CO2] and [HCO3 + ], resulting in small increases in rubisco saturation and small decreases in quantum yield (Figure S4-5).

Efficiency of chloroplast membrane bicarbonate channel is strongly dependent on assumed permeability of chloroplast membrane to CO2
Previous studies (Price et al., 2010;McGrath and Long, 2014) have suggested that the incorporation of bicarbonate transporters into the chloroplast membrane of a land plant could improve net fixation and/or the efficiency of carbon assimilation, and that this could represent a reasonable intermediate stage in a broader biotechnological effort to implement a full CCM in a land plant.Modeling studies on CCM systems typically assume the lipid membrane permeability of 0.35 cm/s, which was experimentally measured and reported in (Gutknecht et al., 1977).However, there is substantial uncertainty as to the value of parameter, with experimental estimates ranging over many orders of magnitude (Evans et al., 2009).The permeability may be as much as an order of magnitude higher than the Gutknecht et al value, as reported in (Missner et al., 2008).We hypothesized that the apparent favorability of employing a chloroplast membrane bicarbonate pump may be highly sensitive to the assumed chloroplast membrane CO2 permeability.
To test this hypothesis, we performed a parameter exploration from an order of magnitude lower than the widely cited (Gutknecht et al., 1977) value up to the (Missner et al., 2008) value in both land plant and algal systems, calculating net fixation as well as ATP/CO2 and light-use efficiency, as shown in Figure 4.
These results show that the light use efficiency of a chloroplast membrane bicarbonate transporter is highly sensitive to the value of the chloroplast envelope's permeability to CO2, with a large range of permeabilities resulting in 2X more ATP usage per unit of CO2 fixed.In the land plant model, we see increases in both rubisco saturation and quantum yield as BicA pumping activity increases when lipid membrane permeability values are equivalent to, or below that reported in (Gutknecht et al., 1977) (Figure 4A-B).At permeabilities higher than this, increased BicA activity actually decreases quantum yield, though net fixation still increases (Figure 4A-B).We see a similar picture in the algal model (Figure 4E-F), suggesting that the differences in DIC form, concentration, and diffusivity do not greatly impact the sensitivity of this strategy to the specific value of lipid membrane permeability to CO2.The decrease in quantum yield in models with high lipid membrane permeability to CO2 is driven by increased leakage of CO2 from the chloroplast back into the cytosol after it interconverts with the bicarbonate just pumped by BicA (shown as flux V15 in Figure 1).As lipid membranes become more permeable to CO2, its tendency to escape the chloroplast before being fixed by rubisco increases.Lowering the external CO2 concentration does, however, change the energy efficiency penalty of increased BicA activity significantly (Figure 4C-D;G-H).Even at higher lipid membrane permeability values, we see only minimal decreases in quantum yield with increased BicA bicarbonate pumping.(Gutknecht et al., 1977) value for lipid bilayer permeability to CO2 as well as a transition in the y-axis from increments of 0.1X to 1X fold changes.

Efficiency of a plasmalemma bicarbonate channel is strongly dependent on external DIC levels and limited by the rate of equilibration between CO2 and bicarbonate
We found that although the strategy of pumping bicarbonate from the cytosol to the chloroplast may incur substantial energy costs, implementing a bicarbonate pump at the plasmalemma may be more effective.This makes sense considering that in aqueous systems at near-neutral pH, most of the DIC in the system is in the form of bicarbonate.We incorporated a plasmalemma bicarbonate transporter and explored the efficiency of such a system across different external DIC concentrations and activities of the transporter in both algal and land plant systems (Figure 5).
Figure 5: Predicted rubisco saturation and quantum yield in land plant and algal models with a BicA bicarbonate pump present in the plasmalemma membrane, as a function of assumed lipid membrane permeability to CO2 and BicA Vmax.Fold change of lipid membrane permeability is relative to the value reported in (Gutknecht et al., 1977).(Gutknecht et al., 1977) value for lipid bilayer permeability to CO2 as well as a transition in the y-axis from increments of 0.1X to 1X fold changes.
In the land plant model, the plasmalemma bicarbonate pump is not an effective means of increasing either net fixation or energy efficiency.As anticipated, the pump does work in the algal case (Figure 5).The key difference appears to be that the external environment in the algal system, which is suffused with bicarbonate ions, can maintain reasonably high steady-state concentrations in the vicinity of the cell to support the bicarbonate pumping activity (Figure 5C-D).In contrast, in the land plant system all dissolved bicarbonate available to the cell must first enter the system as CO2 in the intercellular airspace, dissolve into the water in the apoplast, and then spontaneously hydrate to H2CO3 and deprotonate into bicarbonate.Although the protonation/deprotonation between H2CO3 is extremely fast, the hydration/dehydration is not (first-order rate constant of hydration of CO2 to H2CO3 is 6 x 10 -2 s -1 (Mitchell et al., 2010)).The result is an almost instantaneous depletion of the HCO3 -concentration in the apoplast space, with insufficient spontaneous hydration flux to replenish it (Figure 5G).Adding carbonic anhydrase activity to the apoplast allows for much faster regeneration of the external HCO3 - concentration, allowing BicA to impact rubisco saturation (Figure 5A-B).However, the pH of the apoplast, although variable, tends to be slightly to moderately acidic (Yu et al., 2000), resulting in low HCO3 -concentrations in the land plant model even with the apoplast carbonic anhydrase included (Figure 5G).It is only when the apoplast pH is made substantially more basic (pH of 8) and a carbonic anhydrase is included that the land plant model can replicate the algal model's rubisco saturation and quantum yield gains by using a plasmalemma bicarbonate pump (Figure 5E-F).

Figure 6:
The ratio of the marginal cost in photons of one unit of net CO2 fixation in land plant (A) and algal (B) models resulting from adding a PCCM relative to the average cost of fixing one molecule of CO2 in those same models without CCMs, as a function of lipid membrane permeability and external CO2 concentrations.Fold change of lipid membrane permeability is relative to the value reported in (Gutknecht et al., 1977).Blue indicates that for a given lipid membrane permeability / external CO2 concentration combination, the model containing a CCM has a lower marginal cost of CO2 fixation -ie., is more light-efficient -than the average cost of CO2 fixation in the model lacking a CCM.Red indicates that for a given parameterization, the model containing a CCM has a higher marginal cost of CO2 fixation than the average cost of CO2 fixation in its CCM lacking counterpart.The black lines in each plot indicate the (Gutknecht et al., 1977) value for lipid bilayer permeability to CO2 as well as a transition in the y-axis from increments of 0.1 to 1 in the X-fold changes.
We compared the energy-use efficiency of PCCM integration by comparing the predicted cost in photons of fixing CO2 molecule in four different models: (i) a land plant model with a PCCM, (ii) a land plant model without a PCCM, (iii) an algal model with a PCCM, and (iv) an algal model without a PCCM.By dividing the increase in net CO2 fixation in models (i) and (iii) relative to models (ii) and (iv) we estimated the marginal cost of in photons of fixing an additional CO2 molecule using a PCCM in our land plant and models (Figure 6).As we observed when examining the efficiency of the plasmalemma and chloroplast envelope BicA bicarbonate pumps, the assumed permeability of lipid membranes can have an impact on efficiency; in this case, however, the relative marginal cost values do not change dramatically between an assumed permeability equivalent to that used in previous studies (1.0 in Figure 6A-B) and the higher value closer to that reported in (Missner et al., 2008).
In the algal models, the use of the PCCM appears to only become marginally efficient with respect to light usage below an external [CO2] of 4.38 uM.In contrast, the CCM is efficient in the land plant model below a substomatal [CO2] of 243 ppm.

As cell wall thickness increases and cell wall effective porosity decreases, PCCMs become more favorable in land plant models
Given the findings regarding PCCMs in land plants highlighted above, it is interesting that many species of hornworts have pyrenoids -are there any meaningful biophysical differences between hornworts and other land plants that could explain these differences?As highlighted in (Meyer et al., 2008;Flexas et al., 2021) hornworts and other bryophytes have cell walls that are both substantially thicker and less porous compared to other land plants.From the mesophyll conductance values reported for angiosperms and bryophytes reported in (Meyer et al., 2008;Flexas et al., 2021), and with the assumption that other internal resistances to CO2 diffusion are similar between bryophytes and embryophytes, we can estimate that the effective porosity of a bryophyte like a hornwort must be on the order of four orders of magnitude smaller than in a typical C3 angiosperm.We explore parameters within this range of possible porosity values and across multiple external CO2 concentrations (Figure 7).Below effective porosities on the order of 10 -1 , which fall in the range we would expect of angiosperms, our model shows that the plant struggles to fix CO2 without a CCM.With a PCCM, however, the model can achieve some level of net CO2 fixation all the way down to effective porosities of 10 -3 .Below porosities of 10 -3 , we do not observe net CO2 fixation in the model without a PCCM, and at a porosity of 10 -4 , both models with and without PCCMs struggle to fix carbon.In terms of light-use efficiency, the model with a PCCM achieves a greater quantum yield of photosynthesis than the model without a PCCM below effective porosities of 10 -2 .

Discussion
We initially hypothesized that the conspicuous absence of biophysical CCMs in almost all land plant lineages, in contrast to algae where they are widespread (Raven et al., 2005), may be the result of lower efficiency of such systems in land plants relative to algae, and that this results from their different biophysical contexts.To our surprise, we found that PCCMs appear to result in qualitatively similar improvements in quantum yield and net CO2 assimilation in land plant and algal models.In the algal model, the fact that addition of a PCCM does not result in efficiency gains until relatively low external DIC levels are reached is surprising, given that Chlamydomonas reinhardtii cells appear to concentrate carbon even at recent "air-level" -approximately 330ppm -CO2 concentrations (Badger et al., 1980).This implies that algae may routinely run their CCMs even when this incurs a quantum yield penalty.In contrast, the intercellular CO2 concentration at which the CCM improves quantum yield in the land plant model ( ~243ppm) is higher than reported estimates of Ci in C4 plants under laboratory, greenhouse, and field conditions (Bunce, 2005).Previous work has described the evolutionary history of C4 photosynthesis (Sage et al., 2018) and identified certain anatomical features -namely Kranz anatomyand environmental factors such as hot, arid conditions that lead to increased transpirational water loss and factors such as Water-Use Efficiency (WUE) as key predictors of C4 emergence.If the estimated quantum yield gains resulting from the introduction of a biophysical CCM to a land plant in this study apply to biochemical CCMs like C4 and CAM photosynthesis, this may represent an additional evolutionary driver towards such systems.
Hornworts are the only land plant lineage that has evolved a biophysical CCM and they have done so multiple times (Villarreal and Renner, 2012).Hornworts, as well as some other bryophytes, are noteworthy for having substantially slower gas exchange between their surroundings and their photosynthetic tissues when compared with vascular land plants (Meyer et al., 2008).. Our results show that a land plant with the low effective cell wall porosities we might expect given their extremely poor gas exchange characteristics, the use of a CCM becomes necessary to achieve net CO2 fixation, which would impose a strong selective pressure for adopting one.The fact that hornworts represent the earliest-diverging extant branch of the land plants, and therefore may have maintained the genes and regulatory networks necessary to adopt a PCCM, may explain why this biophysical CCM strategy has been adopted by hornworts and not other land plants growing in conditions where biochemical CCMS have been selected for.We should note that in the models presented in this study, at effective porosities below 10 -3 , only single digit values of rubisco saturation are achieved even with a biophysical CCM present and active, which may not be sufficient for viability, especially since we do not have or include estimates of respiration in the light in the models.This is despite the fact that mesophyll conductance to CO2 in hornworts, which we are using effective porosity as a proxy for in this study, has been measured to be four-to-five orders of magnitude lower than in angiosperms (Flexas et al., 2021).This suggests that our model underestimates the strength of the hornwort CCM or otherwise does not properly describe some aspect of hornwort CO2 assimilation.The ratio of chloroplast-to-thallus surface area has not been explored in our modeling, but was found in a previous study to be a potentially important determinant of hornwort mesophyll conductance (Carriquí et al., 2019).Future work might aim to incorporate an exploration of chloroplast position and surface area to better account for this in the modeling.
These results shed light on potential challenges associated with improving crop productivity via the introduction of biophysical CCMs.The specific value chosen for the permeability of lipid bilayers to CO2 has a large effect on the predicted energy efficiency of our models, with values higher than those used in previous modeling studies (McGrath and Long, 2014;Fei et al., 2022) but within the range of previously reported literature values (Gutknecht et al., 1977;Missner et al., 2008) resulting in qualitatively different conclusions.We see this in our consideration of BicA-mediated HCO3 -pumping, which had been previously flagged as a promising intermediate step in introducing a biophysical CCM to a C3 plant (Price et al., 2010;McGrath and Long, 2014).As noted in (Fei et al., 2022), barriers to CO2 diffusion form a key component of known functional CCMs, so the finding that the chloroplast membrane may provide enough of a diffusion barrier for the transport of HCO3 -into the stroma and subsequent conversion to CO2 to meaningfully improve net fixation and carbon assimilatory efficiency was surprising.Our results show that at or below the permeability reported in (Gutknecht et al., 1977), which is used in other modeling studies, increasing BicA pumping activity leads to improvements in quantum yield, indicating more efficient CO2 fixation with respect to light use.However, above this value, we see uniform decreases in quantum yield with increased BicA activity.Net CO2 fixation increases with BicA pumping in all cases; therefore, in situations where light is abundant relative to CO2, this decrease in efficiency may not impact plant fitness.However, recent modeling work suggests that Jmax, the maximum rate of ribulose-1,5-bisphosphate (RuBP) regeneration enabled by photosynthetic electron transport, is more limiting to crop yield than limits to the maximum rate of carboxylation (Vmax of rubisco carboxylation) under the projected elevated atmospheric CO2 levels of 2050 and 2100 (He and Matthews, 2023).In this study, improved quantum yields correspond to a combination of (i) lower expenditures of ATP for each CO2 molecule fixed, and (ii) a more favorable ATP/NADPH ratio needed for fixation, resulting in less energy loss from the use of Cyclic Electron Flow during ATP/NADPH rebalancing (Walker et al., 2020).Under conditions of Jmax limitations, differences in quantum yield may become a critical factor in determining yield, making the sensitivity of quantum yield in this and other studies to assumed lipid bilayer permeability to CO2 a matter of critical importance.
Interestingly, previous studies in this area (McGrath and Long, 2014;Fei et al., 2022) have performed sensitivity analyses that include this permeability as a surveyed parameter and its modeled effect is small compared to other parameters.These small local sensitivity values are estimated by observing the change in an output value like light-saturated CO2 assimilation with a ± 10% change in the permeability parameter.This ignores the fact that the uncertainty in this value is in the range of at least an order of magnitude (Evans et al., 2009), and so despite low local sensitivity, the overall change that can result from varying it within reasonable bounds is substantial.The substantial uncertainty in this critical parameter could be reined in by future experimental measurements, though this will still be complicated by the potentially large variation between different plant systems, dynamic remodeling of lipid bilayers in response to developmental and environmental cues, etc.In the absence of well-defined values for this parameter, we encourage future groups modeling such systems to explore a range of values and to characterize the robustness of their conclusions to its variation.
In the near-neutral or slightly basic conditions that most photosynthetic organisms in aqueous environments find themselves in, HCO3 -represents the primary form of Dissolved Inorganic Carbon (DIC) in their surroundings.Due to the impermeability of lipid bilayers to passive diffusion of HCO3 -, the use of this pool of DIC requires organisms to employ an active transport mechanism (e.g.cyanobacterial HCO3 - pumps like BicA (Price et al., 2004)) to move it from the extracellular to the intracellular space, which may often make sense due to the sheer quantity of DIC that is present in the environment.Although land plants ultimately obtain CO2 from the atmosphere, this CO2 must dissolve into water prior to entering photosynthesizing cells, at which point this aqueous CO2 interconverts with other DIC species.This raises the possibility of a similar strategy -pumping HCO3 -from a land plant's apoplast water into the intracellular environment to increase net CO2 fixation -potentially viable.However, our results indicate that the limited spontaneous rate of CO2 and HCO3 -interconversion without the activity of carbonic anhydrase means that this strategy does not work.
Of note here is the fact that a quantitatively very similar system arises in algae growing in acidic environments where external HCO3 -levels are negligible, such as the red alga Cyanidioschyzon merolae (De Luca et al., 1978).In such systems, all DIC must first enter the cell passively as aqueous CO2, at which point it will interconvert primarily between CO2 and HCO3, with the ratio of CO2:HCO3 determined by the cytosolic pH.There is strong evidence that C. merolae has a non-pyrenoid based CCM (Steensma et al., 2023).Such a system could use HCO3 -pumping across the chloroplast envelope as a method of concentrating carbon, but our results suggest that this system would require maintenance of a nearneutral cytosolic pH along with the presence of carbonic anhydrases in the cytosol to be viable.The maintenance of this near-neutral pH in an acidic environment may, in turn, represent a substantial energetic cost to the organism.

Figure 2 :
Figure 2: Net CO2 assimilation versus external CO2 concentrations in carbon assimilation models.The point at which net CO2 assimilation is zero defines the compensation point.(A) The full range of saturation and external CO2 concentrations, and (B) a zoomed-in panel showing the point at which each curve reaches 0% rubisco saturation (i.e. the compensation point).

Figure 3 :
Figure 3: Sensitivity analysis results for (A) the land plant model lacking a CCM, (B) the algal model lacking a CCM, (C) the land plant model with a CCM, and (D) the algal model with a CCM.Orange bars indicate the absolute % change of quantum yield resulting from a 10% change in the indicated parameter, and blue bars represent the same for rubisco saturation.For both of the land plant models, increasing the cytosol radius by 10% resulted in problems with solving the systems numerically, so the cytosol radius was increased by 1% instead and, assuming a linear relationship between the size of radius increase and the change in rubisco saturation and quantum yield, multiplied by 10 to get the values shown in (A-B).

Figure 4 :
Figure 4: Rubisco saturation and quantum yield of land plant and algal models of CO2 assimilation under 100% and 50% external CO2 levels, as a function of lipid membrane permeability to CO2 and BicA bicarbonate transporter Vmax.Fold change of lipid membrane permeability is relative to the value reported in (Gutknecht et al., 1977).(A) Predicted rubisco saturation of a land plant model under 100% external CO2.(B) Predicted quantum yield of a land plant model under 100% external CO2.(C) Predicted rubisco saturation of a land plant model under 50% external CO2.(D) Predicted quantum yield of a land plant model under 50% external CO2.(E) Predicted rubisco saturation of an algal model under 100% external CO2.(F) Predicted quantum yield of an algal model under 100% external CO2.(G) Predicted rubisco saturation of an algal model under 50% external CO2.(H) Predicted quantum yield of an algal model under 50% external CO2.The black lines in each plot indicate the(Gutknecht et al., 1977) value for lipid bilayer permeability to CO2 as well as a transition in the y-axis from increments of 0.1X to 1X fold changes.
Figure5: Predicted rubisco saturation and quantum yield in land plant and algal models with a BicA bicarbonate pump present in the plasmalemma membrane, as a function of assumed lipid membrane permeability to CO2 and BicA Vmax.Fold change of lipid membrane permeability is relative to the value reported in(Gutknecht et al., 1977).(A) Predicted rubisco saturation of a land plant model lacking an apoplastic carbonic anhydrase.(B) Predicted rubisco saturation of a land plant model with an apoplastic carbonic anhydrase.(C) Predicted rubisco saturation of an algal model.(D) Predicted quantum yield of an algal model.(E) Predicted rubisco saturation of a land plant model with an apoplastic carbonic anhydrase and an apoplast pH of 8. (F) Predicted quantum yield of a land plant model with an apoplastic carbonic anhydrase and an apoplast pH of 8.The black lines in each plot indicate the(Gutknecht et al., 1977) value for lipid bilayer permeability to CO2 as well as a transition in the y-axis from increments of 0.1X to 1X fold changes.

Figure 7 :
Figure 7: Rubisco saturation (A) and quantum yield (B) of a land plant model with varying effective porosity values.Blue points / lines represent predicted rubisco saturation or quantum yield in models including a PCCM; orange points/ lines represent predicted saturation or quantum yield in models not including a PCCM.

Table 1 :
Model parameter definitions with source references and, where applicable with notes on derivation.When parameters were derived from parameterization of a previous modeling study, both the modeling study and the original literature reference for the parameter are cited.References in "Ref."

Table 2 :
Predicted compensation points for different models from the present study compared with reference values from the literature.Reference column numbers refer to their numbering in the bibliography.