[15. XII. 1952) 



M. Calvin and P. Massini: The Path of Carbon in Photosynthesis 



451 



carbon acceptor. These were the phosphates of the 

 seven carbon sugar sedoheptulose and of the five car- 

 bon sugars ribulose, ribose and arabinose'. 



The question immediately presents itself as to the 

 relation between these two compounds along the path 

 of carbon assimilation, not only with each other but 

 with the precursors which are already known and the 

 possible products that might be formed from them. 

 The attempt to answer this question focuses our at- 

 tention once again upon some of the shortcomings and 

 limitations of the method of observation that we are 

 using and the nature of the exjjeriment which we are 

 performing. Our initial hope of determining the se- 

 quence of intermediates by a simple observation of a 

 sequence of compounds into which radioactivity has 

 been incorporated in steady state experiments is now 

 complicated by the uncertainty as to the amount of 

 compound present during the steady state. It is easy 

 to visualize a situation in which the actual amount of 

 intermediate present during the steady state is so small 

 as to escape observation by our methods, or perhaps 

 even to be so unstable as to be lost by our methods of 

 observation. This complete failure of a compound to 

 appear on a chromatogram, although it might con- 

 ceivably be an intermediate, is, of course, an extreme 

 case. The more usual situation is one in which most of 

 the intermediates are present but in varying concen- 

 trations in the steady state. Under such conditions a 

 single or even several observations of the relative 

 amount of radioactivity incorporated into a variety of 

 compounds would not necessarily be any real criterion 

 of the relative order of these compounds in the se- 

 quence of events. 



In order to achieve the full value of the method of 

 observation then, it becomes necessary to perform 

 rather extended kinetic experiments in which the ap- 

 pearance of radioactivity in all compounds is plotted 

 as a function of time at sufficiently short intervals to 

 enable a rather accurate and detailed curve to be 

 obtained. Furthermore, the distribution of radioacti- 

 vity among the atoms within each compound should 

 also be determined as a function of time. The validity 

 of any proposed sequence of events could then be de- 

 termined by a comparison of the calculated appearance 

 and distribution curves with those actually observed. 

 In order to calculate such appearance curves, as well 

 as the distribution curves amongst the atoms in each 

 compound, one can set up a system of linear differen- 

 tial equations based upon the following model ; 



CO, 



-+ B 



(1) 



where COj represents the entering carbon dioxide; 

 .4, B, etc. represent intermediates involved in carbon 



' A. A. Bt.MSO.s, J. A. BASSIIA.M, .M. Calvin, A. G. Hall, H. E. 

 HiRSCii, S. Kawaguchi, V. H. Lynch, and N. E. Tolbert, J. Biol. 

 Chcm. 196, 703 (1952). 



dioxide assimilation; S represents more or less final 

 storage product; /? is a measure of the total rate of 

 carbon dioxide assimilation in the steady state ex- 

 pressed in moles of carbon per minute. 



The rate of change of the specific activity of a single 

 carbon atom in A , given by X^ , is then expressed by 

 Equation (2). (The specific activity of the entering 

 carbon dioxide is here taken as unity. [A], the concen- 

 tration of the compound A, is independent of time.) 



^ = w (1-^^)- 



(2) 



The specific activity of the corresponding atom in 

 compound B is given by an exactly similar Equation 

 (3), 



dXo R 



dt 



[B] 



{X,-X^). 



(3) 



Equations of identical form may be written for every 

 atom of every compound that might be considered an 

 intermediate. These equations may be solved expli- 

 citly by means of a differential analyzer provided two 

 parameters are known. These are the total rate of entry 

 of carbon into the system during the steady state, R, 

 and the steady state concentration of each atom which 

 might be considered as lying along the path of carbon 

 assimilation [,4], [B], etc. 



It is clear that if such compounds (whose prime func- 

 tion it is to serve as carbon carriers between the en- 

 tering carbon dioxide and the final storage products in 

 the plant) do indeed exist in biological systems they 

 would very soon become saturated with radioactivity. 

 By this is meant that the amount of radioactivity ob- 

 served in that particular compound would very soon 

 reach a maximum value and remain that way. The 

 reason for this is that by definition the amount of these 

 intermediate compounds is not changing, and also is 

 small compared to the total amount of carbon the plant 

 assimilates during the experiment. Since all of the 

 carbon, or at least most of it, must pass through these 

 reservoirs of intermediates they will very soon acquire 

 the same specific activity as the entering carbon di- 

 oxide. In contrast to this, those materials which are 

 not functioning as simple intermediates but rather are 

 functioning as storage reservoirs, or are very distant 

 from the immediate photosynthetic intermediates, will 

 not acquire radioactivity as rapidly, or if they do they 

 will not become saturated as rapidly as those which are 

 directly mvolved in the path of carbon assimilation. 

 The amount of radioactivity found in those compounds 

 which saturate in a relatively short time now provides 

 a relatively easy method of determining the size of the 

 functioning reservoirs of these compounds which are 

 directly engaged in the path of carbon assimilation. A 

 simple measurement of this amount compared to the 

 specific activity of the entering carbon dioxide will 

 provide a measure, in moles per unit volume of the 



85 



