The ins and outs of CO2

Highlight CO2 supply to Rubisco can involve diffusive CO2 fluxes or a CO2 concentrating mechanism. The mechanisms involve CO2 loss in photorespiration or by leakage, respectively.


Introduction
The textbook equations for oxygenic photosynthesis and for dark respiration have CO 2 as, respectively, the inorganic C substrate and the inorganic C product. This is the case for the core autotrophic carboxylase of oxygenic photosynthetic organisms, ribulose-1,5-bisphosphate carboxylase-oxygenase (Rubisco), with CO 2 as its inorganic carbon substrate, and for the decarboxylases of dark respiration with CO 2 as their inorganic C product (Raven, 1972a; Table 5.2 of Raven, 1984; Table 3 of Raven, 1997a). Add to this the Overton prediction over a century ago that CO 2 has a high permeability in lipid bilayers (see Endeward et al., 2014) and it appears at first sight that the textbook equations describe not just the inorganic C substrate for photosynthesis and inorganic C product of dark respiration, but also the inorganic C species crossing cell membranes between the external environments and intracellular sites of inorganic C consumption and production.
However, it is clear that this picture is significantly oversimplified in (at least) two ways. One is that we now know of CO 2 -permeable channels (a subset of the aquaporins, and analogues) in some cell membranes, and there is considerable debate as to their functional significance if the CO 2 permeability of the lipid bilayer is very high (Boron et al., 2011;Itel et al., 2012;Endeward et al., 2014;Kai and Kaldendorf, 2014). The second over-simplification is that there are known CO 2 concentrating mechanisms (CCMs), involving active transport of some inorganic C species (or H + ) and/or C 4 or crassulacean acid metabolism (CAM) biochemistry, accounting for about half of global primary productivity. This assertion is based on the global net primary productivity values of 56 Pg C per year on land and 49 Pg C per year in the ocean (Field et al., 1998), the assumption that the ratio of global C 4 gross primary productivity (almost all terrestrial) to total gross primary productivity, i.e. 0.23 (Still and Berry, 2003), also applies to net primary productivity, and the assumption that not less than 0.8 of the marine global net primary productivity is carried out by organisms with CCMs . These assumptions give a total CCM-based global net primary productivity of (0.23 × 56) + (0.8 × 49) or 52 Pg C per year out of a total of 105 Pg C per year global net primary productivity.
CCMs necessarily involve an energy input to generate a net flux of inorganic C from the environment with a relatively low CO 2 concentration to the active site of Rubisco where a higher steady-state CO 2 concentration is maintained during photosynthesis. This means that the direction of the CO 2 free energy gradient (inside concentration > outside) is the opposite of that for photosynthesis with C 3 physiology and biochemistry (inside < outside). Accordingly, in an organism expressing a CCM, the high CO 2 permeability of the pathway from the environment to Rubisco required for high rates of photosynthesis in organisms with C 3 physiology and biochemistry would result in a decreased net rate of photosynthesis and increased energy requirement per net CO 2 assimilated . The final result is an increased energy cost of CCMs relative to that of diffusive entry with C 3 physiology and biochemistry. Important progress in understanding bidirectional fluxes of inorganic carbon in an organism expressing a CCM has been made in a recent paper in the Journal of Experimental Botany (Eichner et al., 2015). Using the marine diazotrophic cyanobacterium Trichodesmium, this work combined two experimental approaches, membrane inlet mass spectrometry to distinguish CO 2 from HCO 3 fluxes (Badger et al., 1994) and measurements of the natural abundance of 13 C relative to 12 C (Sharkey and Berry, 1985), with modelling. A very important conclusion is that internal cycling of inorganic C is significant for the natural isotope abundance of 13 C: 12 C in the organism, and for cellular energy budgets. This commentary considers wider aspects of CCMs and of leakage of inorganic carbon from them, and how the findings of Eichner et al. (2015) might help further interpretation of data on other organisms, including eukaryotic algae and vascular plants.

Species of inorganic C involved in carboxylases and decarboxylases
All of the unidirectional decarboxylases examined (functioning far from thermodynamic equilibrium), i.e. those of the tricarboxylic acid cycle and the oxidative pentose phosphate pathway, produce CO 2 (Raven, 1972a,b). By analogy with such unidirectional decarboxylases, the product of glycine decarboxylase, the enzyme responsible for CO 2 production in the photorespiratory carbon oxidation cycle, is also very likely to be CO 2 .
Enzymes that function in vivo sufficiently close to thermodynamic equilibrium, and hence can function as carboxylases and decarboxylases, both consume and produce CO 2 (Table 5.2 of Raven, 1984;Häusler et al., 1987;Jenkins et al., 1987; Table 3 of Raven, 1997a). Significantly for the present article, the decarboxylase function of three of these enzymes (phosphoenolpyruvate carboxykinase; NAD + malic enzyme; NADP + malic enzyme) is involved in the decarboxylation step of C 4 and CAM photosynthesis (Jenkins et al., 1987).
Among unidirectional carboxylases, operating far from thermodynamic equilibrium, a number use CO 2 as the inorganic C substrate (Table 5.2 of Raven, 1984;Häusler et al., 1987;Jenkins et al., 1987; Table 3 of Raven, 1997a;Firestyne et al., 2009). Importantly for the present article, these CO 2consuming carboxylases include Rubisco, the core carboxylase of all oxygenic photosynthetic organisms, as well as the 5-aminoimidazole ribonucleotide carboxylase required for purine synthesis.
Finally, some unidirectional carboxylases consume HCO 3 - (Table 5.2 of Raven, 1984; Table 3 of Raven, 1997a). One of these is phosphoenolpyruvate carboxylase, an essential anaplerotic enzyme in almost all oxygenic photosynthetic organisms (Table 4 of Raven, 1997a) as well as the 'C 3 + C 1 ' carboxylase of organisms with C 4 photosynthesis (with the exception of the ulvophycean marine macroalga Udotea flabellum: see Raven, 1997a) and with CAM photosynthesis. A possible alternative 'C 3 + C 1 ' carboxylase for C 4 and CAM photosynthesis is pyruvate carboxylase, which also uses HCO 3 as the inorganic C substrate (Table 5.2 of Raven, 1984; Table 3 of Raven, 1997a). Other carboxylases using HCO 3 include acetyl CoA carboxylase used in the synthesis of long-chain fatty acids, and carbamoyl phosphate synthase, essential for citrulline, and hence arginine, synthesis (Table 4 of Raven, 1984; Table 3 of Raven, 1997a).
CO 2 permeability of lipid bilayers and the role of CO 2 -conducting aquaporins and analogous protein pores There is still significant uncertainty as to the mechanism of CO 2 permeation of biological membranes (Boron et al., 2011;Itel et al., 2012;Endeward et al., 2014;Kai and Kaldendorf, 2014).
A particular problem is the role of proteinaceous CO 2 channels if the intrinsic CO 2 permeability of the lipid bilayer is very high, although there is evidence of increased photosynthesis and growth in terrestrial C 3 plants expressing CO 2 -transporting aquaporins (Uehlein et al., 2003(Uehlein et al., , 2008Heckwolf et al., 2011) The most convincing evidence for the role of aquaporins in terrestrial C 3 plants comes from Hanba et al. (2004) and Tsuchihira et al. (2010). Table 1 shows the permeability coefficient for CO 2 of planar lipid bilayers of various compositions, and for the plasmalemma vesicles derived from high and low CO 2 -grown Chlamydomonas reinhardtii. In all three cases attempts were made to eliminate the influence of diffusion boundary layers on each side of the membrane on the measured permeability.

CO 2 entry in organisms lacking a biophysical CCM
The classic example of these is the C 3 vascular land plants.
It is now clear that CO 2 is the species of inorganic carbon entering the cells from the cell wall (Colman and Espie, 1985;Espie and Colman, 1986;Espie et al., 1986;Maberly, 2014). The assumption is that terrestrial C 4 and CAM vascular plants also rely on CO 2 entry from the cell wall to the cytosol where carbonic anhydrase equilibrates CO 2 with HCO 3 -, the inorganic C substrate for PEPc (Colman and Espie, 1985;Nelson et al., 2005).
For C 3 plants the transport of CO 2 from the outside of the cell wall to Rubisco involves diffusion of CO 2 across the plasmalemma and across the outer and inner chloroplast membranes and, in the aqueous phase, through the cell wall, the cytosol and the stroma (Colman and Espie, 1985). It is implicitly assumed that there is no carbonic anhydrase in the cell wall (Raven and Glidewell, 1981;Colman and Espie, 1985) of C 3 plants, though there seems to be no experimental evidence demonstrating this. Carbonic anhydrases could equilibrate CO 2 and HCO 3 in the cytosol and stroma and so enlist the predominant (at the pH of the cytosol and stroma) inorganic species, HCO 3 -, in CO 2 transport across these aqueous phases, with the required H + flux carried inwards by protonated buffers with a return flux outwards of the deprotonated buffers (Raven and Glidewell, 1981;Colman and Espie, 1985; Table 1. Permeability coefficient for CO 2 in planar lipid bilayers and plasmalemma vesicles, corrected as far as possible for limitation by aqueous diffusion boundary layers Also shown are the modelled 'optimum' or 'maximum' (for functioning in the CCM) CO 2 permeability of the wall of cyanobacterial carboxysomes and/or the estimated CO 2 permeability of the wall of cyanobacterial carboxysomes.

Experimental system
CO 2 permeability m s -1

-6
Hopkinson et al. (2014) Method for all three data sets involves measurement of inorganic carbon fluxes, expressed as CO 2 , under a known CO 2 concentration difference across the membrane across planar membrane bilayers (Gutknecht et al., 1997;Missner et al., 2008) or plasmalemma vesicles of Chlamydomonas (Sültemeyer and Rinast, 1996). Carbonic anhydrase was added to both sides of the membrane to minimize the gradient of CO 2 across the aqueous diffusion boundary layers on each side of the membrane. Niinemets et al., 2009;Tazoe et al., 2009Tazoe et al., , 2011. There is very significant interspecific variation in the magnitude of the mesophyll conductance (= permeability) of C 3 seed plants Niinemets et al., 2009;Tazoe et al., 2009; see Table 2). Turning to submerged aquatic organisms, a number have CO 2 entry followed by diffusive flux to Rubisco, resembling C 3 land plants, although aquatic vascular plants lack stomata. These organisms include a number of freshwater and marine algae, aquatic bryophytes, and freshwater vascular plants (Raven, 1970;MacFarlane and Raven, 1985, 1990Kübler et al., 1999;Sherlock and Raven, 2001;Maberly and Madsen, 2002;Raven et al., 2005;Maberly et al., 2009;Maberly, 2014). While these organisms share some of the physiological characteristics found in organisms with CCMs, e.g. the absence of a competitive interaction between CO 2 and O 2 in photosynthetic gas exchange (Kübler et al., 1999;Sherlock and Raven, 2001;Maberly et al., 2009), the overall influence of environmental factors points to diffusive CO 2 entry.

CO 2 entry in organisms expressing a biophysical CCM
A biophysical CCM that involves diffusive CO 2 entry was first proposed by Walker et al. (1980;see Briggs, 1959) for ecorticate giant internodal cells of freshwater green algal macrophytes of the Characeae growing in relatively alkaline waters. The localized active efflux of H + across the plasmalemma causes a localized decrease in pH in the cell wall and diffusion boundary layer, to approximately 2 pH units below that in the medium. As HCO 3 diffuses into the acid zone, the equilibrium CO 2 :HCO 3 increases 100-fold, as does the rate of HCO 3 conversion to CO 2 in the absence of carbonic anhydrase (Walker et al., 1980). Subsequently, expression of carbonic anhydrase in the acid zones was demonstrated, further increasing the rate of HCO 3 to CO 2 conversion . Intracellular acid-base regulation requires alkaline zones between the acid zones. This mechanism also occurs in some freshwater flowering plants where the acid zone is on the abaxial leaf surface and the alkaline zone is on the adaxial leaf surface (Maberly and Madsen, 2002). The high CO 2 concentration generated in the acid zones can, after crossing the plasmalemma by diffusion, give an internal CO 2 concentration rather less than that in the acid zone but still sufficient to constitute a CCM with the CO 2 concentration inside the cell higher than that in the bulk medium (Walker et al., 1980;. As well as CO 2 leakage from the acid zones to the bulk medium, CO 2 could also leak from the cytosol back to the bulk medium through the alkaline zones. A similar mechanism is thought to occur in many marine macrophytes as a mechanism of using external HCO 3 - (Raven and Hurd, 2012). However, the evidence for this is (a) inhibition of external HCO 3 use by pH buffers that, ex hypothesis, eliminate the acid zones, (b) inhibition of external carbonic anhydrase using a membrane-impermeant inhibitor as well as, in some cases, (c) showing that photosynthesis is not decreased by inhibitors of one group of plasmalemma HCO 3 transporters (Raven and Hurd, 2012). There have been no direct demonstrations of the acid zones in macroalgae because, although they can be visualized when they occur in the freshwater Characeae and vascular macrophytes, they must (if they exist!) occupy smaller areas in marine macroalgae and in seagrasses (Raven and Hurd, 2012).
An analogous mechanism involves external HCO 3 entry at the plasmalemma and across the chloroplast envelope membranes, not necessarily giving higher internal than external concentration, with HCO 3 entry to the thylakoid lumen via (ex hypothesis) HCO 3 --transporting channels (Raven, 1997b;Jungnick et al., 2014;. The low pH of the thylakoid lumen, with the presence (at least in Table 2. Permeability coefficient ('mesophyll conductance') for CO 2 entry for the pathway from the outside of the external aqueous diffusion boundary layer to Rubisco in C 3 biochemistry No data seem to be available for the corresponding CO 2 movement to PEPc in C 4 or CAM biochemistry. Conversion of photosynthetic rates for the plants on a projected leaf area basis (from Table 1 of Warren, 2008) to the area of mesophyll cells exposed to the intercellular gas space uses a ratio of 25 m 2 m 2 mesophyll cells exposed to the intercellular gas space projected leaf area (from pp. 380-381of Nobel, 2005). Conversion of the difference in CO 2 concentration between the outside of the cell wall to the chloroplast stroma expressed in terms of atmospheric mol fraction (μmol CO 2 mol -1 total atmospheric gas) from Table 1 of Warren (2008) to mmol CO 2 dissolved in each m 3 of leaf water uses a conversion factor of 1 mmol CO 2 m -3 dissolved in leaf water for each 20.4 μmol CO 2 mol -1 total atmospheric gas (from pp. 377 and 384 of Nobel, 2005). For a ventilated thalloid liverwort the ratio of 9 m 2 mesophyll cells exposed to the intercellular gas space per m 2 projected thallus area (Green and Snelgar, 1982), and for a hornwort or and unventilated liverwort thallus the ratio is 1 (Green and Snelgar, 1982), with other data from Meyer et al. (2008).
Chlamydomonas) of a carbonic anhydrase, gives a rate of CO 2 production, and an equilibrium CO 2 concentration, similar to that in the extracellular acid zones of some freshwater macrophytes (Raven, 1997b;Moroney and Ynalvez, 2007;Jungnick et al., 2014;. The final step in the CCM is diffusion of the CO 2 from the lumen to the stroma, and especially to the pyrenoid where most of the Rubisco occurs in Chlamydomonas (Raven, 1997b;. CO 2 leakage could occur from the pyrenoid back to the bulk medium. Energetically downhill entry of CO 2 as part of a CCM occurs in cyanobacteria, although without localized surface acidification (see data of Maeda et al., 2002, and models of Mangan and Brenner, 2014;Eichner et al., 2015) (Fig. 1). Three further essential components are, first, active HCO 3 influx at the plasmalemma, and the unidirectional conversion of CO 2 to HCO 3 energized by the NDHI 4 component of cyclic electron flow round photosystem I at the outer surface of the thylakoid membrane. Second, the carboxysomes, containing Rubisco and carbonic anhydrase, whose protein subunit walls probably have a limited permeability to CO 2 (see estimates in Table 1). The cytosolic HCO 3 from these two sources enters carboxysomes through pores also allowing permeation of anions (Raven, 2006) and H + (Menon et al., 2010) or, perhaps, OH -. Finally, HCO 3 in the carboxysome lumen is acted on by carbonic anhydrase, producing CO 2 that is (mainly) consumed by Rubisco in the carboxysome, though some CO 2 could leak to the cytosol. The extent of CO 2 leakage through the carboxysomal wall is likely to be significant, even with a low CO 2 permeability coefficient across the carboxysomal wall with its positively charged pores, because of the large CO 2 accumulation factor (two to three orders of magnitude) in the carboxysome lumen relative to the cytosol during photosynthesis (Eichner et al., 2015). Modelling by Mangan and Brenner (2014) finds that the optimal carboxysome wall permeability coefficient for CO 2 for maximal CO 2 accumulation in the carboxysome lumen is around 10 -5 m s -1 . Hopkinson et al. (2011) and Hopkinson (2014) propose a general similar mechanism for diatoms, with active HCO 3 influx at the plasmalemma (Nakajima et al., 2013) and parallel non-energized CO 2 influx (Fig. 2). These models involve cytosolic carbonic anhydrase to convert the CO 2 to the equilibrium concentration of HCO 3 -, with active HCO 3 uptake by chloroplasts. This latter step has not yet been identified in diatoms.
Is there a role for active transport of CO 2 ? The occurrence of a CO 2 -stimulated ATPase from the 'microsomal' fraction (= plasmalemma?) of the freshwater green (chlorophycean) alga Eremosphaera viridis, the predominance of CO 2 uptake in photosynthesis in this alga, and the electroneutrality of CO 2 uptake (ruling out cation symport), is consistent with CO 2 uptake by primary active transport (Rotatore et al., 1992;Deveau et al., 1998;Huertas et al., 2000a;Deveau et al., 2001). No other CO 2 transporters that could reasonably function in active CO 2 transport are known. Accordingly, the possibility that other eukaryotes depend on a mechanism of the kind suggested by Beardall (1981) and Hopkinson et al. (2011), involving passive CO 2 entry at the plasmalemma and active HCO 3 transport into the chloroplasts, cannot be ruled out for algae with a CCM and dominant CO 2 uptake, e.g. acidophilic eukaryotic algae, unless it has been shown that there is no HCO 3 transporter at the chloroplast envelope. Rotatore and Colman (1990) showed that isolated chloroplasts of Chlorella ellipsoidea could take up HCO 3 by active Fig. 1. A schematic model for inorganic carbon transport, and CO 2 accumulation and leakage in cyanobacteria. Low affinity transport systems are shown in grey and high affinity systems are shown in black, and are found at the plasmalemma and/or thylakoid membrane. Transporters whose characteristics are unknown are shown in white. Redrawn after Fig. 1 of Price et al. (2002), Badger and Price (2003), and Giordano et al. transport, but had no active CO 2 uptake; however, the HCO 3 influx uptake by isolated chloroplasts is less than that at the plasmalemma on a per cell basis (Rotatore and Colman, 1991a,b). Rotatore and Colman (1991c) suggest that there is active uptake of CO 2 at the plasmalemma of Chlorella saccharophila and C. ellipsoidea, although the possibility suggested by Beardall (1981) and Hopkinson et al. (2011) of passive CO 2 followed by active entry of inorganic C into chloroplasts cannot be ruled out.

HCO 3 entry in organisms expressing a biophysical CCM
Use of HCO 3 is indicated by more rapid photosynthesis than can be accounted for by the uncatalysed rate of HCO 3 to CO 2 conversion (Briggs, 1959). The 'direct' use of HCO 3 involves influx of the anion at the plasmalemma, as compared with the 'indirect' use by external conversion to CO 2 as described in the previous section (see Briggs, 1959). The physiological methods of demonstrating direct use of HCO 3 involve the known absence, or inhibition, of external carbonic anhydrase(s). In cyanobacteria (Eichner et al., Hopkinson et al., 2014) and eukaryotic algae such as diatoms (Nakajima et al., 2013), HCO 3 entry has been shown by physiological methods, and also by molecular genetic techniques, including ectopic expression and tests of functionality of the HCO 3 transporter gene. The processes in cyanobacteria (Mangan and Brenner, 2014;Eichner et al., 2015) ( Fig. 1) and diatoms (Hopkinson et al., 2011;Hopkinson, 2014) (see Fig. 2) have been recently modelled.
In other algae HCO 3 entry has been shown by physiological methods, including the absence of inhibition of photosynthesis by pH buffers or by inhibition of external carbonic anhydrase, and inhibition by inhibitors of anion exchange proteins (Raven and Hurd, 2012). In some cases, e.g. the eustigmatophycean marine microalga Nannochloropsis gaditana, all of the inorganic carbon entering in the CCM involves direct entry of HCO 3 -(e.g. Munoz and Merrett, 1989;Huertas and Lubián, 1997;Huertas et al., 2000bHuertas et al., , 2002. In most cases, there is entry of both CO 2 and HCO 3 in CCMs (Korb et al., 1997;Tortell et al., 1997;Burkhardt et al., 2001;Giordano et al., 2005;Rost et al., 2006aRost et al., ,b, 2007Tortell et al., 2008) and, in a few cases (see above) only CO 2 enters in algae with CCMs.
Isolated, metabolically active chloroplasts of some green algae with CCMs show CO 2 and HCO 3 uptake into the chloroplasts as well as into whole cells (Amoroso et al., 1998, van Hunnik et al., 2002, Giordano et al., 2005, and references therein). Yamano et al. (2015) show cooperative expression of the plasmalemma HCO 3 -HLA3 ABC transporter and the chloroplast envelope LCIA formate/nitrite transporter homologue (Wang and Spalding, 2014) in C. reinhardtii. LCIA is probably a HCO 3 channel (Wang and Spalding, 2014;Yamano et al. 2015); Wang and Spalding (2014) point out that such a channel could not act to accumulate HCO 3 in the stroma relative to the cytosol since the electrical potential difference across the chloroplast envelope is stroma negative relative to the cytosol.

Leakage from the intracellular inorganic C pool of CCMs
Significant attention has been paid to leakage of CO 2 from terrestrial C 4 plants; this has been thoroughly reviewed by Kromdijk et al. 2014 (Table 3 and Supplementary Table S1, available at JXB online). For typical C 4 anatomy with mesophyll cells with intercellular gas spaces and a single bundle sheath layer with limited exposure to intercellular gas spaces and, in some cases, a suberin (mestome) sheath that could further limit CO 2 leakage, Kromdijk et al. (2014) give an excellent critique of the methods used to determine the leakiness to CO 2 (CO 2 efflux as a fraction of gross CO 2 influx) and list their outcomes. These are 14 CO 2 labelling to determine the size of the bundle sheath inorganic carbon pool (and hence CO 2 efflux) or to directly estimate CO 2 efflux, the deviation of the quantum yield of CO 2 assimilation from the value predicted from biochemistry assuming no CO 2 leak, and the natural abundance of stable carbon isotopes in the organic matter of the plant (determined by destructive sampling, or from online measurements of CO 2 before and after gas flow over photosynthesizing plants) relative to that of source CO 2 .
All of these methods have problems (Kromdijk et al., 2014;von Caemmerer et al., 2014). The values for leakiness vary between -0.03-0.70. For the much less common case of terrestrial single-cell C 4 photosynthesis, the leakiness is similar to that for typical C 4 anatomy determined by similar methods (King et al., 2012). The permeability of the bundle sheath cells for CO 2 (1.6-4.5.10 -6 m s -1 : Table 4), derived from the CO 2 efflux from the pool accumulated by the CCM and the driving force of the difference in CO 2 concentration between the CCM pool and the medium, is at least an order of magnitude higher than the permeabilities for cyanobacteria (Table 4). However, the bundle sheath permeability is two Table 3.

Leakage of inorganic C from CCMs as a fraction of the inorganic C pumped into the intracellular pool for in terrestrial C 4 flowering plants, hornworts, eukaryotic algae, and cyanobacteria
Values are from Supplementary Table S1 except for C 4 terrestrial flowering plants where the more detailed data in Table 1 of Kromdijk et al. (2014) was used. For C 3 plants, leakage of CO 2 from photorespiration is <0.2 of gross CO 2 fixation (see text).

Organism
Range of CO 2 leakage estimates as a fraction of gross CO 2 entry, from Supplementary Table S1 Mean leakage from estimates in Supplementary Table S1 or (C 4 terrestrial flowering plants) the more detailed data in Table 1 of Kromdijk et al. (2014)  2.49 ± 0.13.10 -8 m s -1 (standard error, n=4) -3.36 ± 0.14.10 -8 m s -1 (standard error, n=18) Salon et al. (1996a,b) Synecchococcus 1 HCO 3 -1.47 ± 0.23.10 -9 m s -1 (standard error, n = 7) -1.84 ± 0.17.10 -9 m s -1 (standard error, n=7) CO 2 1.6-4.5.10 -6 m s -1 (no estimates of errors given) Furbank et al. (1989) 1 The quantification of the efflux of HCO 3 is less direct than that of CO 2 efflux. As mentioned by Salon et al. (1996b), the permeability coefficient for HCO 3 is a minimal value since the inside-negative electrical potential difference across the plasmalemma is not accounted for in the calculations.
orders of magnitude less than the mesophyll permeability in C 3 plants ( Table 2).
Leakage of an increased fraction of the CO 2 released into the bundle sheath by the biochemical CO 2 pump at low light is thought to be a reason for the rarity of shadeadapted C 4 plants (see Bellasio and Griffiths, 2014). Bellasio and Griffiths (2014) point out that there is an ontogenetic shading of older leaves in high light-adapted C 4 plants, and that up to 50% of C 4 crop photosynthesis occurs in shaded leaves, and investigated CO 2 leakage in shade-acclimated leaves of the sun-adapted Zea mays. They found that CO 2 leakage as a fraction of PEPc activity (= biochemical CO 2 pump) stayed constant with decreasing light, thus differing from expectation of a relative increase in leakage. The basis for the this constancy is a decreased PEPc activity relative to that of Rubisco, and fixation of an increased fraction of the CO 2 generated from respiration in bundle sheath cells.
Less attention has been paid to leakage of CO 2 from terrestrial CAM plants (Cockburn et al., 1979;Winter and Smith, 1996;Nelson et al., 2005;Nelson and Sage, 2008;Winter et al., 2015). Cockburn et al. (1985) examined the shootless orchid Chiloschista usneoides where CAM occurs (in the absence of other photosynthetic structures) in the astomatous velameniferous root. The absence of stomata means that the usual terrestrial CAM method of diurnal closure of stomata decreasing CO 2 leakage during deacidification and CO 2 refixation by Rubisco is unavailable. Cockburn et al. (1985) showed that the intercellular CO 2 concentration during deacidification is not significantly different from that of the surrounding atmosphere, while the intercellular CO 2 concentration during dark acidification is lower than that of the surrounding atmosphere. While lower intercellular CO 2 concentration in the deacidification phase than is the case of stomata-bearing CAM structures decreases the leakage of CO 2 from intercellular gas spaces in the stomata-less roots, it also means that carboxylase activity of Rubisco is likely to be substantially below saturation, and the Rubisco oxygenase activity is likely to be significant.
For aquatic vascular plants with CAM there is also no possibility of stomatal limitation of leakage of CO 2 produced during deacidification in the light. For isoetids there is very little loss from the possible leakage of CO 2 from the astomatal, cuticularized, photosynthetic part of the leaf, and even loss from any lower, less cuticularized, part of the leaf might be limited or abolished by the high CO 2 concentration in the surrounding sediment that contains mineralizing particulate organic matter derived by sedimentation from the plankton. The non-isoetid submerged aquatic CAM flowering plant Crassula helmsii also lacks the leakage-limiting stomatal closure mechanism of terrestrial Crassula spp. C. helmsii can show net CAM fixation from external CO 2 in the dark and also net photosynthetic C 3 CO 2 assimilation from external CO 2 in parallel with refixation of internal CO 2 generated in deacidification from malic acid, with, presumably, implications for CO 2 leakage (Newman and Raven, 1995;Maberly and Madsen, 2002;Klavsen and Maberly, 2010).
Of course, the great majority of aquatic primary producers carrying out almost all of the aquatic primary productivity involving CCMs do not express CAM. Essentially all of the work on leakage of CO 2 from intracellular pools of the CCM in aquatic organisms comes from cyanobacteria and eukaryotic microalgae; very little is known of leakage of CO 2 from algal macrophytes or submerged aquatic vascular macrophytes that concentrate CO 2 by C 4 metabolism or a biophysical CCM. Perhaps the clearest example of CO 2 leakage comes from the work of Tchernov et al. (1997Tchernov et al. ( , 1998Tchernov et al. ( , 2003 using membrane inlet mass spectrometry (MIMS). This method gives estimates of changes in CO 2 and O 2 in solution, with the difference between the two (if the photosynthetic quotient is assumed to be 1) representing the HCO 3 flux, typically (see above) HCO 3 influx. Tchernov et al. (1997Tchernov et al. ( , 1998Tchernov et al. ( , 2003 found an increase in external O 2 and also CO 2 , with the computed HCO 3 influx exceeding the organic carbon production rate computed from O 2 production. Especially at high light, the HCO 3 influx can significantly exceed the rate of photosynthesis, with the 'excess' inorganic carbon lost as CO 2 in (for example) the cyanobacterium Synechococcus and the eustigmatophycean eukaryotic alga Nannochloropsis (Tchernov et al., 1997(Tchernov et al., , 1998(Tchernov et al., , 2003. There are also cases of CO 2 influx exceeding the organic C production, implying net HCO 3 efflux. However, the general case with MIMS measurements is that of CO 2 decrease, or at least no increase, in the light. Here the MIMS method can be used to estimate CO 2 efflux in the light from the CO 2 efflux immediately after the cessation of illumination (Badger et al., 1994;Salon et al., 1996a,b;Eichner et al., 2015; Table 3 and Supplementary  Table S1, available at JXB online). Badger et al. (1994) found a leakage of not more than 0.1 of net photosynthesis in low inorganic carbon-grown cells of Synechococcus, while for low CO 2 grown Chlamydomonas the corresponding leakage is 0.5 at low inorganic C and 0.1 at high inorganic C. Again using Synechococcus, Salon et al. (1996a,b) and Salon and Canvin (1997) were able to distinguish CO 2 efflux from HCO 3 efflux immediately after darkening; the total inorganic C efflux in the presence of carbonic anhydrase was measured, as was the CO 2 efflux under non-equilibrium conditions, and the difference is the HCO 3 efflux. The CO 2 efflux was only 0.08 of the maximum CO 2 influx, while the HCO 3 efflux was 0.45 of the maximum HCO 3 influx. The CO 2 permeability coefficient determined from the measurements and expressed in terms of the plasmalemma area was 3.10 -8 m s-1 , while it was 1.6-2.5 m s -1 in terms of the carboxysome area (Tables 1, 14). The HCO 3 permeability coefficient expressed in terms of the plasmalemma area is at most 1.4-1.7.10 -9 m s -1 (Table 4); the value is an upper limit because the inside-negative electrical potential component was not used in the calculation (Salon et al. 1996b; see also Ritchie et al. 1996).
In the case of Trichodesmium the leakage (CO 2 efflux:gross inorganic carbon uptake) calculated using MIMS is 0.3-0.7 for two CO 2 levels and with or without NO 3 -(Eichner et al., 2015), as compared with values of 0.5-0.9 in previous work on this organism (see Kranz et al., 2009Kranz et al., , 2010 (Table 3). The other main method for estimating leakage of CO 2 from aquatic organisms expressing a CCM is from natural abundance 13 C/ 12 C of particulate organic matter gained by photolithotrophic growth and of the 13 C/ 12 C of external inorganic carbon species (Sharkey and Berry, 1985;Eichner et al., 2015; Table 3 and Supplementary Table S1). This method is also used for estimating leakage of CO 2 from terrestrial C 4 plants (see above). Eichner et al. (2015) found a difference between the MIMS and the natural abundance 13 C/ 12 C estimates of leakage, with the latter method giving values of the 0.82 and 1.14. They point out that the values > 1 are theoretically impossible; Eichner et al. (2015) suggest kinetic fractionation between CO 2 and HCO 3 in the cytosol and/or enzymatic fraction by the 'energized, unidirectional carbonic anhydrase' NDH-1 4 as possible causes of the very high leakage estimates. An analogous role might be played by the LCIA/ LCIB system in C. reinhardtii (Wang and Spalding, 2014), so that estimates of leakage from carbon isotope ratios may be too high in Chlamydomonas and possibly in other eukaryotic algae as well. This possibility is acknowledged in Table 3 and Supplementary Table S1 (available at JXB online).
The mean value for the leakage determined by MIMS for cyanobacteria and eukaryotic algae in Supplementary  Table S1 is, as indicated in Table 3, respectively 0.407 ± 0.214 (standard deviation, n=5) and 0.36 ± 0.16 (standard deviation, n=14). The mean values for hornworts with CCMs and C 4 terrestrial flowering plants are 0.263 ± 066 (standard deviation, n=3) and 0.260 ± 0.106 (standard deviation, n=20), respectively. There is a trend (not significant) for lower fractional leakage in terrestrial C 4 plants and hornworts than for cyanobacteria and eukaryotic algae.
As for C 4 plants, so with cyanobacterial and algal CCMs: the prediction is an increasing fraction of the inorganic C pumped into the intracellular pool being lost as CO 2 efflux with decreasing incident photosynthetically active radiation, and that algae relying on diffusive CO 2 entry from the medium to Rubisco would be more common in low-irradiance habitats (review by Raven et al. 2000). The limited data available agree with these predictions (Raven et al., 2000(Raven et al., , 2002Burkhardt et al., 2001;de Araujo et al., 2011;Cornwall et al., 2015; see Table 3). Turning to temperature,  show that algal CCMs occur at lower temperatures than does terrestrial C 4 photosynthesis. Kranz et al. (2015) showed that the energy cost of algal CCMs decreased at low temperatures; it is not known if this is the case for terrestrial C 4 photosynthesis.
Leakage from the photorespiratory carbon oxidation cycle(s) Tcherkez (2013) gives an excellent critique of the CO 2 fluxes associated with C 3 photosynthesis, photorespiration, and respiration. With a carboxylase:oxygenase ratio of Rubisco in vivo in a C 3 plant in the present atmosphere of 3:1, CO 2 production in the photorespiratory carbon oxidation cycle is 0.167 of gross CO 2 assimilation in photosynthesis (Raven, 1972a,b;Tcherkez, 2013). There is about 15% recycling of the photorespiratory CO 2 and 'dark' respiratory CO 2 production in photosynthesizing structures (Raven, 1972a,b;Tcherkez, 2013), so the CO 2 release into the environment as a fraction of gross photosynthesis is 0.167 × 0.85 or 0.14; it is likely that an upper limit is 0.20. This is at the low end of the range for leakage in C 4 plants and in algae CCMs (Table 3).
The various C 3 -C 4 intermediate flowering plants have photosynthetic gas exchanges that show varying mixtures of C 3 and C 4 characteristics (Hylton et al., 1988;Rawsthorne et al., 1988a,b;von Caemmerer, 1989;Rawsthorne and Hylton, 1991;Morgan et al., 1993). This work shows the expression of most or all the glycine decarboxylase activity, and some of the Rubisco carboxylase-oxygenase, in bundle sheath cells. This location of the decarboxylase of the photorespiratory carbon oxidation cycle, with some Rubisco, in tightly packed bundle sheath cells increases recycling of CO 2 from glycine decarboxylase by the carboxylase activity of Rubisco relative to leakage of CO 2 back to the intercellular spaces.
CCMs increase the steady-state CO 2 :O 2 ratios at the site of Rubisco activity; this decreases the ratio of Rubisco oxygenase activity to that of Rubisco carboxylase activity. The decreased rate of production of phosphoglycolate involves a decreased rate of the pathway(s) converting phosphoglycolate into phosphoglycerate and triose phosphate that can be used in core metabolism and/or complete oxidation to CO 2 (Eisenhut et al., 2008;Hagemann et al., 2010;Young et al., 2011;. Even this low flux is essential, since deletion of all three of the pathways of phosphoglycolate metabolism (photorespiratory carbon oxidation cycle; tartronic semialdehyde pathway; complete oxidation via oxalate) is lethal (Eisenhut et al., 2008;Hagemann et al., 2010;. Comparable work has not been yet been carried out in photosynthetic eukaryotes with CCMs where, at least in embryophytes, the pathway of phosphoglycolate metabolism is the photorespiratory carbon oxidation cycle. However, it is known that the C 4 and CAM CCMs decrease the rate of phosphoglycolate synthesis and flux through the photorespiratory carbon oxidation cycle relative to what occurs in otherwise comparable C 3 plants.

Conclusions
Quantifying the flux of CO 2 into and out of cells is difficult. All known irreversible decarboxylases produce CO 2 ; CO 2 is also the product/substrate of enzymes that can act as carboxylases and decarboxylases. Whether reversible of irreversible, decarboxylases produce CO 2 , which can potentially leak out of cells. Some irreversible carboxylases also have CO 2 as their substrate; others use HCO 3 -. There is still controversy as to the relative role of permeation through the lipid bilayer and of movement through membrane proteins such as CO 2 -selective aquaporins in the downhill, non-energized, movement of CO 2 . Such movement is involved in CO 2 entry in terrestrial and aquatic organisms with C 3 physiology and biochemistry, as well as terrestrial C 4 plants and all CAM plants. Although there is also some evidence of active CO 2 transport at the plasmalemma of algae, downhill CO 2 transport is part of some mechanisms involved in the use of external HCO 3 and CCM function. Further work is needed to test the validity of the mechanism based on localized surface acidification in marine macrophytes, and on HCO 3 conversion to CO 2 in the thylakoid lumen. HCO 3 active influx at the plasmalemma underlies all cyanobacterial and some algal CCMs. HCO 3 can also enter chloroplasts of some algae, possible as part of a CCM. Leakage from the intracellular CO 2 and HCO 3 pool of CCMs sometimes occurs as HCO 3 -, but typically occurs as CO 2 . Leakage from cyanobacterial and microalgal CCMs, and terrestrial C 4 plants and hornworts with CCMs, usually involve half or less of the gross inorganic C entering in the CCM, but can be as high as 80%. CO 2 leakage to the environment from photorespiration in C 3 plants is less than 20% of gross photosynthesis. Leakage from terrestrial CAM plants, algal macrophytes, and vascular aquatic macrophytes with CCMs (C 4 , CAM, biophysical CCMs) has been less extensively examined. From what is known, CO 2 leakage can be appreciable in many photoautotrophs with CCMs and increases the energetic cost of net inorganic carbon fixation (see .

Supplementary data
Supplementary data are available at JXB online. Table S1. Leakage of inorganic C from CCMs as a fraction of the inorganic C pumped into the intracellular pool.