390 S. ARONOFF 



The trigonometric solutions provide a convenient method of calcula- 

 tion of the terms involving the paired complex numbers. The steady 

 state is therefore approached as a difference between unity and the 

 sum of a diminishing logarithmic and a damped periodic function. 

 Theoretically, parameters might be chosen where the steady state is 

 approached in a damped, oscillatory manner. However, with the 

 parameters we have used, term three never exceeds term two and the 

 curve is strictly monotonic, as Fig. 3 shows. 



If withdrawal of isotope is established suddenly (that is, Co = 0) , 

 then the loss of radioactivity from each of the compartments is a 

 curve equivalent to the inversion of the accretion curves. 



The isotope accretion curves are, in fact, qualitatively in agreement 

 with the experimental data (1), despite the arbitrary choice of 

 parameters. Thus, there is the initial near-linear rate for PGA ( = 

 compartment G) and the initial sigmoid rates for the pentoses, as well 

 as for the residual sugars. A plot of the curves as per cent of total ac- 

 tivity vs. time also results in the negative slope for G corresponding 

 to that found experimentally for PGA. 



Under isotopic steady-state conditions, the total radioactivity per 

 compound is proportional to the pool size of the compound. A change 

 in one of the rate constants or the CO2 concentration will result in 

 transient changes, eventually leading to the establishment of new 

 steady states. The radioactivity of the compounds may then be uti- 

 lized to describe these changes, as has been shown experimentally by 

 Wilson (4) in Calvin's laboratory. A discussion of these transients, as 

 well as a fuller exposition of the methods employed here, is presented 

 elsewhere. 



Acknowledgment. We wish to acknowledge the generous financial support 

 of the National Science Foundation. 



Discussion 



"Witt : What is the time scale? 



Aronoff : Arbitrary time units. 



Lumry: We have worried quite a bit about the kind of system you have just 

 discussed and have found it to be of limited usefulness because of the frequent 

 possibility that not all elementary steps are first-order in substrate concentration. 

 For example, an enzymatic step operating under conditions of enzyme saturation 

 introduces a zero-order step so that an entirely different type of mathematical 

 framework becomes necessary. Secondly, your drive for the whole mechanism is 



