FRANOK-HERZFELD THEORY 929 



Franck and Herzfeld assumed equilibrium (27.55a) to be established practically 

 instantaneously, whereas reaction (27.55b) was assumed to have a finite velocity, and 

 thus to be capable of becoming a "bottleneck" of photosynthesis. This occurs when 

 either the substrate concentration [A-C02], or the enzyme concentration [Ea] is low, 

 or, more generally, when the product of the two concentrations is small. According to 

 (27.55), the concentration of the "loose" complex is: 



(27.56) [A-COs] = K [AJICO^] 



(For the sake of consistency — cf. equation 27.5- we use as equilibrium constant the in- 

 verse of Franck and Herzfcld's K). The rate of the bottleneck reaction (27.55b) is: 



(27.57) {dlAC02]/dl) = ^•a[A•C02][E] = k^K[A][C02][EA] 



We assume— as we did in all our derivations so far— that no kinetic factors other than 

 those connected with the supply of carbon dioxide affect the rate of photosynthesis. 

 Under these conditions, the equations of the carbon dioxide curves can be derived by 

 calculating the stationary concentrations [A] and [Ea], inserting them into (27.57) and 

 then calculating the stationary concentration [ ACO2] by equalizing the rate of production 

 of [ACO2] given by equation (27.57) and the rate of reduction of this product by light. 



In the Franck-Herzfeld theory, all carrier molecules, A, may be considered, for 

 kinetic purposes, as attached to a molecule of the sensitizer (chlorophyll), so that the 

 substrate molecules bound to A can undergo direct photochemical change; putting it 

 more cautiously, only those A molecules are taken into consideration in kinetic equations 

 that are attached to chlorophyll. Their total number can be designated as Ao. Simi- 

 larly, all chlorophyll molecules are supposed to carry acceptor molecules, A; putting it 

 more cautiously, only the absorption of light by those chlorophyll molecules that are as- 

 sociated with A is taken into consideration. We designate the total number of such 

 molecules as Chlo. This number probably can be reduced by certain inhibitors, such as 

 urethan or other narcotics, that displace the acceptor A from chlorophyll. (The same 

 applies, according to Franck, to "self-narcotization" by the unfinished product of 

 photosynthesis to which reference was made in chapter 24.) 



In Franck's picture, the rate constant k* in equation (27.6) can be written as k*I: 



(27.58) P = -nid[AC02]/dt) = A;*7[AC0.2] 



Here, A;*7[AC02] is the rate of absorption of light by the acceptor A in combination 

 with CO2, k* being essentially an average absorption coefficient of the specimen under 

 investigation. The factor n is equal to 1 in the Franck-Herzfeld mechanism; but k*I 

 is, in the steady state, not more than one eighth of the total rate of absorption. 



If one assumes, as Franck and Herzfeld did, that this absorption coefficient is the 

 same whether chlorophyll is associated wath ACO2 or with any of the seven reaction 

 intermediates {cf. scheme 7.VA), then in the steady state the amounts of [ACO2] and 

 of seven intermediates must all be the same. This means that: 



(27.59) Ao = ( = Chlo) = [A] + [A -002] + 8 [ACO2] 



where Ao is the total available quantity of the acceptor A bound to chlorophyll. 

 Equalizing (27.57) and (27.58), we obtain: 



(27.60) IACO2] = (k,K[\][EA][C02])/k*r 



The stationary value of [Ea] can be calculated by equalizing the rates of reactions 

 27.55b) and (27.55c); this gives: 



(27.61) [Ea] = A;:E°/(A:.[A-COo] + k:) 



