928 CONCENTRATION FACTORS CHAP. 27 



k* and [CO2] are high, is the same as in formula (27.41), i. e., equal to n 

 times the maximum rate of formation of ACO2 by reaction (27.37). 

 The equation of the individual carbon dioxide hyperbolae is : 



(27.52) P/(Pn,ax. - P) = {keJil + fc*)K%[C02]A* 



They reach half saturation at : 



(27.53) ,/JC02] = k*/K,(k,,El + fc*) 



and have the following initial slope (independent of k*, and thus of light 

 intensity) : 



(27.54) {dP/d[C02])o = nKeke.A^El 



The assumption of a stable ACO2 compound was used by Franck and 

 Herzfeld (1941) in their detailed kinetic theory of photosynthesis— the 

 most elaborate to be found in the Uterature. The rather complex chemical 

 mechanism on which the kinetic analysis was based was illustrated by 

 scheme 7.VA in Volume I. 



It would have been inconvenient for Franck and Herzfeld to use a different postu- 

 late concerning the stability of ACO2, because they assumed that the carrier is associated 

 not only with carbon dioxide molecules, but also with seven reduction intermediates. 

 To consider the equilibrium ACO2 ^ A + CO2 as reversible, while postulating a firm 

 attachment to the same carrier of the reduction intermediates, would have meant added 

 mathematical complications; while to assume a different reversible association equilib- 

 rium for each intermediate (as was once suggested in chapter 9) would have been still 

 more cumbersome. Thus, Franck and Herzfeld chose the simplest way when they as- 

 sumed the complexes of A with CO2 as well as with all seven intermediates to be practi- 

 cally undissociable (except by light — a complication discussed in Vol. I, p. 167, and in 

 chapter 29). 



Because of the assumption of an undissociable complex, the derivation of Franck 

 and Herzfeld contains no equivalent of section a. Since they did not take into account 

 the effects of slow diffusion, it also contains no equivalent of section b. The aspects of 

 the carbon dioxide supply problem that Franck and Herzfeld did consider were the 

 phenomena treated in section c, i. e., slow carboxylation, caused either by low carbon 

 dioxide concentration, or by carboxylase deficiency. 



Their treatment of these two effects was somewhat different from that given in sec- 

 tion c because they postulated a different mechanism of catalysis. Instead of the reac- 

 tion sequence (27.36, 37), Franck and Herzfeld assumed the following three reactions: 



K 



(27.55a) CO2 + A , A • CO2 



(formation of a "loose" complex) 



(27.55b) ACO2 + Ea > AGO, + EI 



(catalyzed formation of a "stable" complex and inactivation of the catalyst) 



k' 



(27.55c) E; ^—^ Ea 



(reactivation of the catalyst) 



