INTERPRETATION OF CARBON DIOXIDE CURVES 937 



stal)le as or even more stable than indicated by these values. We recall 

 that in chapter 8(Vol. I) a compilation of experimental data showed the 

 known free energies of carboxjdation of compounds of the type of (RH + 

 CO2 -» RCOOH) to be about + 10 kcal/mole. It was also mentioned that 

 Ruben had suggested attributing the extraordinary stability of the ACO2 

 compound in photosjTithesis to a coupling of carboxylation with an exer- 

 gonic transphosphorylation — the transformation of a "high energy" into 

 a "low energy" phosphate ester. Another explanation of the same type 

 would be to assume the coupling of carboxylation Avith a parallel or con- 

 secutive exergonic oxidation-reduction, a coupling that actually occurs in 

 the uptake of carbon dioxide catalyzed by certain enzymes derived from 

 yeast and bacteria (as described by Lipmann and Tuttle 194.5; see also 



Ochoa 194G). 



There is one obvious experiment by which the carboxylation constant 

 derh-ed from the carbon dioxide curves of photosynthesis could be checked 

 — precise measurements of the carbon dioxide uptake in the dark as a func- 

 tion of the concentration [CO2] in the medium. This could be done by 

 means of radioactive carbon, or by ordinary analytical methods. So far, 

 no such measurements have been made. The observations of Ruben and 

 co-workers (c/. Vol. I, chapter 8) seem to indicate, however, that the com- 

 plex ACO2 is dissociated in vacuum, albeit very slowly, and thus possesses 

 a finite, although perhaps very small, dissociation pressure (c/., however, 

 chapter 36 for the interpretation of C*-measurements). 



(h) Are Experimental Carhon Dioxide Curves Hyperbolae? 



It will be noted that all theoretical carbon dioxide curves discussed in 

 this chapter were hyperbolae. Smith (1937) analyzed the empirical car- 

 bon dioxide curves and concluded — in contrast to Burk and Lineweaver 

 (1935)— that many of them reach saturation more rapidly than a hyperbola 

 approaches its asymptote. He has therefore attempted to obtain a better 

 analytical representation of the carbon dioxide curves by changing the ex- 

 ponents in equation (27.9). The empirical equation: 



(27.77) P/VpL.. - P' = K[CO,\ 



was found by him to fit satisfactorily his own results, as well as those of 

 Warburg, Emerson and Green, and Hoover, Johnston and Brackett. In 

 the saturation region, where (Pmax. - P) < P, equation (27.77) should not 

 differ much from the simpler quadratic relationship : 



(27.78) P/(Pm.x. - P) = K'[COiV 



Exponential functions often are used in the interpretation of curves that rapidly 

 reach saturation. Harder (1921) tried to represent his results by the formula: 



