INTERPRETATION OF CARBON DIOXIDE CURVES 927 



level is reduced from nakeaE°AAo to { ) A-ea^^A^o. Thus, here again, the effect of 



fe) 



the limiting process becomes felt when the nonlimiting rate is still far below the imposed 

 "ceiling." 



(d) Nondissociahle ACO2 Corn-pound. The Franck-Herzfeld Theory 



So far, we have considered the carbon dioxide curves as, basically, 

 ACO2 saturation isothermals, merely distorted by slow diffusion, slow 

 carboxylation and limited quantity of the carboxylase Ea. An alternative 

 was mentioned several times before. The carboxylation equilibrium may 

 lie practically completely on the side of association, and the effect of the 

 factor [CO2] on the rate of photosynthesis may be due entirel}^ to kinetic 

 phenomena, such as the limited rates of diffusion and carboxylation. The 

 corresponding kinetic equations can easily be derived from the more general 

 formulae given in sections h and c by putting fc^ = 0, i. e., assuming that 

 the rate of decarboxylation is negligible. For example, if the carbon di- 

 oxide limitation comes exclusively from slow carboxylation (while the sup- 

 ply of carbon dioxide by diffusion is ample), we can start directly with equa- 

 tion (27.31); omitting the k^^ term in the denominator of this equation, 

 we obtain: 



(27.47) P = nKAo[C02]k* /(K + ^a[COo]) 



(If k* «: ks[C02], this equation is reduced to P = nA;*Ao as expected.) 

 This equation, too, represents hyperbolic carbon dioxide curves: 



(27.48) P/(Pmax. - P) = K[C02]/k* 



with half saturation at: 



(27.49) ./JCOa] = A;*Aa 



and the initial slope: 



(27.50) {dP/d[C02])o = nkM 



It will be noted that, in this case, all carbon dioxide curves make the same 

 angle with the [CO2] axis, independently of A:^ (i. e., of the light intensity). 

 Half saturation, on the other hand, occurs at [CO2] values that are propor- 

 tional to k* (i. e., increase with increasing light intensity). 



The same method can be extended, to account also for saturation ef- 

 fects caused by limited amount of the carboxylating catalyst ^ai e. g., 

 by assuming fc^ = in formula (27.37). Equation (27.40) is reduced, by 

 this assumption, to: 



(27.51) P = n2fefceaA:?AoE° [C02]/(KefceaEi[C02] + Kek* [CO2] + k*) 



The "absolute ceiling" of this family of hyperbolae, approached when both 



