930 CONCENTRATION FACTORS CHAP. 27 



After inserting (27.61) into (27.60), one can use (27.56) and (27.59) to eliminate [A] and 

 [A.CO2] and to obtain the desired equation for [ACO2] — and according to (27.58) also 

 for P — in terms of [CO2], Ao and E^. Because of the assumed two-step mechanism of 

 formation of [ACO2] (with the loose complex A-C02 as an intermediate), the resulting 

 equation is quadratic. Its solution — which again represents a family of hyperbolae — is 

 a rather complex expression, and we do not need to quote it here. 



For high values of both [CO2] and /, the expression for P approaches asymptotically 

 the value: 



(27.62) PZTr.: = nKKElAo/ikaAo + K) 



(with the lower index referring to [CO2] and the upper to /). In the two extreme cases, 

 when either kaAo ]^ K, or vice versa, expression (27.62) reduces itself either to nkj^l 

 (t. e., the maximum rate of reaction 27.55c), or to nA-aE^An (the maximum rate of reaction 

 27.55b). 



The relations are much simpler if the rate of reaction (27.55c) is assumed to be 

 rapid (compared with the rate of photosynthesis P), so that [^a] ' is practically equal to 

 zero, and [Ea] to E^. In this case, one obtains an equation containing only first 

 power of P, the solution of which is: 



(27.63) P = k,,KElA,[C02]k*l/{k*I + k*IK[C0.2] + 8 k^KEUCO,]) 

 This is an equation of a family of hyperbolae (with / as parameter) : 



Half saturation (P = i/jPrnax.) is reached when: 



(27.65) VJCO2] = k*mKkn + 8 k^KEl) = 1 ( ^ + ^Sk.El/k^I) ) 



It is shifted, with increasing light intensity, toward the higher [CO2] values. The initial 

 slope of the curves (27.63) is: 



(27.66) {dP/d[C02])o = nkaKElAo 



Because, in formula (27.55b), the formation of ACO2 was assumed to be irreversible, the 

 slope (27.66) is independent of light intensity. (In other words, at very low carbon di- 

 oxide concentrations, all ACO2 formed is reduced by light, whatever the intensity of the 

 latter.) Thus, as stated before, the carbon dioxide curves represented by equations 

 such as (27.47) or (27.63) have more pronounced "Blackman characteristics" than the 

 curves obtained with the assumption of a dissociable ACO2 complex. 



Of course, the hypothesis of a stable association of the acceptor A. with chlorophyll 

 is independent of the other postulates of the Franck-Herzfeld theory; the latter can be 

 combined also with the assumption of a dissociable ACO2 complex. 



(e) Back Reactions in the Photosensitive Complex 



So far, we have discussed the carbon dioxide curves only from the point 

 of view of the "preparatory" dark processes at the "reduction end" of 

 photosynthesis, since these are the stages of photosynthesis most closely 

 related to the "carbon dioxide factor." 



The influence of the preparatory reactions at the "oxidation end" 



