KINETICS OF RADIOCARBON INCORPORATION 397 



j)n)vi(U'(l from an exlernal Hource in a reaction whioli again is not first-order in 

 substrate concentration. 



Aronoff : Indeed, it is just as valid to say tliat it does not hold if there are sec- 

 ond-order reactions. Anything but the first-order would make the scheme invalid 

 as postulated. 



Myers : No, it would just reduce the number of terms. 



Lumry : No, AronofT's system is strictly limited to catenarj' chains of elementary 

 reactions each of which is first-order in a product of the preceding step. If some 

 enzyme is working to full capacity, its concentration and the rate of its uni- 

 molecular reaction yielding product will limit the overall reaction, thus acting 

 as a bottleneck not included in Aronoff's scheme. 



Bassham : I would like to make three comments, if I may. 



1. We have the same kind of overshoots on turning off the light that you get 

 with decrease in the CO2. 



2. I would have thought that if you were going to be limited to three compart- 

 ments, it might have been better to have put the pentose-monophosphate in the 

 compartment for ribulose diphosphate. The reason for this is that in the carbon- 

 reduction cycle there are two points at which external factors are required, at 

 least according to the present hypothesis. One is the reduction of PGA and the other 

 is the conversion of ribulose-monophosphate to ribulose diphosphate. Another 

 reason is that the pentose monophosphates are made by several different path- 

 ways while the ribulose diphosphates are made presumably by only one pathway 

 from ribulose monophosphate. 



3. Still another comment I want to make is that Dr. Bradley, who worked in 

 our laborator_y, has made some similar kinds of calculations and he has also had 

 some difficulty in getting the condition for these overshoots you mentioned. 



Aronoff: My interest in this problem was stimulated by the model which 

 Bradley and Calvin used. This was, however, a linear model, not cyclic. To that 

 extent it cannot apply to the system that we are considering. The reason that 

 the system was divided in the way it was, apart from sheer convenience, was that 

 the presentation of yours was in terms of the di-phosphate sugar. If you presented 

 your data in terms of the amount of activity in ribulose diphosphate per time 

 unit, then I would be very happy. However, there are no specific data for that 

 particular fraction. The scheme is nevertheless valid because all the material falls 

 into those sugars as depicted. 



Bassham : Yes, but the various pentose phosphates are made by several different 

 pathways. 



Aronoff : There is a total of three different pathways going into that compart- 

 ment, and all three are included in the one constant. 



Bassham : Wouldn't it be better to stick to the condition where there is just 

 one reaction, especially since in that reaction an external factor is introduced, 

 namely ATP? 



Aronoff: For analyses of this type one should have a diflferential analyzer. 

 Unfortunately, I have to do this with my slide rule, or, occasionally, a borrowed 

 calculating machine. With this equipment a three-compartment system is compli 

 cated enough. 



