THEORETICAL REMARKS 1251 



of S into P will approach that of the noncatalytic reaction; below Tc, it 

 will approach that of the catalytic reaction. Thus, the absolute value of 

 the slope of the log v = f{l/T) plot will change, with increasing tempera- 

 ture, from a smaller to a larger absolute value. As shown by Burton 

 (1936), among others, the transition will be gradual, rather than sudden, 

 i. e., the log v = J{l/T) plot (where v = v -\- V means the total reaction 

 velocity) will be curvilinear over a range of 20° or more, depending on the 

 difference between the two activation energies. 



Changes in the slope of the temperature curves also can be caused by a 

 sequence of consecutive reaction steps — a so-called "catenary reaction series" 

 {cj. chapter 26), which resembles a radioactive decay series (except that 

 the velocity of each step depends on temperature). This concept has 

 been much used in the explanation of the temperature dependence of 

 biological and biochemical processes. It stems from Blackman's idea of 

 "limiting factors," already discussed in chapter 26, and is thus historically 

 connected with the theory of photosynthesis. As described in that chap- 

 ter, Blackman first spoke vaguely of the "slowest factor" in a process deter- 

 mined by several external factors; this notion was later replaced (c/., for 

 example, Romell 1926, 1927) by the more precise concept of the slowest 

 ste'p in a sequence ("catenary series") of chemical reactions. This step 

 was often called the "master process" or "master reaction," not because of 

 its intrinsic importance for the chemical result of the transformation, but 

 for its "limiting" effect on the rate. Putter (1914) applied the master 

 reaction concept to the interpretation of temperature coefficients. Crozier, 

 in a series of papers (1924 and later), analyzed the temperature curves of 

 numerous biological processes by dividing them into straight sections 

 corresponding to different "master processes," connected by short curvilin- 

 ear segments at the transition temperatures, Tc. This procedure was criti- 

 cized, particularly by Burton (1936), who showed — for the case of a se- 

 quence of monomolecular reactions — ^that the transition regions can never 

 be as narrow as suggested by Crozier. 



In photosynthesis, the supply of carbon dioxide (by diffusion and car- 

 boxylation), and several enzymatic dark reactions of the primary photo- 

 chemical products are steps in a "catenary series." It can thus happen 

 that, starting with the state of "enzymatic hmitation" {i. e., saturation 

 with respect to both light and carbon dioxide), we may pass, by a mere in- 

 crease in temperature, into the state of "carbon dioxide limitation." In 

 contrast to the first-considered case of two competing reactions (in which 

 the reaction having the lower activation energy predominates at the lower 

 temperatures) the case of two consecutive reactions is characterized by the 

 fact that the one with the higher activation energy is rate-determining at 

 lower temperatures. 



