Quantification of extracellular carbonic anhydrase activity in two marine diatoms and investigation of its role.

Many microalgae induce an extracellular carbonic anhydrase (eCA), associated with the cell surface, at low carbon dioxide (CO2) concentrations. This enzyme is thought to aid inorganic carbon uptake by generating CO2 at the cell surface, but alternative roles have been proposed. We developed a new approach to quantify eCA activity in which a reaction-diffusion model is fit to data on (18)O removal from inorganic carbon. In contrast to previous methods, eCA activity is treated as a surface process, allowing the effects of eCA on cell boundary-layer chemistry to be assessed. Using this approach, we measured eCA activity in two marine diatoms (Thalassiosira pseudonana and Thalassiosira weissflogii), characterized the kinetics of this enzyme, and studied its regulation as a function of culture pH and CO2 concentration. In support of a role for eCA in CO2 supply, eCA activity specifically responded to low CO2 rather than to changes in pH or HCO3(-), and the rates of eCA activity are nearly optimal for maintaining cell surface CO2 concentrations near those in the bulk solution. Although the CO2 gradients abolished by eCA are small (less than 0.5 μm concentration difference between bulk and cell surface), CO2 uptake in these diatoms is a passive process driven by small concentration gradients. Analysis of the effects of short-term and long-term eCA inhibition on photosynthesis and growth indicates that eCA provides a small energetic benefit by reducing the surface-to-bulk CO2 gradient. Alternative roles for eCA in CO2 recovery as HCO3(-) and surface pH regulation were investigated, but eCA was found to have minimal effects on these processes.

To overcome the inefficiencies of Rubisco, many phytoplankton operate a CO 2 -concentrating mechanism (CCM) that increases Rubisco's rate of carbon fixation and reduces oxygen fixation by increasing the concentration of CO 2 around the enzyme. CCMs typically consist of inorganic carbon (C i ) pumps, carbonic anhydrases (CAs) to equilibrate HCO 3 2 and CO 2 , and a compartment to confine Rubisco, such as the pyrenoid or carboxysome, minimizing the volume in which CO 2 is elevated (Badger et al., 1998;Kaplan and Reinhold, 1999;Giordano et al., 2005). Intracellular carbonic anhydrases (iCAs) play multiple roles in CCMs, including the conversion of accumulated HCO 3 2 to CO 2 around Rubisco and the prevention of CO 2 leakage (Badger, 2003). Some organisms also have an extracellular carbonic anhydrase (eCA) associated with the cell wall, plasma membrane, or periplasmic space. The role of eCA has been enigmatic, although it is clearly related to the CCM. In Chlamydomonas reinhardtii, where eCA has been most thoroughly studied, the major eCA (Cah1) is up-regulated at low CO 2 , and its regulatory network includes a transcription factor that induces the expression of other CCM genes as well (Yoshioka et al., 2004;Ohnishi et al., 2010). In other organisms, eCA activity generally increases, in some cases dramatically, at low CO 2 , supporting its association with the CCM, but the genetic details of regulation are not known (Nimer et al., 1997;Rost et al., 2003).
When first discovered in microalgae, eCA was thought to facilitate CO 2 influx by keeping surface CO 2 at bulk solution concentrations (Moroney et al., 1985). Many microalgae take up CO 2 to support photosynthesis, but because of the low concentration of CO 2 in most natural waters and the slow rate of HCO 3 2 dehydration, this uptake can lead to some depletion of CO 2 in the diffusive boundary layer surrounding the cell. eCA accelerates the dehydration of HCO 3 2 to CO 2 within the boundary layer, increasing the surface CO 2 concentration. Support for this role has come from experiments showing that inhibition of eCA reduces photosynthetic rates and C i accumulation in disparate microalgae, including the green alga C. reinhardtii, the dinoflagellate Prorocentrum micans, the prymnesiophyte Phaeocystis globosa, and the diatom Thalassiosira weissflogii (Moroney et al., 1985;Nimer et al., 1999;Elzenga et al., 2000;Burkhardt et al., 2001).
Although there is strong support for the role of eCA in CO 2 supply, some observations suggest that it may have additional or alternative roles. In some organisms, blocking eCA does not inhibit photosynthesis, and in C. reinhardtii, knocking out the major eCA had only minor effects on photosynthesis (Van and Spalding, 1999;Moroney et al., 2011). In C. reinhardtii, these results may be explained by the fact that only a small fraction of the total eCA activity is apparently required to support photosynthetic CO 2 uptake, so that if inhibition is not fully effective, CO 2 could still be kept high at the cell surface (Moroney et al., 1985;Palmqvist et al., 1990;Moroney et al., 2011). Such excess may point to other roles for eCA. On the basis of a correlation between HCO 3 2 uptake and eCA activity, Trimborn et al. (2009) suggested that eCA in diatoms may be used to recover leaked CO 2 , converting it to HCO 3 2 to enhance uptake. eCA may also have a role in pH homeostasis, which is a common role for CA in heterotrophic organisms (Boron, 2004;Swietach et al., 2010).
We sought to better understand the role of eCA in two diatoms by making quantitative measurements of eCA rates and modeling the effect of eCA on boundarylayer chemistry. Our approach to quantify eCA activity is an adaptation of a common method to measure CA activity based on the enzyme's acceleration of 18 O removal from labeled C i . This technique has been used to measure the kinetics of isolated CA enzymes (Silverman, 1982), iCA activity (Tu et al., 1978), and eCA activity (Palmqvist et al., 1994;Delacruz et al., 2010). The advance presented here is to extract a quantitative, intrinsic measure of surface eCA activity by applying a simple box model of 18 O-exchange kinetics to the data that accounts for the localization of the enzyme. In contrast, previous methods to measure eCA activity have effectively treated the activity as dispersed throughout the solution and, in some cases, are semiquantitative (Palmqvist et al., 1994;Elzenga et al., 2000;Delacruz et al., 2010). Previous approaches based on 18 O exchange use the long-term rate of 18 O removal as a quantitative but empirical measure of eCA activity (Palmqvist et al., 1994;Delacruz et al., 2010). Another technique uses the rate of equilibration of 14 C between CO 2 and HCO 3 2 , quantifying eCA activity as an increase in the rate of CO 2 hydration in the bulk solution (Elzenga et al., 2000;Martin and Tortell, 2006). A key advantage of our approach is that eCA catalysis is treated as a surface phenomenon, allowing the measured activities to be used in modeling the effects of eCA on boundary-layer chemistry. Using the eCA rates measured in the diatoms, we assessed the potential role of eCA in CO 2 supply, CO 2 recovery, and pH homeostasis.

RESULTS
To determine eCA activity on the cell surface, paired measurements of 18 O-labeled C i exchange were made in the presence and absence of an eCA inhibitor. When an eCA inhibitor is present, the 18 O-CO 2 data were used to determine iCA activity and CO 2 and HCO 3 2 fluxes into the cell (Tu et al., 1978). Subsequently, surface eCA activity was quantified by comparing simulations using a model that describes the temporal evolution of the isotopologs of C i in and around a cell ( Fig. 1; see "Materials and Methods"), with 18 O removal rates measured in the absence of an eCA inhibitor.

iCA Kinetics and Mass Transfer Coefficients
Our method for the determination of eCA activity requires that iCA activity and mass transfer coefficients for passive CO 2 and HCO 3 2 fluxes be known. These terms were determined from 18 O-removal kinetics when eCA activity was inhibited using the CA inhibitor acetazolamide (AZ) or dextran-bound acetazolamide (DBAZ; Tu et al., 1978;Hopkinson et al., 2011). iCA activities depended on culture conditions, ranging between 80 and 200 s 21 for Thalassiosira pseudonana and between 20 and 150 s 21 for T. weissflogii. Mass transfer coefficients for CO 2 (f c ) were 1.3 6 0.4 3 10 28 cm 3 s 21 for T. pseudonana and 2.9 6 0.9 3 10 28 cm 3 s 21 for T. weissflogii, while HCO 3 2 mass transfer coefficients were less than 1 3 10 212 cm 3 s 21 for T. pseudonana and 1.9 6 1.6 3 10 210 cm 3 s 21 for T. weissflogii, similar to previously reported values (Hopkinson et al., 2011).
Accurate determination of iCA activity and CO 2 and HCO 3 2 mass transfer coefficients requires that eCA be fully inhibited. 18 O removal follows a biphasic pattern in which there is an initial, rapid removal of 18 O as CO 2 enters CA-containing cells followed by a slower, longterm loss of 18 O due to the depletion of 18 O from HCO 3 2 (Silverman et al., 1976;Fig. 2). We used the long-term rate of 18 O removal or "phase II slope" (calculated as the slope of a linear fit through natural log-transformed 18 O atom fraction data) as an empirical measure of eCA activity to establish that eCA effectively inhibited the CA inhibitors ( Fig. 3; Delacruz et al., 2010). Application of increasing concentrations of AZ or DBAZ to cells expressing eCA reduces the phase II slope to near background, uncatalyzed exchange rates, verifying that eCA activity was effectively eliminated. The presence of iCA accelerates long-term 18 O removal slightly above  Table III). Fluxes between the compartments are described using mass transfer coefficients, and the reactions are treated using first-order rate constants. the background rate. We verified that neither AZ nor DBAZ had a detectable effect on iCA activity of low-pHgrown cells (where eCA is absent; see below) and so did not pass through the plasma membrane to any significant extent (data not shown).

Determination of eCA Rate Constants
After determining the rate constants for iCA and CO 2 and HCO 3 2 mass transfer coefficients, eCA activity in T. pseudonana and T. weissflogii was quantified by fitting the box model of isotope exchange to the observations (see Eqs. 1-6 in "Materials and Methods"). k sf , the first-order rate constant for eCA-catalyzed CO 2 hydration, is used as a measure for eCA activity, since it can be directly compared with the boundary-layer mass transfer coefficient for CO 2 (f c-BL ) to assess the effectiveness of eCA (see "Materials and Methods"). The model gave good fits to the 18 O-CO 2 data in most cases, and the eCA activities were consistent in replicate runs ( Fig. 2A). eCA activities (k sf ) varied with culture and assay conditions, ranging between 0 and 3.5 3 10 27 cm 3 s 21 for T. pseudonana and between 0 and 40 3 10 27 cm 3 s 21 for T. weissflogii.
In some runs, the model fits could not account for a depletion of the 13 C 18 O 16 O intermediate species later in the assay (Fig. 2B). This signature suggests reduced exchange between the surface layer and the bulk solution (Silverman et al., 1981), and the fit can be improved by reducing the diffusive HCO 3 2 flux to the cell surface (e.g. due to the presence of an extracellular matrix that reduces the diffusivity of charged ions; Stewart, 2003). However, this improvement of the fit alters the estimated eCA activity by less than 20% (Fig.  2B). Similarly, eCA activity is not sensitive to the choice of the size of the surface boundary-layer volume ( Table I). The effect of potential residual eCA activity when determining iCA rate constants and cross-membrane fluxes was also assessed using the eCA box model. eCA activity and HCO 3 2 permeability have similar effects on 18 O-CO 2 behavior, because both expose the extracellular HCO 3 2 pool to CA and so accelerate the long-term rate of 18 O removal. If eCA was not fully inhibited during the determination of iCA activity and mass transfer coefficients, the activity would be treated as increased HCO 3 2 transfer through the cell membrane (greater f b-M ). To determine the maximal residual eCA activity, we fit 18 O-CO 2 data from runs in which eCA should have been completely inhibited (50 mM or greater AZ or DBAZ) to the eCA box model (Eqs. 1-6), setting HCO 3 2 membrane permeability to zero (f b-M = 0) and treating iCA activity (k cf ), CO 2 permeability (f c-M ), and eCA activity (k sf ) as unknowns. The potential residual eCA activities (T. pseudonana, 5.2 6 7.1 3 10 29 cm 3 s 21 ; T. weissflogii, 5.4 6 4.6 3 10 28 cm 3 s 21 ) were low relative to measured eCA activities. Thus, both the empirical analysis ( Fig. 3) and the modeling approach show that the eCA inhibitors were highly effective.
eCA Kinetics: Effect of pH and C i To characterize eCA enzyme kinetics, strong eCA activity was induced by growing cultures to high density  without pH or CO 2 control (final culture pH of 8.6-8.8). The cells were then concentrated and immediately assayed for eCA activity at a range of pHs and C i concentrations. Enzyme activity (k sf ) increased linearly with pH in T. pseudonana (7.8-8.6) and in T. weissflogii (7.5-8.4; Fig. 4, A and B) over a pH range typical of marine environments. CA activity typically shows a logarithmic increase with pH as water at the active site is deprotonated (Silverman and Lindskog, 1988). Our observations indicate a linear response, which may reflect the small pH range tested or result from differences between solution and cell surface pH.
We assessed the effect of C i concentration on eCA reaction rates. eCA activity was measured at pH 7.9 and varying C i from 0.5 to 12 mM, with corresponding CO 2 concentrations ranging from 5 to 115 mM (Fig. 4, C and D). In T. pseudonana, nonlinearity in the reaction rate (CO 2 hydration rate) versus substrate concentration (CO 2 ) was observed only at the very highest CO 2 concentration. In T. weissflogii, there is more significant nonlinearity, allowing a Michaelis-Menten function to be fit to the data. From this fit, the half-saturation constant of eCA for CO 2 is 87 6 10 mM. These results show that CO 2 hydration and HCO 3 2 dehydration are effectively first order with respect to substrate concentration in the environmentally relevant range (approximately 2 mM C i , CO 2 of 5-20 mM), validating our use of a first-order rate constant as a measure of eCA activity.
eCA Expression: Effect of CO 2 and pH T. pseudonana and T. weissflogii were grown for several generations at different pHs (7.7-8.6) maintained by a pH buffer 4-(2-Hydroxyethyl)piperazine-1propanesulfonic acid (EPPS) at constant C i (2 mM), concentrated, and assayed for eCA activity at constant pH (8.0) and C i (2 mM) to determine the effect of growth conditions on eCA expression. Under these culture conditions, pH and CO 2 covary with CO 2 , ranging between 24 mM at pH 7.8 and 3 mM at pH 8.6. In T. pseudonana, eCA activity was undetectable from pH 7.8 to 8.1 but then increased dramatically above this pH (Fig. 5A). eCA activity in T. weissflogii was undetectable only in cells grown at the lowest pH (7.8) and then increased quickly to a high, constant value from pH 8.0 to 8.6 ( Fig. 5B). iCA activity (k cf ) also increased substantially from low to high culture pH in both species (T. pseudonana, 80-200 s 21 ; T. weissflogii, 2.0 3 10 212 7.29 3 10 28 8.2 3 10 212 7.34 3 10 28 4.8 3 10 211 7.31 3 10 28 1.1 3 10 210 7.32 3 10 28 20-150 s 21 ). Complementary experiments in which the culture pH was held constant but C i was varied also showed that low CO 2 induced eCA expression in T. pseudonana (Fig. 5C). The T. pseudonana eCA activity data from the constant C i and constant pH experiments converge, following a single trend, when plotted as a function of CO 2 concentration in the growth medium, showing that eCA expression was primarily controlled by CO 2 (Fig. 5D).

Effect of eCA Inhibition on Photosynthesis
We tested the effects of short-term eCA inhibition on photosynthesis. At a concentration of AZ sufficient to inhibit all detectable eCA activity (50 mM), there was no consistent effect of short-term eCA inhibition on photosynthesis under environmentally relevant conditions of C i availability (C i , 2 mM; pH 7.8-8.6; Fig. 6A). We assessed the effects of AZ ranging from 1 to 500 mM on photosynthesis in T. pseudonana and T. weissflogii grown without pH control to pH 8.7 and assayed at the same pH, but we found no significant inhibition of photosynthesis even at the highest AZ concentrations (data not shown). Only at very low CO 2 concentrations (1 mM; pH 8.7; C i , 1 mM) did short-term eCA inhibition consistently reduce photosynthesis, inhibiting oxygen production by 42% 6 5% in T. weissflogii and by 25% 6 8% in T. pseudonana (Fig. 6B).

Effect of eCA Inhibition on Growth
To test the long-term effects of eCA inhibition, growth rates of the two diatoms were measured in the presence and absence of DBAZ (Table II). The cultures were grown for 4 to 6 d under the same environmental conditions as other cultures (20°C, 16/8-h photoperiod at 125-150 mmol photons m 22 s 21 ) with 20 mM DBAZ added initially and 5 mM additional DBAZ added in the morning of day 3. In T. weissflogii, DBAZ reduced growth by approximately 10% at pH 8.4 (5 mM CO 2 ) but had no effect on growth at pH 7.8 (24 mM CO 2 ), demonstrating that the inhibitor did not have any nonspecific effects on metabolism. DBAZ had no significant effect on growth of T. pseudonana at pH 8.4.

Model Assessment of eCA on Surface Boundary-Layer Chemistry
We used a spatially resolved reaction-diffusion model of the diffusive boundary layer to quantify the effect of eCA on boundary-layer chemistry (for details, see "Materials and Methods"). The primary role of eCA is thought to be the maintenance of bulk solution CO 2 concentrations at the cell surface during photosynthesis. To assess this role, a model simulation was run in which a diatom takes up CO 2 at two-thirds its photosynthetic rate, which is typical of cultured marine diatoms (Burkhardt et al., 2001;Rost et al., 2003;Hopkinson et al., 2011). Average photosynthetic rates measured in this study were used in the simulation (T. pseudonana, 1.7 3 10 217 mol cell 21 s 21 ; T. weissflogii, 7 3 10 217 mol cell 21 s 21 ). The analysis shows that the measured eCA activities are sufficient to maintain cell surface CO 2 near bulk concentrations despite photosynthetic carbon uptake in both species (Fig. 7). In all cases, however, the absolute size of the CO 2 gradient is Figure 5. Expression of eCA as a function of culture pH and C i . A and B, When grown at a constant total C i (2 mM) but varying pH, both diatoms induce eCA at high pH/low CO 2 (A, T. pseudonana [Tp]; B, T. weissflogii [Tw]). The level of activity is sufficient to reduce surface-to-bulk CO 2 gradients, as shown by the effectiveness index (E; Eq. 13). C, When T. pseudonana was grown at constant pH (7.7 or 8.1) but varying C i , eCA was induced at low C i . D, All the T. pseudonana data converge when plotted as a function of CO 2 , showing that it is the major control on eCA expression. relatively small. In the absence of eCA, the concentration difference between the bulk solution and the cell surface is only 0.2 mM for T. pseudonana and 0.35 mM for T. weissflogii.
An alternative role for eCA in the recovery of leaked CO 2 as HCO 3 2 for subsequent uptake has also been suggested (Trimborn et al., 2008). As CO 2 leakage is just the inverse of CO 2 uptake, the modeled effects of eCA on CO 2 gradients are very similar. In both diatoms, fully induced eCA activity is able to convert nearly all the leaked CO 2 to HCO 3 2 . However, even when eCA is effective, the changes in surface HCO 3 2 concentrations are minuscule. The largest increase in HCO 3 2 concentration is 0.7 mM, which is only a 0.04% increase (Fig. 8A).
Finally, eCA could also be involved in the control of surface pH, since the C i system dominates pH buffering in seawater. One scenario, discussed below, involves H + uptake equimolar to HCO 3 2 uptake to compensate for intracellular H + consumption required to convert HCO 3 2 to CO 2 for photosynthesis. This scenario was simulated with rates of H + and HCO 3 2 uptake at the cell surface equal to photosynthetic rates, but we found that eCA activity had no effect on the surface H + perturbation induced by this uptake, because of rapid acid/base equilibration among buffer species (data not shown). CO 2 uptake creates a pH disequilibrium in the boundary layer that can be reestablished by eCA (Fig. 8B), but the effect on the H + concentration is very small.

DISCUSSION
Although there is strong evidence that eCA is linked to the CCM, its exact role has been controversial ( Van and Spalding, 1999;Trimborn et al., 2008;Moroney et al., 2011). Enhancement of CO 2 availability for photosynthesis is the most logical role for eCA, since CO 2 concentrations are low in most natural waters and can become depleted in cell boundary layers. But alternative roles in the recovery of leaked CO 2 and pH homeostasis have also been suggested, based in part on observations that the elimination of eCA does not always reduce photosynthesis. The lack of a quantitative, intrinsic measure of eCA activity has hindered the evaluation of its role. Here, we have developed an approach to quantify eCA activity, applied it to two marine diatoms, and evaluated the potential role of eCA in these organisms through an analysis of the effect of eCA activity on surface boundary-layer chemistry.
Enhancement of CO 2 Supply eCA is commonly thought to facilitate CO 2 influx by dehydrating HCO 3 2 at the cell surface. Many microalgae take up CO 2 for photosynthesis (Badger et al., 1994;Burkhardt et al., 2001), which is most likely driven by a diffusive gradient (Kaplan and Reinhold, 1999;Hopkinson et al., 2011), despite the fact that HCO 3 2 is much more abundant than CO 2 in the ocean. Net CO 2 uptake into the cell can be supported either by diffusion of CO 2 from the bulk solution or generation of CO 2 from HCO 3 2 within the boundary layer, which for microalgae would need to be catalyzed by eCA because uncatalyzed HCO 3 2 dehydration is slow (Wolf-Gladrow and Riebesell, 1997).
Consistent with a role for eCA in CO 2 supply, we find that eCA is up-regulated at low CO 2 concentrations and that induction occurs at a higher CO 2 concentration in the larger diatom T. weissflogii, which is more prone to diffusive limitation (    , 1974;Riebesell et al., 1993). Typically, the effect of CO 2 on eCA expression is assessed by varying pH at a constant C i concentration or by bubbling cultures with air containing varying levels of CO 2 (Nimer et al., 1997;Rost et al., 2003). In both approaches, CO 2 and pH are closely coupled, with CO 2 decreasing as pH increases, but it is generally assumed that CO 2 is the key variable regulating eCA activity. Both T. pseudonana and T. weissflogii expressed eCA at low CO 2 /high pH (Fig. 5, A and B) in such an experiment, as is commonly observed. But by additionally culturing T. pseudonana at constant pH but variable C i (Fig. 5C), we were able to clearly show that eCA activity responds to low CO 2 concentrations, rather than changes pH or HCO 3 2 , consistent with a role for eCA in CO 2 uptake (Fig. 5D).

Gavis
A key finding, made possible by the quantitative nature of the eCA measurements, is that the amount of eCA expressed by both diatoms is appropriate to support CO 2 uptake, but not excessive. As shown in Equations 11 to 13 (see "Materials and Methods"), the relative magnitude of the boundary-layer mass transfer coefficient (f c-BL ) and eCA activity (k sf ) controls the sources of CO 2 (diffusion or dehydration) for net uptake and describes the extent to which eCA is able to mitigate CO 2 drawdown in the boundary layer. eCA activity at low CO 2 in T. pseudonana and T. weissflogii is two to 10 times greater than the boundary-layer mass transfer coefficient (f c-BL ; T. pseudonana, 5.9 3 10 28 cm 3 s 21 ; T. weissflogii, 1.4 3 10 27 cm 3 s 21 ), such that eCA activity is nearly optimal for the abolishment of bulk solution to surface CO 2 gradients (Fig. 5). A spatially resolved model confirms that the eCA activities are able to maintain surface CO 2 concentrations at near bulk concentrations ( Fig. 7; for model description, see "Materials and Methods"). The lack of excess eCA for CO 2 supply in these diatoms contrasts with C. reinhardtii, where there is apparently excess eCA for CO 2 supply (Moroney et al., 1985), which could be taken to imply that it has other roles.
While the magnitude of the CO 2 drawdown at the cell surface is relatively small (0.2-0.35 mM; Fig. 7), it is similar in size to the CO 2 gradient across the cytoplasmic membrane that drives CO 2 influx. For example,  has only a minor effect on the H + concentration during CO 2 uptake. Both panels show results from simulations with T. weissflogii, since the effects of eCA, although still small, are more significant for this species.
given the permeability of the T. weissflogii membrane to CO 2 (Hopkinson et al., 2011), a 0.4 mM CO 2 gradient across the plasma membrane would be needed to support CO 2 uptake at the rate estimated for our culture conditions. The high permeability of membranes to CO 2 means that this influx occurs passively, which is potentially more energy efficient than active uptake of HCO 3 2 , but requires the cell to generate a CO 2 gradient across the cytoplasmic membrane. In the absence of eCA, intracellular CO 2 would need to be drawn down further to maintain CO 2 uptake, which diatoms are capable of doing, as shown by their ability to take up CO 2 over a wide range of extracellular CO 2 concentrations (Burkhardt et al., 2001), but at the cost of increased energetic expenditure.
Short-term inhibition of eCA at CO 2 concentrations greater than 1 mM did not reduce photosynthesis, presumably because cytoplasmic CO 2 concentrations could be lowered to maintain CO 2 influx (Fig. 6A). Photosynthesis was only reduced when extracellular CO 2 concentrations decreased to 1 mM (Fig. 6B), at which point the cytoplasmic CO 2 concentration was 0.4 mM in T. pseudonana and 0.2 mM in T. weissflogii, as estimated using boundary-layer mass transfer coefficients and the cytoplasmic membrane permeability for each species. The cells apparently could not lower their intracellular CO 2 concentrations further, and for T. weissflogii, the intracellular CO 2 concentration was so low that greater reduction would not significantly increase CO 2 influx. Long-term inhibition of eCA reduced the growth of T. weissflogii at low CO 2 (Table II), consistent with an increased energetic cost of C i acquisition without eCA, although inhibition of eCA had no detectable effect on the growth of T. pseudonana, perhaps because its smaller size minimizes the magnitude of the bulk-to-surface CO 2 gradient and the energetic costs associated with compensating for this gradient. However, even a small energetic savings that allows minor increases in growth rate can have major consequences for the ecological success of plankton in the ocean (Tilman, 1977).

Alternative Roles for eCA
Alternative roles for eCA in the recovery of leaked CO 2 and the regulation of cell surface pH have been suggested (Trimborn et al., 2008). The CCM is not perfectly efficient, in large part because of the high permeability of membranes to CO 2 , leading to CO 2 leakage out of the chloroplast or plasma membranes. While eCA could effectively convert leaked CO 2 to HCO 3 2 , the increase in HCO 3 2 concentration achieved by CO 2 recovery would be very small compared with the approximately 1.8 mM HCO 3 2 concentration in seawater (Fig. 8A). Assuming that diatom HCO 3 2 transporters follow Michaelis-Menten kinetics, in which the greatest sensitivity of uptake rate to substrate is a linear increase at low substrate concentrations, the increased cell surface HCO 3 2 concentration would allow at most a 0.04% increase in uptake rate. Additionally, diatoms exhibit a net CO 2 influx rather than a net CO 2 efflux under normal conditions (Burkhardt et al., 2001;Hopkinson et al., 2011), so there is no CO 2 leaking from the cell to be recovered.
CAs are commonly involved in pH regulation (Boron, 2004), so it is conceivable that eCA may be involved in pH maintenance, since the C i system is the main pH buffer in seawater. The best example of the role of eCA in pH maintenance comes from human cancer cells, where high rates of respiration lead to a high acid load (in the form of CO 2 ). By converting CO 2 to HCO 3 2 and H + outside the cell, eCA helps to maintain an alkaline internal environment at the expense of a more acidic extracellular environment (Swietach et al., 2010). Photosynthetic organisms such as diatoms, on the other hand, import CO 2 and HCO 3 2 for carbon fixation. Since CO 2 is ultimately the species fixed by Rubisco, the import and subsequent consumption of CO 2 has no net effect on intracellular acid/base balance. However, imported HCO 3 2 must be converted to CO 2 for fixation, consuming a proton in the process. Organisms that transport HCO 3 2 then need to import a proton (or export OH 2 ) for each molecule of HCO 3 2 . eCA could help supply H + to the cell surface to balance HCO 3 2 uptake, potentially accounting for the observed correlation between eCA and HCO 3 2 uptake in several marine phytoplankton (Trimborn et al., 2008). Simulation of the effect of eCA on boundary-layer pH for diatoms importing HCO 3 2 and H + revealed that the boundary-layer pH changes induced by uptake are very small because of rapid reactions among the buffer species HCO 3 2 /CO 3 22 and B(OH) 4 2 /B(OH) 3 . Furthermore, eCA does not alter the small pH changes, because the slow CO 2 /HCO 3 2 equilibrium is not significantly involved in boundary-layer pH buffering in this case. Alternatively, eCA could help establish pH equilibrium during CO 2 uptake. We simulated the effect of eCA on boundary-layer pH, assuming that the diatoms obtain all their carbon for photosynthesis from CO 2 . eCA does have an effect on boundary-layer pH in this case, and the highest rates are effective at reestablishing pH equilibrium, but the absolute effect of eCA on H + concentration is very small (Fig. 8B).

CONCLUSION
Using a newly developed approach to quantify eCAcatalyzed CO 2 hydration rates, eCA activity was measured in two diatoms, T. pseudonana and T. weissflogii, and its potential roles in CO 2 supply, CO 2 recovery, and pH regulation were investigated. In support of the role of eCA in photosynthetic CO 2 supply, its activity increased at low CO 2 concentrations, was appropriate to abolish bulk-to-surface CO 2 gradients, and was greater in the larger diatom (T. weissflogii), which is more prone to diffusive limitation. The differences in CO 2 concentration between the bulk solution and the cell surface that are eliminated by eCA are small (less than 0.5 mM), but small gradients drive significant passive CO 2 influxes in these diatoms (Hopkinson et al., 2011). The consequences of short-term inhibition of eCA can be overcome by decreasing the cytoplasmic CO 2 concentration to maintain CO 2 influx rates. However, this requires increased energetic expenditure, which may explain the decreased growth rate of T. weissflogii when eCA was inhibited. We investigated alternative roles for eCA in the recovery of leaked CO 2 for HCO 3 2 uptake and pH regulation but found that eCA activity would not have a significant effect on boundary-layer HCO 3 2 and H + concentrations. Taken together, these results support a role for eCA in CO 2 supply.

Culturing
The diatoms Thalassiosira pseudonana (CCMP1335) and Thalassiosira weissflogii (CCMP1336) were obtained from the National Center for Marine Algae and Microbiota and maintained in Aquil medium (Price et al., 1988). For most experimental work, the algae were grown in Aquil made from a natural seawater base with 5 mM 4-(2-Hydroxyethyl)piperazine-1-propanesulfonic acid (EPPS) buffer to maintain constant pH and C i conditions. To assess the pH and C i dependence of enzyme kinetics, cultures were grown in Aquil to high density without pH or CO 2 control (final culture pH of 8.6-8.8) to induce strong eCA activity. For experiments in which C i concentrations were varied, North East Pacific Culture Collection Enriched Seawater, Artificial Seawater (NEPCC ESAW) medium was used with 5 mM EPPS buffer added (Harrison et al., 1980). This medium uses an artificial seawater base, and C i was left out in the initial medium preparation, being added later at the desired concentration. All cultures were grown in an incubator at 20°C under fluorescent lights (125-150 mmol photons m 22 s 21 ) on a light/dark cycle (16 h on, 8 h off). Cell numbers were counted daily with a Coulter Counter, and cells were harvested during exponential growth.
The initial pH of the culture medium was adjusted with HCl or NaOH (stored in sealed serum vials to avoid CO 2 absorption) and measured on the total hydrogen ion scale using thymol blue (Zhang and Byrne, 1996). The C i concentration was measured at the beginning and end of the experiments using membrane inlet mass spectrometry (MIMS;Beckmann et al., 2009;Hopkinson et al., 2011). Additional carbon system parameters (CO 2 , HCO 3 2 , and CO 3 22 concentrations) were calculated from pH and C i (Dickson and Goyet, 1994;Lueker et al., 2000).

O-Exchange Experiments
The rate of 18 O removal from labeled C i was used to determine iCA and eCA activities. 18 O-labeled 13 C-C i (2 mM, unless otherwise noted) was added to assay buffer (C i -free artificial seawater, 20 mM Tris at pH 8.0, unless otherwise noted) in a MIMS chamber. Temperature in the chamber was maintained at 20°C using a water jacket. 18 O-CO 2 species were monitored by MIMS for approximately 10 min to determine the background rate of CO 2 hydration/ HCO 3 2 dehydration, after which cells were added to the chamber from a concentrated suspension. 18 O removal catalyzed by cellular CA was then monitored in the dark for 15 to 20 min. To determine iCA activity, an inhibitor of eCA was added prior to the addition of cells. In most cases, 50 mM AZ was used, but 50 mM DBAZ (Ramidus) was used in select experiments to confirm that diatom membranes were not permeable to AZ.

Photosynthetic Rates
The effect of eCA inhibitors on photosynthesis was assessed from measurements of oxygen production made using MIMS. Assay buffer with 2 mM C i , unless otherwise noted, was added to the MIMS chamber, and cells were added from a concentrated suspension. Light was provided from a tungsten lamp at 200 mmol photons m 22 s 21 . Oxygen production was monitored for approximately 10 min, at which point AZ or DBAZ was added and oxygen production was monitored for a further approximately 10 min. Measurements were made at the same pH as the cultures were grown and at pH 8.0.

eCA Model Development
The eCA box model considers 18 O-CO 2 and 18 O-HCO 3 2 isotopologs in three compartments: the bulk solution, the boundary layer at the cell surface, and the intracellular space ( Fig. 1; Table III). Fluxes between the compartments are described by mass transfer coefficients, and the uncatalyzed and catalyzed CO 2 hydration/HCO 3 2 dehydration reactions, responsible for 18 O removal, are treated as first-order reactions, since the enzyme is undersaturated for C i (Fig. 4). The model is described by the following system of differential equations: with variables and parameters as described in Table III.
The solution volume (V e ) was measured directly, and the intracellular volume was determined using a Coulter Counter. The volume of the boundary layer compartment (V s ) was set to 8 3 10 212 cm 3 , reflecting a surface layer thickness on the order of 0.1 mm. The uncatalyzed CO 2 hydration/HCO 3 2 dehydration rates in the bulk solution (k uf , k ur ) were determined from 18 O removal rates prior to the addition of cells, and the observed values agree well with published rates (Johnson, 1982). The mass transfer coefficients for diffusive flux between the bulk solution and the boundary layer (f c-BL , f b-BL ) were calculated assuming the cells are spherical, with radii determined from Coulter Counter measurements (T. pseudonana, 2.5 mm; T. weissflogii, 6 mm): where R is the cell radius and D is the diffusivity of CO 2 (1.65 3 10 25 cm 2 s 21 at 20°C) or HCO 3 2 (1.05 3 10 25 cm 2 s 21 at 20°C; Pasciak and Gavis, 1974). The parameters for iCA activity (k cf , k cr ) and the mass transfer coefficients for membrane passage (f c-M , f b-M ) were determined from analysis of 18 O-exchange rates in the presence of an eCA inhibitor (Tu et al., 1978;Hopkinson et al., 2011). eCA-catalyzed hydration/dehydration rate constants (k sf , k sr ) are related to each other via the CO 2 /HCO 3 2 equilibrium constant, assuming microscopic reversibility. k sf , the first-order rate constant for eCA-catalyzed CO 2 hydration, was determined by optimizing the model fit to the 18 O-CO 2 data (Supplemental Data S1).

Models of Surface Boundary-Layer Chemistry
To assess the effects of eCA on boundary-layer chemistry, we developed a simple analytical approximation and a one-dimensional numerical reaction diffusion model. The analytical model treats the case in which there is a net CO 2 influx (photosynthetic uptake) to, or efflux (leakage) from, the cell. A net CO 2 influx (an efflux is similar except for a change of sign) is supported by diffusion of CO 2 from the bulk solution and, when eCA is present, the net generation of CO 2 from eCA-catalyzed HCO 3 2 dehydration. Diffusion through the boundary layer is dependent on the CO 2 gradient between the bulk solution and the cell surface. For a spherical cell, the net diffusive CO 2 flux (NC D ) is: The net generation of CO 2 from HCO 3 2 dehydration at the cell surface is: In the marine environment, which our assay and culture conditions replicate, HCO 3 2 concentrations are high, approximately 1.8 mM, and so are not significantly depleted at the cell surface. Taking the HCO 3 2 concentration at the surface to be equal to the bulk solution, and using the fact that at equilibrium the forward and backward reaction rates will be equal (k sf [CO 2 ] = k sr [HCO 3 2 ]), Equation 9 can be rewritten as: In effect, the net CO 2 supply from eCA depends on the same CO 2 gradient as the diffusive supply, although the physicochemical processes underlying these net CO 2 sources are very different. The diffusive flux is driven by the actual spatial CO 2 gradient, whereas net CO 2 production by eCA is the result of disequilibrium between CO 2 and HCO 3 2 at the cell surface. The total net CO 2 influx is the sum of the diffusive and reactive supply: This equation shows that the importance of diffusion or eCA activity for net CO 2 supply depends on the relative sizes of f c-BL and k sf , justifying k sf as a measure of eCA activity.
Rearranging Equation 11, we can find an expression for the surface CO 2 concentration: which shows that as eCA activity (k sf ) increases, the surface CO 2 concentration approaches that of the bulk solution. To measure the impact of eCA on CO 2 exchange between the cell and the bulk solution, we define the effectiveness of eCA (E) as: which varies between 0 (no impact of eCA) and 1 (eCA dominates over diffusive exchange). E is both the fraction of net CO 2 supply supported by eCA and the fraction of the maximum potential CO 2 gradient abolished by eCA activity.
For a more detailed evaluation of the effect of eCA on boundary-layer carbon chemistry and pH, a spherical reaction-diffusion model was developed. The model domain extends from the cell surface 100 mm out to the bulk solution. Chemical concentrations are held constant in the bulk solution but are allowed to vary at the cell surface due to imposed uptake and export fluxes and reaction-diffusion within the boundary layer. Dissolved C i species (CO 2 , HCO 3 2 , and CO 3 22 ) and other important components determining seawater pH [H + , OH 2 , B(OH) 3 , and B(OH) 4 2 ] are included in the model. Bulk solution pH, C i , and total boron were set at typical oceanic values (pH 8.14; C i , 2 mM; total boron, 415 mM). All reactions are treated kinetically using rate constants from Zeebe and Wolf-Gladrow (2001) and diffusion coefficients from Boudreau (1997). The model was solved in Matlab.

Supplemental Data
The following materials are available in the online version of this article.
Supplemental Data S1. Description of scripts used to process isotope exchange data and implement the eCA box model.