INTERPRETATION OF CARBON DIOXIDE CURVES 935 



Among the characteristics of the various theoretical equations derived 

 above for the carbon dioxide curves, which might be used for comparison 

 with the experiment, are the relations between half-saturating carbon di- 

 oxide concentration and light intensity (c/. equations 27.12, 17, 22, 33, 44, 

 45, 49, 53, 65, and 75), and between the initial slope and light intensity 

 (equations 27.11, 18, 23, 34, 46, 50, 54 and 66). 



The value of 1/JCO2] is independent of k* {i. e., of light intensity) and 

 equal to \/K^ only to the extent to which the carbon dioxide curves are 

 proportional to the saturation curves of the ACO2 complex (eq. 27.12). 

 It has been suggested by some that this assumption is legitimate whenever 

 the carbon dioxide curves are found to be hyperbolic. Thus, Burk and 

 Lineweaver (1935), having satisfied themselves that the carbon dioxide 

 curves of Warburg, Harder, James, van der Paauw, and Emerson and 

 Green (Table 27.1) follow the hyperbolic saturation law, proceeded to 

 calculate from them the carboxylation constants K^ and obtained values 

 ranging from 1 X 10^^ to 10 X lO"'' l./mole (at room temperature). The 

 corresponding free energies of carboxylation, AFa(= RT loge K^) are be- 

 tween — 6.9 and —8.3 kcal/mole. 



It was mentioned on page 908 that, according to Whittingham (1949), 

 the half-saturating CO2 concentration of Chlorella is shifted down to 0.5 

 or 1.0 X 10 -^ mole/1, if care is taken to avoid inhibition phenomena at 

 low CO2 concentration, by allowing 2-3 hour induction period (if the cells 

 were grown in high [CO2]) or, still better, by using cells gro^vn in low [CO2] 

 (e. g., in air). 



The heat of carboxylation also was estimated by Burk and Lineweaver. From the 

 absolute rate values found by Emerson and Arnold, at 6° and 24° C. in flashing light, 

 they calculated AH a = 1.3 to 6.2 kcal/mole. However, Table 8. VIII shows that the 

 fixation of carbon dioxide by organic molecules is accompanied — as is natural in reactions 

 in which small molecules are attached to larger ones— by a decrease in entropy, —TAS 

 being as large as +8 or even +16 kcal/mole at room temperature. Thus, if — AF of 

 carboxylation is 7-8 kcal/mole, - AH should be of the order of 15-20 kcal— considerably 

 larger than the estimate of Burk and Lineweaver. 



Our derivations in sections b, c and d show that the carbon dioxide 

 curves may be strongly affected by slow diffusion, or slow carboxylation, 

 without losing the hyperbolical shape. Equations (27.17, 22 and 33) show 

 that these two factors cause i/2[C02] to increase linearly with increasing 

 light intensitij. The constant K^ can in this case be obtained by linear ex- 

 trapolation of 1/JCO2] to / = 0. Figure 27.9 shows that the data of 

 Harder, Hoover and co-workers, and Smith (compare Table 27.1) extra- 

 polated in this way, give 1/2CO2 values in the neighborhood of 5 X 10"® 

 ilf, and thus K^ values of about 2 X lOS corresponding to AF = —7.9 

 kcal. /mole. 



