INTERPRETATION OF CARBON DIOXIDE CURVES 925 



the influence of the Hmiting process is felt long before the rate approaches 



the limit. 



Carboxylation was treated so far as a one-step reaction, with a rate 

 proportional to the concentration [C02]a- I* is known, however (c/. Vol. 

 I, page 203), that carboxylation in photosynthesis is cyanide-sensitive, 

 and thus undoubtedly a catalytic reaction. It must therefore consist of 

 several steps, such as the formation of a substrate-catalyst complex, and 

 the transformation of this complex. We have no information as to the 

 precise nature of these steps, but it can be assumed that at very low [CO2] 

 values, the rate-determining step will be one with a rate proportional to 

 [CO2], e. g., reaction (27.36). Under these conditions, the above-given 

 derivations will be valid for the catalyzed as well as for direct carboxyla- 

 tion. At the higher [CO2] values, however, other steps or the carboxyla- 

 tion process may become rate-determining — steps limited in their maxunum 

 efficiency by the available amount of the relevant catalyst (carboxylase). 

 A [C02]-independent "ceiling" will thus be imposed on the rate of the over- 

 all process, which will be determined by the product of the amount of the 

 catalyst available and the average time a catalyst molecule requires to 

 complete the desired transformation. 



The specific form of the corresponding kinetic equations will depend 

 on the postulated mechanism of the catalytic action, and, as stated above, 

 we have at present no reasons to favor any one mechanism among the sev- 

 eral compatible with our general knowledge of the mechanism of enzymatic 

 processes. 



As an illustration, we will go through a calculation based on the simple mechanism: 



K 



(27.36) COo + Ea . Ej, ■ CO2 



*.' 



(using Ea, as in Volume I, as symbol for the carboxylase). 



(27.37) Ea -CO, + A :^i=^ Ea + ACO2 



(For the sake of simplicity, we neglect diffusion and use [CO2] where [C02]a should be 

 used.) The equilibrium constants K, and K,^ are subject to the condition: 



(27.38) ifeA'ea ( = p >< ^ ) = K. 



We assume that equilibrium (27.36) is established practically instantaneously, and 

 remains undisturbed during photosynthesis, but that equilibrium (27.37) is less rapidly 

 attained, and can therefore be displaced in light.* Designating by El the total avail- 



* The assumption that (27.36), too, is a slow reaction would lead to more com- 

 plicated quadratic equations for [ACO2] and P, similar to those obtained in section b 

 for the combined effects of slow diffusion and carboxylation. 



