INTERPRETATION OF CARBON DIOXIDE CURVES 917 



cal flow plienomena outside and inside the plant. We cannot be sure at 

 present whether any of the observed carbon dioxide curves reflect reason- 

 ably well the effect of carboxylation equilibrium (or of the rate of carboxy- 

 lation), or whether practically all carbon dioxide dependence of photosyn- 

 thesis, known so far, is due to diffusion phenomena, with possible addi- 

 tional distortions by the time effects noted on page 908. 



Despite this unsatisfactory state of our experimental knowledge, we 

 will go through with some kinetic derivations leading to general equations 

 for the shape of carbon dioxide curves, as affected by the several factors of 

 slow diffusion, limited rate of carboxylation, reversibility of carboxylation 

 and limited supply of light energy. We will thus obtain a kind of skeleton 

 analytical theory of the carbon dioxide curves, which could prove useful 

 for devising and interpreting future kinetic measurements — if only inves- 

 tigators of the kinetics of photosynthesis would change their present habit 

 of considering only their own limited data, and ignoring all but their own 

 ad hoc derived equations. 



(a) Carboxylation Equilibrium 



Two steps in photosynthesis, the rate of which depends directly on the 

 factor [CO2] are: First, diffusion of carbon dioxide from the medium to 

 the reaction site, and second, the first chemical reaction of carbon dioxide. 

 In chapter 8 (Vol. I), we decided that this reaction is a nonphotochemical, 

 catalytic carboxylation. We usually described it by the formula CO2 -^ 

 {CO2}, but since the concentration of the "carbon dioxide acceptor" (until 

 now symbolized by braces) enters explicitly into many of the following ki- 

 netic equations, we will from now on designate it as A, and the product of 

 carboxylation as ACO2. (Franck and Herzfeld, 1941 , used the more specific 

 symbols RH for acceptor and RCOOH for the product.) 



The two [CO.j]-dependent steps can then Ijc written as follows: 



Ki 



(27.1) CQ2 . ^ (CO,)a 



(where (C02)a refers to carbon dioxide in the immediate neighborhood of 

 the acceptor, and k^ is a diffusion constant) and: 



(27.2) (C02)a + A , '^ ^ ACQ., ( > reduction) 



a 



The reduction of ACO2 may be either a direct photochemical process (as 

 assumed by Franck and Herzfeld; cf. scheme 7.VA), or a nonphotochemi- 

 cal reaction with an intermediate, as postulated in many other schemes 

 in chapters 7 and 9. Even in the latter case, the rate of reduction is hkely 

 to be a function of light intensity, because the partner with which the com- 



