922 CONCENTRATION FACTORS CHAP. 27 



Inserting this value of [ACO2] into (27.6), we obtain: 

 (27.16) - = 2^;; 



^(k^k* Ao + klkd + k*kd + kJ<:d[C02]\ _ Aofcd[C02]A;* 

 ^\ 2K / 



This equation represents, for different vakies of the parameter A-* {i. e., 

 for different light intensities), a set of hyperbolae. Similarly to the "pri- 

 mary" carbon dioxide curves (27.8), these hyperbolae approach the satura- 

 tion values (27.10), but, in contrast to the primary curves, they do not all 

 reach half saturation simultaneously. The expression for the half-saturat- 

 ing external carbon dioxide concentration can be derived from (27.15) by 

 assuming [ACO2] ^ 3^4o, and is as follows: 



(27.17) .,.1C0,, . i- [1 + *; &A^^'] 



This equation shows that, because of delayed diffusion and carboxylation, 

 the half-saturation point advances with increasing light intensity toward 

 higher carbon dioxide concentrations — a behavior actually shown by most 

 if not all of the experimental carbon dioxide curves (c/. figs. 27. 2A, 27. 2B 

 and 27.3). 



The initial slopes of the curves (27.16) are not proportional to k*, as 

 were the slopes of the primary curves according to equation (27.11), but 

 are given by the equation: 



(27.18) (rfP/d[C02])o = nkMkdk* /{k^Aokt + Kkd + kdk*) 



This equation shows that carbon dioxide curves for all k^ values are con- 

 fined within an angle formed by the axis of the abscissae and a slanting 

 straight line ("roof"): 



(27.19) Pur.. = ^^l^'l\^ [CO:^] 



and, of course, also under the horizontal ceiling (27.10). Equations 

 (27.16), (27.17), (27.18), and (27.19) represent the combined effects of slow 

 diffusion and slow carboxylation. If only one of these factors is operative, 

 the equations can be simplified. Pure diffusion limitation can be assumed 

 if the maximum diffusion supply is much smaller than the maximum rate of 

 carboxylation, while pure carboxylation limitation must prevail under the 

 reverse condition. In the first case: 



(27.20) kd<^kM 



