1018 THE LIGHT FACTOR. I. INTENSITY CHAP. 28 



curves cease to be straight lines and become hyperbolae. We can refer 

 here to equation (27.16), which describes the combined effects of slow dif- 

 fusion and slow carboxylation, or to equations (27.21) and (27.31), which 

 express these two effects separately. In intense light, the hyperbolae 

 p = f(k*) approach one of the following two saturation levels, either: 



(28.3) P"^""- = nkdlCOi] 



if the rate of diffusion is the limiting factor; or: 



(28.4) -?•"" = nk^ Ao[C02] 



if the rate of carboxylation is limiting. It will be noted that both satura- 

 tion values are proportional to [CO2]; in other words, this approximation 

 provides for no "absolute saturation" with respect to both / and [CO2]. 

 Half-saturation is reached, in the case of limitation by diffusion, at: 



(28.5) r/k*r = {K,k,[C02] + 2 ki)/2 KM 

 and, in the case of limitation by carboxylation, at : 



(28.6) V/"* = ^■^' + ^-'[COj] 



In both cases, half-saturating light intensity increases linearly with carbon 

 dioxide concentration. The initial slopes of the light curves are the same 

 as those of the straight lines (28.1). This means that at low carbon di- 

 oxide concentrations, the light curve families are of the Bose type, the 

 Blackman type being approached at the higher values of the parameter 



[CO2]. 



"Absolute" saturation follows, as usual, as soon as we postulate a rate- 

 limiting step, the maximum velocity of which is independent of both [CO2] 

 and light intensity, but is determined entirely by the available amount of 

 a catalyst. Equations (27.40) or (27.51), derived for the case of limitation 

 by carboxylase deficiency, contain in their denominators terms proportional 

 to the product, k* X [CO2]; when light intensity and carbon dioxide con- 

 centration are both very high, this term becomes predominant and the 

 yield approaches the "absolute" saturation value: 



(28.7) P'S,H: = nA-eaEoAo 



which is the maximum rate of the catalytic formation of ACO2 by reaction 



(27.37). 



For the reaction mechanism discussed in section d of chapter 27 (non- 

 dissociable ACO2 complex attached to chlorophyll for the duration of the 

 eight photochemical steps, as in the Franck-Herzfeld theory), with the 

 simplification (28.8) used in deriving equation (27.03), we have: 



(28.8) [EaI^E: 



