THE "cardinal POINTS" AND THE "LIMITING FACTORS" 863 



nitudes as the concentration of a reactant (CO2) , the amount of the sensi- 

 tizer (chlorophyll), the rate of supply of light energy, and temperature. 



Maskell (1928-), in a paper from Blackman's laboratory, made one 

 more attempt to justify Blackman's law in its original form. He suggested 

 that the cause of the apparent deviations from this law lies in "mutual in- 

 teraction of factors." Here is one example of what he meant: In the 

 "carbon dioxide-limited state," the rate-determining carbon dioxide con- 

 centration must be that prevailing in the immediate neighborhood of the 

 chloroplasts. Because of the consumption of carbon dioxide by photo- 

 synthesis, this concentration is not necessarily identical with the outside 

 concentration (in the atmosphere or in the ambient solution) , but depends 

 on the rate of diffusion of carbon dioxide from the medium to the chloro- 

 plasts, and thus on the aperture of the stomata. Consequently, if illumina- 

 tion causes changes in this aperture, it may indirectly affect the rate of 

 photosynthesis even in the "carbon dioxide-limited" state, not because the 

 rate is "truly" sensitive to both light intensity, /, and carbon dioxide con- 

 centration, [CO2], at the same time, but because illumination influences the 

 effective value of the factor [CO2]! 



However, the insistence that a "true" luiiiting factor must exist under 

 all conditions is alien to reaction kinetics. The relation between the "law 

 of limiting factors" and the general concepts of reaction kinetics was first 

 clearly stated by Romell in 1926. He pointed out that Blackman's term 

 "slowest factor" is meaningless, and that one can only speak of a slowest 

 process in a sequence of processes. The rate of a simple homogeneous re- 

 action usually is a function of all the relevant factors, e. g., the concentra- 

 tions of all reactants, temperature and (in a photochemical process) light 

 intensity. "Limitation" effects of the type suggested by Blackman can oc- 

 cur only if the reaction, the over-all rate of which is being measured, con- 

 sists of several successive steps, with one step supplying the reactants for 

 the next one. If the supply process is slow, it becomes a "bottleneck," 

 and the velocity of the over-all reaction may become independent of all fac- 

 tors which do not affect this one "limiting" or "rate-determining" step. A 

 simple example is provided by many photochemical reactions, where the 

 supply of light-activated molecules is the "bottleneck," or limiting process. 

 Whenever "Blackman behavior" is observed in practice, it can be assumed 

 that one is dealing with a series of consecutive reactions that includes (at 

 least) one step of limited maximum efficiency. The rate of the over-all 

 process then cannot exceed the maximum rate of passage of the system 

 through this "bottleneck." 



The bottleneck stage of photosynthesis may be the supply uf light en- 

 ergy, or the supply of a reactant or the removal of a reaction product. We will 

 consider these three cases more closely in section 3 of this chapter. We will 



