## Efficiency of conversion of absorbed light

Once the light energy is absorbed by the chloroplast pigments of the phytoplankton or aquatic macrophytes it is used, by means of the photo-synthetic fixation of CO2, to generate useful chemical energy in the form of carbohydrate. We shall now consider the efficiency of this conversion of excitation energy to chemical energy.

An upper limit to the efficiency is imposed by the nature of the physical and chemical processes that go on within photosynthesis. We saw in Chapter 8 that the transfer of each hydrogen atom from water down the electron transport chain to NADP requires two photons, each driving a distinct photochemical step. The reduction of one molecule of CO2 to the level of carbohydrate uses four hydrogen atoms (2 x NADPH2) and so requires eight photons. Putting it another way, to convert one mole of CO2 to its carbohydrate equivalent (one sixth of a mole of a glucose unit incorporated in starch) requires not less than eight molar equivalents, i.e. 8 moles of photons. The energy in a photon varies with wavelength (e = hc/X) and so we shall obtain an average value by taking advantage of the observation by Morel and Smith (1974) that for a wide range of water types 2.5 x 1018 quanta of underwater

PAR = 1 J, with an accuracy of better than 10%. We may thus regard typical underwater light as containing 0.24 MJ (megajoules) of energy per mole photons and so 8 moles of photons is equivalent to 1.92 MJ. The increase in chemical energy associated with the photosynthetic conversion of one mole of CO2 to its starch equivalent is 0.472 MJ. Thus, of the light energy absorbed and delivered to the reaction centres, about 25% is converted to chemical energy as carbohydrate and this is the maximum possible efficiency.

To equate the plant biomass to carbohydrate is an oversimplification, since the aquatic plants also contain protein, lipids and nucleic acids, none of which conform closely in their overall composition to CH2O. The biosynthesis of these substances requires additional photosynthetically generated reducing power and chemical energy in the form of NADPH2 and ATP, and so requires additional light quanta per CO2 incorporated. The true minimum quantum requirement per CO2 for growing cells is likely to be about 10 to 12 rather than 8,1099 which brings the maximum efficiency down to 16 to 20%. Thus the best efficiency we can hope for in the conversion of absorbed light energy to chemical energy in the form of new aquatic plant biomass is about 18%.

The conversion efficiency or quantum yield actually achieved by a given phytoplankton population or macrophyte can be determined from measurements of the photosynthetic rate and the irradiance, provided that information on the light absorption properties of the plant material is available. Using the absorption spectrum, 400 to 700 nm, rates of light absorption for a series of wavebands can be calculated and summed. For example, the rate of absorption of PAR by phytoplankton per unit volume of medium at any given depth, z, is dQJz) f700

dv J 400

where ap(1, z) is the absorption coefficient at wavelength 1 of the phyto-plankton population existing at depth zm, and E0(1, z) is the scalar irradiance per unit bandwidth (nm-1) at wavelength l and depth z m.

A useful concept here is that of the effective absorption coefficient of the phytoplankton for the whole PAR waveband. This is defined by

and as an alternative to eqn 10.15 we can therefore write

The specific absorption coefficient of the phytoplankton for PAR, df*(z), is defined by substituting a^*(l, z) for ap(1, z) in eqn 10.16: also ap(z) = [Chl] af*(z)so that d—() = [Chl]d*f(z) Eo (PAR, z) (10.18)

dv f

In any attempt to calculate the rate of energy absorption by phytoplankton (and, by implication, quantum yield - see below) with eqn 10.18, using estimated values of a$*(z) the fact that, as we saw earlier, the effective specific absorption coefficient of the phytoplankton for PAR can vary markedly with depth must be taken into account.

It is often more convenient to work in terms of downward, rather than scalar, irradiance, but E0 is always greater than Ed (see Fig. 6.10, §6.5) by a factor that depends on the angular structure of the light field at that particular depth. Following Morel (1991) we shall indicate this 'geometrical' correction factor by g. This correction is not trivial: for wavelengths in the photosynthetically important 400 to 570 nm region, and for phytoplankton concentrations in the 0.1 to 1.0mgchl am-3 range, Morel (1991) calculated values of g varying between 1.1 and 1.5. Using the geometrical correction factor we can now write another expression for the rate of absorption of PAR by phytoplankton per unit volume of medium at depth z m, namely d-Jz) f700

dv 400

where Ed (1, z) is the downward irradiance per unit bandwidth (nm-1) at wavelength 1 and depth z m.

An alternative approach starts from the fact that the rate of absorption of radiant energy per unit volume at depth zm is given by

dv where E(z) is the net downward irradiance at depth z m and KE is the vertical attenuation coefficient for net downward irradiance. From this it can readily be shown that d-(z)

where Ku is the vertical attenuation coefficient for upward irradiance and (as is usually the case) Ku « Kd, and R(z) is irradiance reflectance (Eu[z]/ Ed [z]). If we choose to ignore the contribution of the upwelling flux - a reasonable approximation in most marine waters, with reflectance values of only a few per cent, but not in turbid waters - then we can write

dv for the total rate of absorption of energy per unit volume, as a function of downward irradiance. To calculate the rate of absorption of energy by phytoplankton we make use of the fact that in any given waveband the proportion of the absorbed energy that is captured by the phytoplankton is ap(1, z)/at(1, z), the ratio of the absorption coefficient due to phyto-plankton to the total absorption coefficient, at that wavelength. The rate of absorption of PAR by phytoplankton per unit volume of medium, as a function of downward irradiance is therefore given by dQJz) f700

pK~- [ap(1, z)/at(1, z)] Kd(1, z) Ed(1, z) d1 (10.23)

### J 400

dv where Kd (1, z) is the vertical attenuation coefficient for downward irradiance at wavelength 1 and depth zm. In eqns 10.15, 10.16 and 10.19 we can, of course, replace ap(1, z) with [Chl](z) af *(1, z), the product of the phytoplankton concentration (mgchl a m~3) and the specific absorption coefficient (m2mgchl a-1) at wavelength 1, of the phytoplankton population present at depth z m.

To arrive at an accurate determination of photosynthetic efficiency, the spectral variation both of the light field and of absorption by the biomass should be taken into account, along the lines indicated above, and numerous workers have sought to do this.111,244,376,727,728,778,940,1190 Useful information can, however, still be obtained from photosynthesis measurements combined with broad-band irradiance data. Since, as we saw earlier, the fraction of the total absorbed PAR that is captured by the phytoplankton is approximately [Chl]kc/Kd(PAR), then from eqn 10.22 we can write

for the rate of absorption of light energy by phytoplankton per unit volume, at depth z m. Estimates of energy absorption by phytoplankton (and consequently of quantum yield - see below) made with eqn 10.24

can, however, be grossly inaccurate if the variation of kc with the type of phytoplankton present, the background colour of the water and the depth (kc varying with depth in a similar manner to af) are not taken into account.

It is useful in dealing with the present topic to have a specific symbol for the rate of absorption of PAR by phytoplankton per unit volume of medium at a given depth. We here introduce the symbol w, defined by x(.) = ^ (10.25)

dz where w(z) can have the units Wm-3, or MJm-3 h-1, or quanta (or mmoles photons) m-3 s-1. We can, in addition, define w*(z) to be the specific rate of absorption of PAR by phytoplankton per unit volume at depth z m, i.e. the rate per unit phytoplankton concentration, expressed in terms of mgchl am-3. Thus w(z) = [Chl] w*(z), and w*(z) has the units Wmgchl a-1, or quanta (or mmoles photons)s-1 mgchl a-1. For any given aquatic system, w(z) is determined by using one or other of eqns 10.15, 10.17, 10.23 and 10.24, or some equivalent procedure.

To obtain the energy conversion efficiency at a given depth we divide the rate of accumulation of chemical energy per unit volume at that depth by the rate of absorption of light energy by phytoplankton per unit volume. Given a specific photosynthetic rate of P* (CO2) moles CO2 fixed mgchl a-1 h-1, and an increase in chemical energy of 0.472MJ associated with the fixation of each mole of CO2, then the rate of accumulation of chemical energy per unit volume is 0.472 [Chl] P* (CO2) MJ m-3 h-1. Dividing by w(z) we obtain the conversion efficiency

w(z) being expressed in MJm"3h" (quanta measurements can be converted using 2.5 x 1024 quanta = 1 MJ, see above). Alternatively, if P* is expressed in terms of mg carbon fixed mg chl a ^h"1, P* (C), then, since there is an increase in chemical energy of 3.93 x 10 5MJ associated with the fixation of 1 mg C, the conversion efficiency is given by

3.93 x 10"5[Ch/]P*(C) 3.93 x 10"5P*(C) , ec = -TT- = -p-- (10.27)

Another way of expressing the efficiency of conversion of absorbed light energy to chemical energy by aquatic plants is the quantum yield, f. This is defined to be the number of CO2 molecules fixed in biomass per c quantum of light absorbed by the plant. Given the quantum requirement per CO2 fixed, imposed by the mechanism of photosynthesis (see above), it follows that the quantum yield could never be greater than 0.125, and for growing cells, even under ideal conditions, is unlikely to exceed about 0.1. Quantum yield and per cent conversion efficiency are, of course, linearly related. Allowing 0.472 MJ chemical energy per CO2 fixed and 0.24 MJ per mole photons of underwater PAR, we arrive at ec = 1.97f (10.28)

Equations corresponding to 10.26 and 10.27 can be written for the calculation of quantum yield from w(z) or w*(z) and specific photosynthetic rate f = mMCQj = P^ (10.29)

w(z) in these equations has the units moles photons m~3 h_l.

The quantum yield attained by an aquatic plant is a function of the light intensity to which it is exposed. That this is so is apparent from the variation of specific photosynthetic rate with irradiance (Fig. 10.3). Ignoring for the moment any changes in chloroplast shape or position with light intensity, we may assume that the rate of absorption of quanta is proportional to the incident irradiance. Thus, at any point in the photosynthesis versus irradiance curve the value of P/Ed (see Fig. 10.3) is proportional to the quantum yield.

For a plant to be able to make efficient use of light quanta being absorbed at a given rate, the activity of the electron transfer components in the thylakoid membranes and of the enzymes of CO2 fixation in the stroma must both be high enough to ensure that the excitation energy collected by the light-harvesting pigments is utilized as fast as it arrives at the reaction centres. If this situation exists, then a moderate increase in light intensity, causing a proportionate increase in quantum absorption rate, leads to a corresponding increase in the specific rate of photosynthesis. In the initial, linear, region of the P versus Ed curve this is what is happening. Over this range of intensity, P/Ed is constant and has its highest value, indicating that the plants are achieving their highest conversion efficiency and quantum yield. If the absorption characteristics of the plant are known, then this maximum value of P/Ed can be used to calculate fm, the maximum quantum yield.

As the incident light intensity is further increased, the rate of absorption of quanta reaches the point at which excitation energy begins to arrive at the reaction centres faster than it can be made use of by the electron transfer components and/or the CO2 fixation enzymes. At this stage some of the additional absorbed quanta (over and above those the system can readily handle) are utilized for photosynthesis, and some are not, the energy of the latter being eventually dissipated, mainly as heat. For this reason, in this range of light intensity, increments in Ed are accompanied by less than commensurate increases in P, i.e. the slope of the curve progressively diminishes, until eventually the point is reached at which APIAEd becomes zero. In this light-saturated state, the electron transfer and/or CO2 fixation enzymes (most likely, the latter) are working as fast as they are capable, and so any additional absorbed quanta are not used for photosynthesis at all. From the end of the linear region through to the light-saturated region, since photosynthetic rate does not increase in proportion to irradiance (PIEd steadily falls - Fig. 10.3) the quantum yield and conversion efficiency necessarily undergo a progressive fall in value. This is accentuated further if, at even higher light intensities, photoinhibition sets in. If the cells contain photoprotective carotenoids, in which absorbed light energy is dissipated as heat rather than being transferred to the reaction centre, then to the extent that these capture the incident light, the quantum yield must be proportionately reduced at any light intensity.

The characteristic manner in which P varies with Ed can, as we saw earlier, be represented mathematically in a number of different ways (eqns 10.8, 10.9, 10.10, 10.11). Since quantum yield and P IEd are linearly related, then for each particular form of the function, P = f(Ed), there will be a corresponding expression for quantum yield as a function of Ed, i.e. f = Constant.Ed-1.f(Ed). Using the tanh form (eqn 10.9) Bidigare et al. (1992) arrived at

and using the exponential form (eqn 10.11) we obtain

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