PHOTOSYNTHESIS OF CARBON COMPOUNDS 461 



of this carboxyl carbon, or 0.5 /xmole, is derived immediately from CO^; the other 

 half (carbon atom 3) comes from RuDP. We shall subtract the "C due to newly 

 incorporated "COg from the total i^C found in PGA at each time and for each of these 

 two cases. The specific radioactivity of the remainder may then be compared with 

 the specific radioactivity of the RuDP from which it must be derived. 



In order to make this subtraction it is necessary first to calculate the radiocarbon 

 in the carboxyl group of PGA as a function of the time of exposure of the algae to 

 "COg. This calculation requires in turn a calculation of the saturation curve of the 

 "CO 2 pool", although this could be assumed to be saturated from the beginning 

 without seriously affecting the results. 



Consider the steady state system : 



R R 



CO2 — > Pool 1 — > Pool 2 — >■ etc. 



Let Ci and C^ be the steady state concentrations of Pools i and 2 and let x and v 

 be the degrees of saturation with "C of these pools (respectively) as a function of 

 time of exposure of the algae to "COj. R is the rate of flow of carbon into the system 

 and through the two pools. It is also assumed in this case that the rates of the back 

 reactions are negligible compared to the rates of the forward reactions. 



For a small increment of time, the change in degree of saturation is the difference 

 between the rate of flow of "C into the pool (R) and the rate of flow of carbon out of 

 the pool (Rx), divided by the size of the pool C^; dxidt = (R—Rx)IC^. Integration 

 and determination of the integration constant at / = gives x = i — expt ( — R/Ci)0 . 



During a small increment of time, the change in degree of saturation of the second 

 pool is the difference between the rate of flow of "C into the second pool {Rx) and the 

 rate of flow out [Ry) divided by the pool size C^; 



Integration and determination of constants at i = o leads to two solutions, one for 

 the case Cj + C^- 



and another for the case C^ = C^'. 



y = I — (I — RtjC) exp (— RtjC) 



In applying these equations to the data from steady state Expt. 18 we have assumed 

 a value of Cj = 1.2 /xmoles for the "COg pool" (Fig. i) and a value of 0.2 /^moles/sec 

 (= 12 /ixmoles/min) for R. The resulting values for x are shown by curve A, Fig. 9. 



If reaction D is correct, the PGA carboxyl pool arising from newly incorporated 

 CO2 is 0.5 /Limoles and its degree of saturation jy is given by curve B, Fig. 9. If reaction 

 L is correct, this pool is i.o /xmole and the saturation curve y is that shown as curve C. 

 Curve B times 0.5 and curve C times i.o give, as a function of time, the respective 

 /xmoles of "C in the PGA carboxyl pool derived directly from COj. 



The degree of saturation of the residual carbon atoms of PGA (those which are 

 derived from RuDP) may now be calculated by subtracting from the experimentally 

 determined ["C]PGA these values of the COa-derived carboxyl (0.5 S for reaction D, 

 1.0 C for reaction L) and dividing by the pool sizes of the residual carbons (2.5 and 



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