3.1 Introduction

The original purpose of this work was to look for a possible explanation for the apparent discrepancy between the global ¹⁴C budget and measurements of the air-sea gas exchange rate made at sea using inert trace gases, as explained in Section 1.2, particularly Section 1.2.12. Catalysis of air-sea CO₂ exchange by carbonic anhydrase produced by marine algae is only one possible hypothesis which might contribute to explaining this discrepancy. This hypothesis seemed worthy of further investigation, not least because it forms an intriguing link between the physiology of microalgae and the global carbon cycle, and because had not yet been investigated as thoroughly as some of the other factors, perhaps on account of its interdisciplinary nature. However, before embarking on detailed experimental work on this topic, it was necessary to check that this hypothesis might be realistic - to make some basic order-of-magnitude calculations to see how much enzyme would be needed, on average, in the sea-surface microlayer to significantly enhance the global air-sea CO₂ flux and possibly explain the discrepancy.

It is important to bear in mind that the preliminary calculations described below were based only on hypothetical distributions of pCO₂ and windspeed, and neglect the effect of temperature variation on uncatalysed chemical enhancement (which will later be shown to be very significant, as shown by the measurements in Section 7.3 ). More thorough calculations of the effect of both catalysed and uncatalysed chemical enhancement on the net global air-sea CO₂ flux, based on real satellite data for windspeed, temperature, and chlorophyll, combined with pCO₂ data from an ocean carbon cycle model, were made after the completion of the experimental work. These results will be presented later in chapter 9. However, the physiological model used in chapter 9, predicting demand for carbonic anhydrase as a function of water pCO₂ and temperature, is essentially the same as developed here ( Section 3.2 ). Combining this model with simple calculations of the effect of chemical enhancement on the net global air-sea CO₂ flux ( Section 3.3 ), suggested that the intercorrelation between pCO₂ and carbonic anhydrase may greatly magnify the overall impact of enzyme catalysis. This was one of the key factors justifying continued experimental investigation of carbonic anhydrase catalysis of air-sea CO₂ exchange, as described in later chapters.

3.2 Development of a simple physiological model to relate CA production to water pCO₂ and temperature.

The pioneering paper of Riebesell et al (1993) combined a reaction-diffusion model with a nutrient uptake model to suggest that CO₂ supply might be limiting the growth of a "typical spherical diatom", and also presented experimental evidence from culture studies to support this hypothesis. This paper did not consider the possibility that production of carbonic anhydrase might alleviate this problem. However it is possible to adapt this model to include (somewhat crudely) the effect of carbonic anhydrase, and thus to consider how useful the enzyme might be to the cell, under various conditions.

It should be noted, that the following adaptation of the model of Riebesell et al (1993) was developed in spring, 1994. Since then, more sophisticated reaction-diffusion models of CO₂ supply to microalgae have been developed, both by these authors (Rau et al 1996, Wolf-Gladrow and Riebesell 1997) and by others (e.g. Smith and Westbroek 1995). However, the basic principles of these models are similar, and would not alter the principal conclusions of this study.

3.2.1 Summary of Riebesell's model for CO₂ supply to a "typical diatom"

3.2.1.1 Reaction- Diffusion model

The equation determining CO₂ supply to the cell assumes an infinite "stagnant film" around a theoretical spherical diatom cell. Of course, diatoms, with their beautiful and diverse silaceous architecture are anything but spherical, but this is only a crude model! As we shall see later, the infinite film isn't as unreasonable as it may seem at first to people accustomed to the finite film or boundary-layer models of air-sea gas transfer.

Firstly, consider a sphere of radius "r" from the centre of the cell, where the concentration of dissolved CO₂ is denoted by "c", and its diffusivity is denoted by "D"

Recalling that flux = area * diffusivity * concentration gradient, at this radius "r" the total flux "f" of CO₂ towards the cell is given by:

f = 4 p r² D dc/dr.

Therefore the flux gradient df /dr = 4 p D d /dr[r² dc/dr],

Dividing this by 4 p r² gives the flux gradient per unit volume f / v
f / v = (D / r²) d/dr [r² dc/dr]

This flux gradient per unit volume is a local gain or loss of CO₂, which must be balanced by the conversion of HCO₃^- to CO₂ .

If we assume that the concentration of HCO₃^- is constant (because it is about 100 times more abundant than dissolved CO2), then it can be shown that:

rate of conversion of HCO₃^- to CO₂ = - k_tot (c¥ - c )

where c¥ is the concentration of CO₂ in the bulk water far from the cell,
and k_tot is the total rate of hydration of CO₂ in seawater as defined in Section 1.5.2 , including both the reaction of CO₂ with water and the reaction of CO₂ with OH-.

Note that k_tot is a CO₂ hydration rate constant, but multiplying this by the term (c¥ - c ) gives us the the overall dehydration rate, since the rates and the equilibrium constant are liked by the usual relationship K_equilibrium = k_hydration / k_dehydration .

So altogether we now have:

- k_tot (c¥ - c ) = (D / r²) d/dr [r² dc/dr]

If we integrate this expression between infinity (the bulk water) and the edge of the cell which has a radius "a", we obtain a formula for c at radius r:

(c - c¥ ) / (c_a - c¥ ) = (a / r) exp[ (a - r) Ö (k_tot / D) ]

3.2.1.2 Comparison with stagnant film model

In this case, if "z" is the distance from the surface and c_s is the CO₂ concentration at the surface, then the flux gradient per unit volume is given by D d²c/dz²

This must be balanced by the conversion of HCO3- as before, so

- k_tot (c¥ - c ) = D d²c/dz²

This integrates to a similar formula (c - c¥ ) / (c_s - c¥ ) = exp[ -z Ö (k_tot/D) ]

Since "z" here is equivalent to (r-a) in the spherical model, the only fundamental difference is the term (a / r) in the spherical model. However, it is this term, which makes the spherical model valid whereas the planar one clearly isn't. For example, we can calculate the e-folding distance "z" from the surface, where (c - c¥ ) / (c_s - c¥ ) = 1 / e

In the planar model this occurs when z = Ö (D / k_tot), and reading from figure 1 of Riebesell et al (1993), Ö (D / k_tot) is about 300m m. However, we know from the global ¹⁴C budget that the average "stagnant film thickness" at the ocean surface must be about one order of magnitude thinner than this.

In the spherical model, on the other hand, the distance "r" where (c - c¥ ) / (c_a - c¥ ) = 1 / e
comes to be about 71 m m (the equation was solved iteratively) if we use the same value for Ö (D / k_tot) and take the cell radius "a" to be 30m m (the same value as used by Riebesell et al 1993). Thus the e-folding distance from the cell surface is only 41 m m, which is much more reasonable.

3.2.1.3 Connection to nutrient uptake formula

dc / dr = (c¥ - c_a) (a /r ) (Ö (k_tot/D) +1 / r) exp [ (a - r) Ö (k_tot/D)]

At the cell surface where r = a,
dc/dr = (c¥ - c_a) (Ö (k_tot / D) +1 / a)

And therefore, recalling that flux = area* diffusivity * concentration gradient

CO₂ flux arriving at the cell surface = 4 p a D (c¥ - c_a) (1+ aÖ (k_tot/D))

The key step in the paper of Riebesell et al (1993) is to link this to the well known nutrient uptake formula of Monod:

V = rate of CO₂ uptake by cell = V_max c_a / (K_s + c_a)

(where V_max is the maximum possible uptake, and K_s is the half-saturation constant. This notaton is used for consistency with Riebesell et al (1993), but note that V and V_max are not the same here as in Section 2.5.2 )

This formula considers the physiological response of the cell to the concentration of nutrient (in this case CO₂) at its surface, rather than the reaction-diffusion process in the water beyond the cell.

Clearly at steady-state the CO₂ flux arriving at the cell surface, and the CO₂ uptake by the cell must be equal. This gives us:

4 p a D (c¥ - c_a) (1+ aÖ (k_tot /D)) = V_max c_a / (K_s + c_a)

This is a quadratic equation, which can be solved for c_a if we know the other terms. The value for V_max used by Riebesell et al (1993) was about 5x10^-15 mol (carbon) s^-1, which, considering their figures 2 and 3 seems to be derived from 2^(1.5) (11/2 doublings per day) * 1.6x10^-10 (mol cell^-1 day^-1) / 86400 (s day^-1). The cell radius was assumed to be 30m m, Ö (D/ k_tot) was taken to be 300m m. The value of K_s used was 5x10^-7 mol, which was taken from the review of Raven and Johnston (1991). Using these values we find that V/V_max = 0.865, or 86.5% of the maximum carbon uptake.

We should note that there are a wide range of values of K_s reported in the literature, corresponding to different species and different experimental conditions. For example, in table 2 of the review of Aizawa and Miyachi (1986) these range from 0.25 to 75μmol. We should also beware that both this factor, and V_max, may vary with environmental conditions -especially temperature.

The final step in Riebesell et al (1993) is to use the Redfield ratio (106C : 16N) to relate the CO₂ uptake to nitrate uptake. The formulae for nitrogen are the same as for carbon, without the aÖ (k_tot/D) term representing reaction. Using typical literature values for K_s, c¥ , and D for nitrate, and forcing the nitrogen uptake to be 16/106 of the carbon uptake, it is possible to show that V/V_max for nitrogen is 0.98, much greater than V/V_max for carbon. Thus, Riebesell et al (1993) drew the main conclusion of their paper, that carbon might be a more limiting nutrient than nitrogen, and backed this up with evidence from experiments with cultures of three species of diatoms (listed in table 2-1 ). Although Raven (1993) pointed out that limitation of photosynthetic carbon uptake does not necessarily imply limitation of phytoplankton growth, this simple model was nevertheless a key step in bringing attention to the question of carbon limitation of microalgae - not due to the lack of inorganic carbon in seawater, but due to the slow conversion of HCO3- to CO₂ which can cross the cell-wall.

3.2.2 Adding carbonic anhydrase to the model

It might seem unlikely that phytoplankton would waste enzyme by releasing it into the water to have an effect beyond the cell wall, but we must recall that, in the example above, the e-folding distance for (c¥ - c) was only 41 m m from the cell wall, that the diffusion of such a large protein molecule is very slow, and at this scale seawater is viscous so loss by turbulence is insignificant. It is therefore possible that cells might release free carbonic anhydrase into the water to aid their CO₂ uptake, especially in the sea-surface microlayer where the enzyme would be concentrated by surface activity. Indeed -this is the whole basis of the hypothesis that the enzyme might catalyse air-sea gas exchange. (Note that some other possible reasons for algal cells to release enzyme are discussed in the concluding chapter, section 10.6).

Incorporating dissolved CA into the model is very straightforward -it is simply a question of adding the catalysed CO₂ hydration rate to the uncatalysed CO₂ hydration rate k_tot, applying the formula for steady-state catalysis which has already been developed in Section 2.5.4 .
Thus the full equation is:
4 p a D (c¥ - c_a) (1+ aÖ (k_tot / D) = V_max c_a / (K_s + c_a)

where: k_tot = E₀ q k_cat / K_m +k_CO2 +[OH-]k_OH
E₀ is the total enzyme concentration, and q is the ratio of free to total enzyme, given by:
q = 1 / {([CO₂] /K_m + [HCO₃^-] / K_m¢ + 1) (1+c_cl /I₅₀)}
The enzyme kinetic constants k_cat, K_m, and K_m¢ are the same as in Section 2.5.2 , and the term (1+c_cl / I₅₀) accounts for chloride inhibition, as explained in section 2.7.3

As discussed in Section 2.7.1 , there have been few measurements of genuine enzyme kinetic constants for carbonic anhydrase taken from microalgae. The constants used in this study, are those measured by Bundy (1986) for CA extracted from the freshwater green alga chlamydomonas reinhardii (see table 2-2 ). They were adjusted for temperature using the activation energy constants measured by Sanyal and Maren (1981) for human CA, as discussed in Section 2.7.2 . A constant I₅₀ for chloride inhibition was taken from Okazaki (1974), as discussed in Section 2.7.3 .

If, for example, we want to find how much CA is needed to increase V / V_max for CO₂ by 5%, (i.e. to 90.8%), we can solve the formula firstly to find c_a , and then to find that the catalysed hydration rate k_tot would have to be increased from an uncatalysed rate of 0.018s^-1 to 0.196 s^-1 (i.e. about ten times faster). Using the data above we find this corresponds to a concentration of carbonic anhydrase of about 30nM.

A 5% increase in V/V_max might not seem particularly significant but we should remember that these cells are doubling 11/2 times every day. Thus a 5% increase in growth rate is one extra doubling every two weeks, which is the typical lifetime of an algal bloom at sea, and would therefore be sufficient to confer an evolutionary advantage.

This reaction-diffusion-uptake model of Riebesell et al (1993) can be represented graphically as shown in figure 3-1 , in which both the reaction-diffusion CO₂ supply formula and the Monod CO₂ uptake curve are shown vertically as a function of c_a (=concentration of CO₂ at the cell-surface) which increases along the horizontal axis. The system is at steady-state where these two lines cross. The equivalent formulae are also given for nitrogen. The addition of dissolved carbonic anhydrase to the model is represented simply on figure 3-1 by increasing the gradient of the line representing CO₂ supply. A very similar diagram showing the impact of enzyme catalysis appears in the reaction-diffusion-uptake model presented by Smith and Westbroek (1995).

An obvious question is, how much enzyme is needed to bring V / V_max for CO₂ to equal
V / V_max for nitrate? Unfortunately, given the data above, there is no solution to this: even with infinite enzyme concentration c_a would only be brought to the same value as c¥ in which case V / V_max for CO₂ is 0.952. Clearly this slope of the lines in figure 3-5 cannot ever be more than vertical (if it were then diffusion of CO₂ would be away from the cell rather than towards it). It is interesting that Riebesell's team have recently detected extracellular carbonic anhydrase on 3 species of diatoms, but measured that the extra photosynthetic carbon uptake due to this catalysis is only a small fraction of the total (Riebesell U., personal communication). Since the maximum possible ratio V/ V_max is only 10% greater than it is already without catalysis in the calculations above, this result is not surprising. Perhaps this is why many species of algae also seem to possess a method to actively transport HCO₃^- across the cell membrane, although such active transport carbon concentrating mechanisms are still poorly understood (see Section 2.3.2 ).

Alternatively, we could place all the CA at the cell surface. If the total amount of carbonic anhydrase per cell is denoted by e _cell , then the extra amount of HCO₃^- converted to CO₂ at the cell surface will be:
(c¥ - c_a) e _cell q k_cat / K_m

Note that (c¥ - c_a) is the same as [A - B/ K_eq] in Section 2.5.4 .

So fitting this into the full equation we get

(c¥ - c_a) [k_cacell + 4 p a D (1+ aÖ (k¢ / D)) = V_max c_a / (K_s + c_a)

where k_cacell = e _cell q k_cat / K_m

In this case, for a 5% increase in growth rate we need 2x10^-17 mol carbonic anhydrase per cell.

As a check to see whether this might be reasonable, we could consider that each molecule of carbonic anhydrase has a diameter of about 5 nm (see Section 2.2.2 ) and therefore a cross sectional area of about 2x10^-17 m². Multiplying by 2x10^-17 moles of enzyme per cell (as above, the same value as the area is a coincidence) and Avagadro's number (6.023x10²³) we get the total cell surface area used up by the CA to be 2.4x10^-10 m². The "typical diatom" in the model has a diameter of 60m m and thus a total surface area of 1.1x10^-8 m². So in this case 2% of the surface is taken up by carbonic anhydrase. This seems quite plausible.

3.2.3 Increase of growth rate due to carbonic anhydrase, as a function of pCO₂ and temperature

So to make any calculation of the possible effect of carbonic anhydrase on the net global air-sea CO₂ flux, we firstly need to estimate the likely distribution of the enzyme in the ocean. This will of course depend partly on the distribution of phytoplankton, which might be represented by satellite chlorophyll data, as used in the calculations in chapter 9 (see Section 9.2.3 for a discussion and maps of the distribution of this data). However, the distribution of carbonic anhydrase will also depend on the physiological demand for this enzyme. Carbonic anhydrase is a large protein molecule which will cost the cell considerable resources to manufacture. Thus phytoplankton will have evolved to produce the external enzyme, only when environmental conditions are such that the enzyme might significantly increase the cell's growth rate. We therefore need to investigate the effect of varying water pCO₂ and temperature on the increase in growth rate due to carbonic anhydrase.

I wrote a computer program (in QBASIC) incorporating both the equations in the previous section, the temperature dependence of all the required kinetic and thermodynamic constants as listed in chapter 6 (see references therein), and the equations for calculating the carbonate equilibria as a function of pCO₂ and carbonate alkalinity (which was kept constant at 2.3mM). This program calculated the percentage increase in growth rate as a function of pCO2, temperature, and either carbonic anhydrase concentration in the water, or at the cell surface. The results are shown by the eight 3D plots in figure 3-2 .

From these plots it is clear that the physiological "benefit" of making extracellular carbonic anhydrase is much greater at low pCO₂. Whether the enzyme is dissolved in the water or at the cell surface, makes little difference to the shape of the plot. The lower plots are shown as a function of the concentration of dissolved CO₂ ([CO₂]_(aq)= c¥ in the equations above) rather than pCO₂. The apparently higher temperature dependence in these plots is due to the much greater solubility of CO₂, in colder water so the ratio [CO₂]_(aq) / pCO₂ is likewise greater.

Clearly, if [CO₂]_(aq) were constant, the need for enzyme would be much greater in cold areas of the ocean. This is because the uncatalysed reaction is much slower in cold water, but the catalysed reaction is less affected by temperature due to its lower activation energy (see Section 2.7.2 ). However, [CO₂]_(aq) is generally much higher in colder areas of the ocean, due to influx from the atmosphere, and it is also affected by biological fluxes, and the temperature dependence of the dissociation constants of carbonic acid in seawater. If we assume instead, that the surface water equilibrates instantly with the atmosphere, then pCO₂ rather than [CO₂]_(aq) would be constant. In this case the temperature dependence is reversed: there is a very slight bias towards warmer areas, where there is less dissolved CO₂ due to the lower solubility.

Of course the situation in the real ocean is somewhere between these two extreme cases. The intercorrelation between the distributions of temperature, pCO2, and physiological demand for carbonic anhydrase will be discussed further when calculating the net global air-sea CO₂ flux using real satellite data, in chapter 9.

Shortly after I had completed the analysis above, Morel et al (1994) published a paper showing that cultures of the marine diatom Thalassiosira Weisfloggii were limited by zinc (the key active component of carbonic anhydrase) but only when pCO₂ in the water was low (see also Section 2.3.4 ). Meanwhile, Berman Frank et al (1994,1995) reported measurements of carbonic anhydrase extracted from blooms of Peridinium Gatunense growing naturally in Lake Kinneret, Israel, and found likewise that carbonic anhydrase was only produced when pCO₂ in the water was low. This was the first confirmation of the hypothesis in natural waters rather than laboratory cultures, although they did not make measurements of dissolved carbonic anhydrase in the water itself.

3.3 Preliminary estimate of potential impact of carbonic anhydrase on air-sea CO₂ exchange

3.3.1 Catalysed chemical enhancement of the air-sea CO₂ exchange rate

However there is a crucial flaw in such a simple calculation - the chemical enhancement effect is much greater at low windspeeds, so making a calculation only for "average conditions" would be very misleading. The same applies to the other principal parameters which determine the enhancement. Therefore we need to use distributions rather than average values of these parameters, to add up the overall effect on global average transfer velocity or net global air-sea CO₂ flux.

All the calculations described below were made using a computer program (written in QBASIC) which exported tables of data to produce the plots shown here (there was a separate calculation for every grid point shown).

The first stage was to calculate all the thermodynamic and kinetic constants as a function of temperature (as described in Section 6.2 and references therein). The carbonate speciation of the seawater was then calculated assuming a constant carbonate alkalinity of 2.3mM rather than a constant total alkalinity. Ignoring the contribution of boric acid dissociation and other minor ions (which in total contribute about 0.1mM to the total alkalinity- see Section 6.3 ) made these preliminary calculations much simpler. The enzyme kinetic constants and the equations for steady-state reaction-diffusion enzyme kinetics were the same as in the previous section (see also Section 2.5.4 and Section 2.7 ). These were combined with the formula of Hoover and Berkshire (1969) for chemical enhancement of air-sea CO₂ exchange, as described in Section 1.5.3 .

This calculation was made many times, for various combinations of enzyme concentrations ranging from 0 to 100 nM, temperatures ranging from 0 to 30 C and windspeeds ranging from 0 to 30 ms^-1, using both the Liss and Merlivat (1986) and the Wanninkhof (1992) parameterisation of the transfer velocity. Initially the water pCO₂ was held constant at 350ppm. The main trends are illustrated by the four plots shown in figure 3-3 . Note that in all of the plots, the transfer velocity increases with height (vertical axis), and the colourscale is also a function of height.

Plot (a) shows transfer velocity as a function of windspeed and carbonic anhydrase concentration. The unenhanced transfer velocity is shown by a black line, and the uncatalysed enhanced transfer velocity by the edge of the surface where CA=0. Clearly the effect of the enzyme catalysis is greatest at windspeeds between 1 to 4 ms^-1, and is negligible above about 7ms^-1, above which the data is not shown. Plot (b) shows the same calculation using the Wanninkhof parameterisation -here the underlying unenhanced transfer velocity is higher, so the enzyme has slightly less effect.

The effect of increasing carbonic anhydrase begins to level off as the concentration increases. This cannot be due to the enzyme kinetic system, since the concentration of substrate is still much higher than the concentration of enzyme, so it must be an intrinsic feature of the reaction-diffusion system described by the Hoover and Berkshire formula -as the reaction becomes faster, there is less CO₂ remaining to react.

The two plots (c) and (d) show the effect of temperature variation for a fixed concentration of carbonic anhydrase, both on the transfer velocity (plot c) and on the transfer velocity multiplied by solubility (d), which would be used to calculate the air-sea CO₂ flux at sea. In plot (d) the greater diffusivity at higher temperatures is cancelled by a lower solubility, as already discussed in Section 1.2.2 , so the temperature dependence of the catalysis alone can be seen. There is slightly more enhancement at higher temperatures, but the trend is not so great as for uncatalysed enhancement due to the lowering of the activation energy by the enzyme (see also Section 7.3 and figures 7-2 and 7-3, where measured enhancements are shown as a function of temperature).

3.3.2 Calculating the average transfer velocity using the Rayleigh windspeed distribution

The formula for the Rayleigh distribution is given below:

f(u) = (pu / 2u_av) exp[-pu² / 4u_av²]

where "u" is the windspeed, and "u_av" is the mean windspeed.

Note that the formula is not the same as given in Wanninkhof (1992), which was not correctly normalised, possibly due to a typing error. The use of the Rayleigh distribution will be discussed in more detail later, in Section 9.3.3 and Section 9.6.4 .

The shape of this distribution is shown by the box to the right of figure 3-4 below. To calculate the average enhanced transfer velocity, this distribution was divided into bands, (as explained in Section 9.3.3 ) and the chemical enhancement formula applied to the transfer velocity calculated for each windspeed. The probabilities for each band were normalised within the computation to ensure that the total probability was exactly one as required.

The main plot in figure 3-4 shows the global average transfer velocity derived from the parameterisation of Liss and Merlivat (1986), as a function of increasing carbonic anhydrase concentration, for a range of temperatures indicated by different coloured lines. The relationship between transfer velocity and enzyme concentration is similar to that of figure 3-3 . The critical point to notice, however, is that now, a concentration of only 60nM enzyme is sufficient to bring the average transfer velocity up to the global average figure derived from the global ¹⁴C budget (look at the green line for T=20C, which corresponds to Sc=660). This enzyme concentration is much less than the 1μM that was calculated by simply using "average" conditions (see above) but still corresponds to quite a high concentration of protein even in the microlayer.

3.3.3 Applying physiological distribution of carbonic anhydrase as a function of pCO2

So far all the transfer velocity calculations have been made assuming a constant water pCO₂ of 350ppm. To estimate the importance of this physiological distribution of enzyme for the net global air-sea CO₂ flux, it is necessary to incorporate a pCO₂ distribution in these calculations, as well as windspeed distribution. At this time there was not, to the best of my knowledge, any appropriate simple pCO₂ distribution proposed in the literature, so I had to create a simple distribution for the purpose of this preliminary investigation. In 1990 the air pCO₂ was approximately 350ppm. Broeker (1986) estimated that the global average D pCO₂ (air-sea) was about 8ppm (it has of course increased slightly since then). However pCO₂ measurements at sea range from a minimum of about 200ppm in polar seas during algal blooms to a maximum of about 500ppm in tropical upwelling areas. To represent this simply, I assumed a normal distribution with mean 342ppm and standard deviation of 60ppm. The air pCO₂ was held constant at 350ppm, giving an average D pCO₂ of 8ppm as required (although there is a seasonal and interhemispheric variation in atmospheric pCO2, this is small compared to variability in the ocean). For computation by the computer program this pCO₂ distribution also had to be divided into bands of 20ppm width (between a minimum of 100ppm and a maximum of 500ppm), and the probabilities of these bands were also normalised to give a total probability of exactly one.

Firstly, the global flux calculations were made for a range of global average concentrations of carbonic anhydrase in the sea-surface microlayer, assuming just a uniform distribution of enzyme. For each pCO₂ band, the carbonate speciation was calculated, and then the Rayleigh windspeed distribution was applied as above. For each combination of windspeed and pCO2, the enhanced transfer velocity was multiplied by the D pCO₂ and the probability of that pCO₂ band and that windspeed to give a flux. These were added up and then divided by the global average D pCO₂ to give an "effective global average transfer velocity".

Secondly, a simple linear distribution of carbonic anhydrase as a function of pCO₂ was applied, such that:

[carbonic anhydrase] µ (500 - water pCO2)

To obtain a particular required global average carbonic anhydrase concentration, the program looped twice through all the pCO₂ bands. The first loop just calculated the global average concentration obtained as a result of applying this distribution of enzyme, and from this a normalising factor was calculated to ensure the correct global average carbonic anhydrase concentration. This was multiplied by the concentrations during the second loop, which were then used to calculate the transfer velocities and fluxes in the same way as above.

Finally, the physiological model developed in Section 3.2 was applied to each pCO₂ band, so that the distribution of carbonic anhydrase was proportional to the percentage increase in growth rate of the "typical diatom". The carbonic anhydrase concentrations were also normalised in the same way as for the linear distribution, before being used to calculate the transfer velocities and fluxes.

The results are summarised in figure 3-5 , which shows "effective global average transfer velocity" including catalysed chemical enhancement, as a function of increasing global average carbonic anhydrase concentration (on a logarithmic scale). The lower box shows the three carbonic anhydrase distributions as a function of pCO2, and the probability function defining the pCO₂ distribution. The colours of the distributions in the box match the colours of the respective transfer velocity curves in the main plot. In addition a blue curve is shown which is the average transfer velocity before any pCO₂ distribution was applied, exactly the same curve as shown in figure 3-4 (for T = 20C). The two horizontal black lines show the unenhanced transfer velocity and the global average derived from the ¹⁴C budget. Note that all these calculations were only made at one constant temperature, of 20C, and using the paramerisation of Liss and Merlivat (1986).

From the figure 3-5 it is clear that skewing the distribution of carbonic anhydrase towards low pCO₂ greatly enhances its effect on the "effective average transfer velocity". If it is distributed uniformly about 60nM carbonic anhydrase is needed to take the "effective average transfer velocity" calculated with the Liss and Merlivat parameterisation up to the figure calculated from the ¹⁴C budget (as already noted observed in figure 3-4 ). However if the carbonic anhydrase is distributed according to the physiological distribution, only about 6nM brings the "effective average transfer velocity" up to the same level, and the effective enhancement for any one average concentration is about 4.5 times greater.

Although, looking at the distribution plot (below Figure 3.5), the physiological distribution appears to be much more skewed towards low pCO₂ than the straight line distribution, the difference in their effect on the "effective average transfer velocity" is not so great. This is because the two distributions are actually quite similar in the centre of the pCO₂ range, which has a high probability, whereas below 200ppm, where the difference between the distributions is greatest, the probability of that pCO₂ occurring is very low.

It may seem strange that the uniform carbonic anhydrase distribution (red line in the plot), rises slightly above that for windspeed averaging only (blue line). This difference is due to the effect of pCO₂ variation on the carbonate speciation in seawater, which affects the factor "t " of the Hoover and Berkshire formula for chemical enhancement (see Section 1.5.3 ). This "t ", the ratio of total to ionic inorganic carbon, is slightly greater at lower pCO2. Effectively, there is slightly greater chemical disequilibrium in the microlayer at low pCO2, and hence slightly greater potential for catalysis. So even with a uniform distribution of enzyme, its effect is slightly biased towards low pCO2. There is also a bias towards low pCO₂ due to the OH- reaction pathway as noted by Keller (1994), but this should not increase with enzyme concentration, which the gap between the red and blue lines clearly does. This bias due to the OH- pathway will be discussed in more detail later (see especially Section 7.5 , Section 9.3.4 , Section 9.6.6 ).

So the results of these preliminary calculations were encouraging: It seemed that an average carbonic anhydrase concentration of only a few nanomolar in the sea-surface microlayer, would be sufficient to significantly increase the net global air-sea CO₂ flux, if the enzyme were distributed according to a physiological distribution as a function of pCO2.

3.3.4 The different effect of the enzyme distribution on ¹⁴C and ¹²C fluxes.

Unfortunately, this interpretation is invalid because the calculation above was made for the net global air-sea ¹²CO₂ flux, whose thermodynamic driving force (D p¹²CO2) is much more finely balanced than that of the net global air-sea ¹⁴CO₂ flux. The net global air-sea ¹²CO₂ flux is the small difference of large regional influxes and effluxes, as explained earlier. The net flux of ¹⁴CO₂, on the other hand, is effectively one-way only: ¹⁴C is produced in the stratosphere, either naturally by cosmic rays or by nuclear bomb testing in the 1950s and 60s, and slowly finds its way to the deep ocean where it decays (see Broecker et al 1985 and other references in Section 1.2.11 ). Since the return flux of ¹⁴C from the ocean to the atmosphere is much smaller, the net air-sea ¹⁴CO₂ flux in any one location is much less dependent on water pCO₂ than the net air-sea ¹²CO₂ flux. Consequently the distribution of chemical enhancement and enzyme catalysis with respect to pCO₂ will not affect the ¹⁴C flux in the same way as the ¹²C flux, even though at any one location chemical enhancement and catalysis by enzyme will increase the transfer velocity for ¹⁴C to the same extent as for ¹²C (ignoring small isotopic fractionation effects).

It is important to understand the meaning of the term "effective average transfer velocity" in figure 3-5 . It is the net global air-sea CO₂ flux divided by the average D pCO₂ (=8ppm), i.e.
effective average transfer velocity = S (k_c,w D pCO2_c,w) / S (D pCO2_c,w),
where the subscript c,w indicates summing over both windspeed and pCO₂ distributions.

The calculations were presented in this way for two reasons. Firstly, the pCO₂ distribution used in this simple calculation is not real, but was created for the purpose of illustrating the importance of the enzyme distribution, and so it did not seem appropriate to present the results as global air-sea CO₂ fluxes. (Note that in chapter 9, where more thorough calculations are made using an ocean carbon cycle model and satellite windspeed and temperature data, the net global air-sea CO₂ flux is given rather than the "effective average transfer velocity").

Secondly, using an "effective average transfer velocity" in this way helps to illustrate why it is not valid to consider chemical enhancement as a "minor factor" which can be incorporated as a "correction" to the parameterisation of the transfer velocity as a function of windspeed and temperature only (e.g. the parameterisation of chemical enhancement proposed by Wanninkhof 1992). It is often stated that the average transfer velocity derived from the ¹⁴C budget is an "empirical" measurement which includes all such "corrections". It is true that we could, in theory at least, use the ¹⁴C flux to derive the global average transfer velocity including chemical enhancement, but this does not constrain the effect of this chemical enhancement on the net global air-sea ¹²CO₂ flux. It is well accepted, for example, that we could not calculate the net global air-sea CO₂ flux simply by taking the global average transfer velocity from the ¹⁴C budget, and multiplying D pCO₂ by this single average transfer velocity everywhere in the world, because the large influxes in windy high-latitude regions where pCO₂ is generally low would be underestimated compared to the effluxes in calmer equatorial regions. It is necessary to measure the windspeed and calculate a separate transfer velocity for each pCO₂ measurement. Basically, in statistical terms, I am just pointing out that E(XY) ≠ E(X) E(Y) unless X is independent of Y. The same is true of chemical enhancement, except that this calculation must also include pCO₂ as a factor influencing the rate. Thus the division of air-sea gas exchange into "kinetic" and "thermodynamic" parameters is not as simple as suggested in the introduction (e.g. Section 1.2.1 ).

Keller (1994) also used the term "effective average transfer velocity" when considering the bias of uncatalysed chemical enhancement towards low pCO₂ due to the OH^- reaction pathway. Unfortunately, as well as neglecting the effect of temperature on the dissociation of water (see Section 7.3.2 ), Keller did not appreciate this critical difference between the ¹⁴C and ¹²C fluxes, and therefore mistakenly claimed that this OH^- reaction effect might resolve much of the transfer velocity discrepancy. On the other hand, when making a simple estimate of the potential effect of catalysis, neither Keller (1994), nor Emerson (1995) considered the distribution of enzyme at all, ignoring both the physiology of the algae which produce it, and the well-known bias of the chlorophyll distribution towards low pCO₂. Moreover, Emerson's application of enzyme kinetic constants is probably incorrect (see Section 2.5.5 ).

Figure 3-6 illustrates how both catalysed and uncatalysed chemical enhancement would have a different effect on the ¹⁴C flux compared to the ¹²C flux. Uncatalysed chemical enhancement will increase the global air-sea ¹⁴C flux, simply because the average transfer velocity is a little faster, but will decrease the net global air-sea ¹²C flux because uncatalysed chemical enhancement is greatest where the temperature is high and the windspeeds are low, which is generally in tropical regions where water pCO₂ is high and there is a net flux of ¹²C from the sea to the air (as shown by the calculations of Boutin and Etcheto 1995). On the other hand, the effect of catalysis by carbonic anhydrase distributed according to physiological demand will be greatest in low pCO₂ regions, and enzyme catalysis will therefore increase the net global air-sea ¹²C flux. It will also increase the global air-sea ¹⁴C flux, but not by such a large proportion because the bias towards low pCO₂ is insignificant in this case. More detailed discussion of this will continue in chapter 9.

3.3.5 Limitations of these calculations: temperature variation, pCO₂ distribution, and intercorrelation between parameters.

However, temperature, windspeed and pCO₂ are themselves highly intercorrelated both globally and locally (for more discussion of such intercorrelation, see Section 1.3 and chapter 9.

With hindsight the standard deviation of the water pCO₂ distribution used in these preliminary calculations (60ppm) was probably too large, although not as large as that used by Keller (1994) who confused the absolute sum of the local CO₂ fluxes, with the one-way molecular diffusion flux (a common misunderstanding, as explained in Section 1.3.8 ). So it should be stressed again that the results in this chapter only give a preliminary order-of-magnitude estimate of how much carbonic anhydrase might be needed to significantly affect the net global air-sea CO₂ flux.

3.4 Gas exchange experiments -various options

Many pioneering dual and triple tracer measurements of the transfer velocity of inert tracer gases at sea, using SF₆, ³He and bacterial spores have been carried out by a partnership between the University of East Anglia, and Plymouth Marine Laboratory (Watson et al 1991, Nightingale et al 1999). However, at the time I arrived in UEA there was not any equipment for accurate measurement of pCO2, nor any gas-tight laboratory tanks suitable for air-water gas exchange experiments. Equipment for measuring pCO₂ existed in Plymouth Marine Laboratory, and Andrew Watson (then based at PML) considered that it might be possible to use some of the pCO₂ equipment and the PML flume tank (although the pCO₂ analysers were only available between cruises, and a gas-tight lid would have had to be constructed for the flume tank). Indeed some preliminary experiments comparing CO₂ and SF₆ transfer velocities in seawater, including added bovine carbonic anhydrase, had been carried out in PML by Cliff Law and Michel Frankignoulle the previous summer. Their promising although puzzling results (unpublished data) were part of the inspiration for initiating further work on this topic, and will be discussed later in Section 7.8.2 . However, due more to the lack of any decisive strategy meeting, rather than to scientific considerations, I did not move to PML and instead began some simple gas exchange experiments in UEA.

3.4.1 Oxygen and pH measurements in an open laboratory tank

On one occasion N₂ had been bubbled through a tank of seawater for about half an hour to deplete CO₂ and O₂ in the water. The reequilibration of these dissolved gases with the laboratory air was then followed using the two electrodes, in order to calculate the transfer velocity. The dissolved O₂ reading dropped during bubbling and then climbed gradually back towards the normal equilibrium level in the air (about 8 mg l^-1) as expected. The pH of the water rose during the bubbling as expected due to loss of CO₂ (thus pulling the equilibrium H⁺ + HCO₃^- <=> CO₂ +H₂O to the right), but then continued to rise slowly after the bubbling ceased, implying that pCO₂ in the water was continuing to fall. This was initially blamed on the slow response of the pH electrode, but after repeating this experiment several times I realised that the pH readings were correct, and the problem lay with dilution of the laboratory air by the bubbling N₂

The volume of the small laboratory was about 60m³, while the volume of the seawater in the tank was 0.016 m³. The dimensionless solubility of CO2 (mol l^-1_water / mol l^-1_air) is approximately unity (see Section 1.2.2 ), but for every molecule of dissolved CO₂ in seawater, there are approximately 100 molecules of HCO₃^-. Therefore, there was initially about 40 times more CO₂ in the air, than in the water. However, each rising bubble of N₂ displaces its own volume of air in the laboratory (which was poorly ventilated), whereas it only has a fraction of a second to remove CO2 from the seawater. If gas exchange went less than 1/40^th of the way towards equilibration during this brief passage through the water, then it would be lower the CO2 concentration in the air, faster than in the water. Consequently, when bubbling ceases, CO2 would continue to leave the tank and the pH would continue to rise. Note that for a bubble 1mm in diameter, 1/40^th equilibration in 0.1s is equivalent to a transfer velocity of about 15cm hr^-1 across the bubble surface, which seems reasonable.

Thus, it was not possible to measure influx CO₂ transfer velocities using this method, which was a pity since one aim of these initial experiments had been to compare influx and eflux transfer velocities for chemically enhanced CO₂ gas exchange. If these were different due to non-equilibrium thermodynamics as suggested by Phillips (1991a, see Section 1.4.4 ) this might complicate the design of future experiments.

A similar back-of-the-envelope calculation indicated that the laboratory air pCO₂ could vary considerably due to human respiration -indeed without any ventilation it could double in only 20 minutes. While not life-threatening, this rate of change would certainly have an impact on the measured flux in or out of the tank. These problems demonstrated that the first requirement for further air-water gas exchange experiments was a tank with a gas-tight lid, and an accurate way to determine air pCO₂. The latter is discussed below, whereas the design for the gas-tight tank will be considered in the next chapter.

Calculations of the transfer velocities from these early measurements, based on exponential equilibration formulae similar to those developed later in Section 4.5 , also demonstrated that the accuracy of the transfer velocity calculated this way is much poorer than the accuracy of the individual measurements. The accuracy of the Schmidt number exponent "n" derived from comparing transfer velocities from two different gases, is even less accurate. It was clear that, due to chemical buffering of the seawater carbonate system, electrode pH measurements were not adequate to monitor small air-water fluxes with sufficient accuracy to investigate minor processes such as chemical enhancement. A data-logger was set up to monitor the pH continuously, with the hope that a computer could perform a complex deconvolution of the data to find the best-fit CO2 transfer velocity, but the available data-logger and computer proved to be inappropriate for this purpose.

3.4.2 Methods of measuring pCO₂ for gas transfer experiments

There are many methods for determining pCO₂ in air and water samples, and it would not be appropriate here to describe them all and consider the advantages and disadvantages of each method in detail. The principles of the various methods have already been introduced briefly in Section 1.3.2 . Table 3-1 below summarises the principal factors which were taken into consideration when deciding which method to adopt for further experiments. The pH methods would not be sufficient in themselves, as separate measurement of air pCO₂ would still be necessary. There are also intrinsic inaccuracies with electrode pH measurements- due to the "residual liquid junction potential" which can make calibration difficult (as discussed, for example, by Whitfield et al 1985), and the unknown activity of the hydrogen ion in seawater, which has to be incorporated into the carbonic acid dissocation equilibrium constants needed to calculate pCO₂ from pH, (as discussed by Dickson 1993). Spectrophotometric pH can be very accurate (e.g. Bellerby et al 1993, Clayton et al 1995) but the method had only recently been developed for use in seawater and would have taken much effort to set up. Automation of gas chromatography measurement techniques is not simple, and discrete samples, are at a clear disadvantage when measuring a kinetic parameter such as the gas exchange rate. It was suggested that ¹⁴C labelled bicarbonate could be added to the water, as in the method of Liss (1973), however the radioactivity hazard would place severe restrictions on the possible experiments. The LiCOR infra-red CO₂ analyser, which continuously measures pCO₂ in a flowing airstream, and is easy to set up and interface with a computer, was clearly the most appropriate apparatus for this research (this analyser will be described in more detail in Section 5.5.1 ). However, we had to apply to a special equipment fund to purchase such an analyser, and it did not arrive until December 1994. The fluorescence experiments and global flux calculations described elsewhere this chapter were carried out during this interval.

3.4.3 Other ideas for gas exchange experiments

The idea of using a temperature change to create an air-water disequilibrium might also be useful for air-sea gas exchange experiments based in a laboratory tank on board a ship. Continuously flowing seawater piped in from the sea might be warmed sufficiently, for example by exchanging heat with the engines, to create a significant air-water disequilibrium not only of CO2, but also of other dissolved gases such oxygen. Concentrations of several gases might be measured both in the water and in a flowing airstream before and after contact with this water in a tank, and thus the air-water fluxes determined continuously, to see whether anything in the seawater itself seemed to be influencing the ratio between the transfer velocities of CO₂ and other gases. However, it was considered more appropriate to make further gas exchange experiments in the more controlled laboratory conditions in UEA.

3.5 Fluorescence measurements of Carbonic Anhydrase

3.5.1 Introduction

The CA concentrations in the microlayer which would be relevant to catalysis of air-sea CO₂ exchange (in the range 1-100nM -as seen in Section 3.3 ) are much lower than the CA concentrations within algal cells or mammalian blood, which were the subject of most previous investigations. Nevertheless, since fluorescence measures the emission of light at a different wavelength from the exciting light, it can be a very sensitive and specific measurement technique, which does not require any purification of samples. As I already had some experience of fluorescence measurements of dissolved organic matter in seawater, as reported in Matthews et al (1995), it seemed worth investigating whether this method might be useful for measuring CA in seawater, particularly in the sea-surface microlayer

3.5.2 Principle of the fluorescence technique

The key feature of this technique of measuring carbonic anhydrase activity (CA) is the energy transfer between tryptophan and the fluorescent probe dansyl amide (DA). Tryptophan is one of three fluorescent amino acids, which are found in all protein molecules (there are seven tryptophan units in one bovine CA molecule), and it can be excited by photons of light just beyond the blue end of the visible spectrum, at a wavelength of about 285nm. The photon which it then emits in the range 320-340nm is just the right wavelength to excite the small polycyclic aromatic molecule DA which normally emits at about 520nm. This energy transfer process is particularly efficient when it occurs within a molecular complex in which DA is bound to the active site of the CA protein molecule. In this case there is also a blue shift from 520nm to 460nm as discussed by Chen and Kernohan, (1967), who found their peak at 320/468nm using a buffer solution of pH 7.4 rather than seawater. By combining CA with DA in this way, not only is the resulting fluorescence intensity much greater than for tryptophan or DA alone, but the emission wavelength is also unique to this CA-DA complex (Drescher 1978), and further from the excitation wavelength which helps to avoid interference from Raman and Rayleigh scattering effects. Since the CA-DA bond is at the active site of the enzyme, it works for all varieties of plant and animal CA, despite the major differences in protein size and structure.

The first task was to identify the optimum excitation / emission wavelength pairs for measurement of CA within the required concentration range in the seawater solute (initially this was real seawater stored over 6 weeks in the dark). This was achieved by making fluorescence measurements over an "excitation emission matrix" (EEM) of wavelength pairs, and plotting the resulting EEM spectra, which is shown in figure 3-7 . Here the positions of the peaks, the energy transfer process and the blue shift are readily apparent. The use of this technique to identify energy transfer processes in seawater fluorescence is discussed further by Matthews et al (1995).

Note that in the example of figure 3-7 , the CA concentration (10^-7 M) is only 1/100th of the DA concentration (10^-5 M) but the CA-DA peak is slightly higher than the DA peak. There was no significant reduction in the DA fluorescence at 325/520nm on addition of CA, as expected due to the great excess of DA. On the other hand, CA tryptophan fluorescence declined by about 65% on adding DA, in line with observations by Chen and Kernohan (1967).

3.5.3 Results and conclusions

Calibration experiments using bovine CA added to both old real seawater and artificial seawater initially seemed quite promising. The relationship between the fluorescence measured at the CA-DA peak and the CA concentration was almost linear at concentrations above 10nM. Below this, however, the curve levelled off (see figure A-1 in appendix), and the fluorescence at the CA-DA peak was low compared to the background variability.

This levelling off may be due to losses by adhesion on the container, or biological or chemical degradation. Curves plotted as a function of added DA, showed that DA was always in excess, but suggested that the reaction was not going to completion.

Nevertheless, it was hoped that it might be possible to detect some CA using this method, in samples of natural seawater from the North Sea spring bloom, collected.off Yarmouth and taken back to the lab as quickly as possible. Both subsurface and microlayer samples were taken, the latter with a "Garret screen" (see Section 2.4.2 ). Unfortunately, the signal to noise ratio was poorer in this natural unfiltered seawater, possibly due to the effect of light scattering by small particles. Although for this reason it was not possible to draw significant conclusions from the measurements at the CA-DA peak, there was a distinct enrichment of tryptophan (protein) fluorescence in the microlayer screen samples, particularly in the samples taken further from the shore.

To further investigate microlayer enrichment, bovine CA was added to a tank of artificial seawater, from which microlayer samples were collected using a glass plate. In the microlayer samples the signal:noise ratio was again poor, possibly because the sampling process picked up particles from the air (the lab was quite dusty at this time). A best guess interpretation of the data, is that the microlayer samples contained twice as much CA as the bulk water.

Finally, the storage of samples was investigated. The activity of CA clearly declined over time, with very little activity remaining a couple of weeks after adding the enzyme to seawater. The fluorescence of Dansyl amide, on the other hand, was not significantly affected by storage. These results are significant, because they imply that there must be some loss process consuming or degrading the CA. Consequently, we would not expect to find any catalytic activity in stored samples of seawater, such as those examined by Goldman and Dennet (1983) and Williams (1983), even if carbonic anhydrase had been present in the sea-surface microlayer in situ.

3.6 Conclusions and Strategy for further work

However, although, there are many published reports of enzyme activity in extracts from algal cultures, measured by various techniques as discussed in chapter 2 and references therein, we still have no measurements of the activity of carbonic anhydrase freely available in the sea-surface microlayer. We do not even know whether the enzyme, although active outside the cell walls, would ever be released into the water and remain active. Although we expect it to be concentrated in the microlayer, its activity may be inhibited by the many other organic molecules and ions also concentrated there. Collecting a sample from the microlayer at sea is difficult, as is measuring the enzyme activity in such a mixture. The fluorescence experiments reported in Section 3.5 showed that there was much more "noise" in microlayer compared to bulk samples. Moreover they also indicated that the lifetime of the enzyme in such samples may be short (as confirmed by later experiments reported in Section 7.6.1 ).

We did consider other techniques for sampling the microlayer and measuring enzyme activity. For example, we could have developed a method to extract and purify the protein from seawater, separating the carbonic anhydrase using gel electrophoresis, and detecting it using an immunoassay or the pH indicator technique described by Graham et al (1984 -see Section 2.6.3 ). However, the principle aim of this research was not to investigate the production of carbonic anhydrase by marine algae, but to investigate whether this enzyme produced in situ can actually catalyse the transfer of CO₂ across the sea-surface microlayer. We could have spent several years purifying and measuring enzyme extracted from cultures or attempting to make measurements of its activity in sea-surface microlayer samples, and still not know, due to the many uncertainties mentioned above, whether it could actually have any effect on the CO₂ transfer velocity. So rather than investigating all the pieces of this puzzle separately (enzyme concentration, activity, inhibition, lifetime and microlayer enrichment, and the reaction-diffusion system of air-water CO₂ exchange), and then from this trying to predict the effect on the air-water CO₂ flux, it seemed more sensible to design a holistic experiment in which we measure the air-water CO₂ flux directly during actively photosynthesising algal blooms. The design of such an experiment is the topic of the next chapter.

Continue to Chapter 4:
Design and Principles of Steady-State-Tank

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