920 CONCENTRATION FACTORS CHAP. 27 



The factor n in (27.5) is either 1 or a fraction of 1, depending on how 

 many molecules CO2, at best, can be reduced to the carbohydrate level, 

 { CH2O } , for each molecule CO2 which undergoes the first reduction step 

 (to AHCO2). If the mechanism of reduction involves only one photo- 

 chemical step (ACO2 -^ AHCO2), followed by a two-step dismutation: 



4hv 



4 AHCO, > 3 ACO2 + HoO + (CH2OI + A 



then /; is 1/4. If an energy dismutation step of the tj^pe discussed in 

 chapter 9 (page 264) also is involved, n is reduced to 1/8. If, on the other 

 hand, CO2 is reduced to the H4CO2 level in a straight series of photochemi- 

 cal reduction steps: 



AGO. ^"' ) AHCO, -^ -^ -^ ATI4CO, > A + H,0 + CH,0 



then 71 is equal to 1. (As a compensation, the constant /;;* can be equal in 

 the dismuation model to the number of the absorbed light quanta, but 

 must be l/n times smaller in the straight reduction model, where 1/n 

 quanta are needed to carry a single CO2 molecule through all four reduc- 

 tion steps.) 



Assuming that the conditions (27.6) and (27.7) are satisfied, we can 

 insert into (27.6) the equilibrium value (27.3) and obtain, for the carbon 

 dioxide curves of photosynthesis, the equation: 



(27.8) P = 7lkt KaAo[C02]a/(l + i^a[C02]a) 



For various values of k* (e. g., for various light intensities, 7), equation 

 (27.8) represents a family of curves of the "Bose type." These curves are 

 hyperbolae : 



(27.9) P/(Pxnax. - P) = K,[C02] 



At the saturating concentrations of carbon dioxide, P approaches asympto- 

 tically the maximum rate: 



(27.10) Pmax. = nk* Ao 



All carbon dioxide curves separate from the beginning, their initial slopes 

 being : 



(27.11) {dP/d[C02].)a = nk*,K,Ao 



They all reach "half saturation" at the same carbon dioxide concentration: 



(27.12) l/JC02]a = 1/i^a 



The empirical carbon dioxide curves deviate more or less widely from this 

 simple type: Even the "Bose type" curves, shown in figure 27. 2A, do not 

 all reach half saturation at the same value of [CO2]. We can attempt to 

 consider the curves (27.8), determined exclusively by static conditions, 



