1252 THE TEMPERATURE FACTOR CHAP. 31 



In photosynthesis, the temperature coefficient dechnes with tempera- 

 ture, thus making an interpretation in terms of a series of consecutive 

 reactions possible at least formally. An example of this kind of hypothesis 

 is the above-mentioned suggestion of Franck, that the higher activation 

 energy, lia, which determines the temperature coefficient in the low tem- 

 perature range, is characteristic of enzymatic carbon dioxide fixation 

 (catalyst E^), w4iile the lower activation energy prevailing at room tem- 

 perature is characteristic of a finishing enzj^matic action. 



The analysis of Burton (1937) indicates that the gradual change in Ea 

 with temperature, as observed in photosynthesis, does not preclude such an 

 explanation. However, it must be pointed out that in the kinetics of 

 photosynthesis (as in the treatment of many biological processes) we usu- 

 ally deal with a steady state, rather than with the transformation of a 

 limited quantity of a substrate. Burton (1937) thought that the concept 

 of a master process cannot be applied to the steady state at all, since to 

 reach this state, the rates of all processes in the catenary series must have 

 adjusted themselves to that of the first irreversible step. This undoubtedly 

 is true; but it is also true that, under different conditions, different steps 

 in a catenary series can assume the role of the "first irreversible step." 

 For example, if an enzymatic reaction consists of two stages : 



(31.15) S+E;;=L=iSE — ^^^ P + S 



(the first being the reversible formation of the substrate-enzyme complex 

 SE, and the second its transformation into the reaction product P and the 

 free enzyme S), the over-all rate equation (£"0 = total amount of enzyme) is; 



(31.16) V = d[F]/dt = kMS]Eo/ik[ + k. + k^ [S]) 

 and this is reduced to: 



(31.17) V = d[P]/dt = A-2^0, if A"i[S] »A-; + k2 

 and to 



(31.18) V = ki'[S]Eo, if A-2»A-:; + AdS] 



The transition from the case (31.17), in which the over-all rate is deter- 

 mined by the "first irreversible reaction," SE -> P -|- E, to the case (31.18), 

 in which the reaction S -j- E -^ SE becomes "irreversible," can be brought 

 about by a change in external conditions, e. g., an increase in temperature. 

 Changes of this kind may well occur in photos3aithesis. 



Wohl (1937, 1940) thought that the high apparent activation energy of photosynthe- 

 sis at low tempei'atures may be attributed to liberation of a comj)lete glucose molecule 

 from a "reduction center" to which it was attached by six links. This process obviously 

 requires high energy, but can perhaps occur at comparatively low temperatures if it also 



