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Working with Light                                                          203

                 are present in the curve: a light-limited region, a light-saturated region, and a light-inhibited region.
                 The basic description of the P–E curves requires a non-linear mathematical function to account for
                 the light saturation effects. Quite a few such functions have been employed with varying degrees of
                 success, such as rectangular hyperbola, quadratic, exponential, and hyperbolic tangent.
                     In our opinion, the rectangular hyperbolic function such as the Michaelis-Menten formulation
                 that describes the nutrient uptake kinetics is quite suitable to describe the dynamic relationship
                 between phosynthetic rate and irradiance, though the Michaelis-Menten formulation shows a
                 much less sharper transition from the limited to the saturated region. The P–E curve (without
                 the light-inhibited) region can be described with the following rectangular hyperbolic function:


                                                       P max   E l
                                                   P E ¼                                   (5:30)
                                                        K m þ E l
                 where P E is the photosynthetic rate at any irradiance E, E l is the spectral irradiance (in
                 mmol m 22  sec 21 ) and K m is the half saturation costant when P E ¼ P max /2 (Figure 5.15a).
                     In the light-limited region, that is, at low irradiance levels, the rate of photon absorption
                 determines the rate of steady-state electron transport from H 2 Oto CO 2 . In the light-limited
                 region, the available light is insufficient to support the maximum potential rate of the light-
                 dependent reactions, and thus limits the overall rate of photosynthesis. In this region, the rate of
                 photosynthesis (P E ) can be described as:

                                                    P E ¼ E l   a                          (5:31)

                 where E l is the spectral irradiance and a is a measure of “photosynthetic efficiency,” or how effi-
                 ciently solar energy is converted into chemical energy. a takes into account that the light absorbed
                 by the algal cell is proportional to the functional absorption cross-section (s PSII ) of the PSII
                 (the effective area that a molecule presents to an incoming photon and that is proportional to the
                 probability of absorption) and to the number of photosynthetic units (n):


                                                    a ¼ s PSII   n                         (5:32)

                     Equation (5.31) shows that photosynthetic rate is linearly proportional to irradiance at low irra-
                 diance levels. Greater is the slope (a) more efficient is the photosynthetic process (Figure 5.15b).
                 Keeping constant the number of photosynthetic units but increasing the functional absorption cross-
                 section the slope will increase. The slope can be normalized to chlorophyll biomass and, if so, a
                                                                   B
                 superscript “B” is added to denote this normalization, thus a . In this case, the curve dimensions
                 are O 2 evolved per unit chlorophyll and quanta per unit area.
                     At very low irradiance level, the rate of oxygen consumption will be greater than the rate of
                 oxygen evolution; hence, respiration is greater than photosynthesis and net oxygen evolution
                 will be negative. Therefore, the P–E curve does not pass through the origin. The irradiance
                 value on the x-axis at which photosynthesis balances respiration is called the light compensation
                 point (E c ). Therefore, the Equation (5.30) becomes:

                                                      P max (E l   E c )
                                                P E ¼                                      (5:33)
                                                     K m þ (E l   E c )

                     This phenomenon (chlororespiration) is more pronounced in cyanobacteria, where the photo-
                 synthetic and respiratory pathways share common electron carriers (cytochromes). The irradiance
                 levels needed to reach compensation point (E c ) are about 10 mmol m 22  sec 21  for shallow water,
                 but are much lower in dim habitats.
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