ENERGY TRANSFER BETWEEN DIFFERENT PIGMENT MOLECULES 1305 



Both 430 and G80 mju quanta — absorbed mainly by chlorophyll a — 

 are less effective in exciting chlorophyll a fluorescence in Porphyridium 

 than 560 m/x quanta, absorbed mainly by phycoerythrin (or 630 m/z 

 quanta, absorbed to a considerable extent by phycocyanin), the ratio being 

 similar to that found in Oscillatoria (about 0.4). Experiments on another 

 red alga, Porphyra lacineata, suggested that the energy absorbed by "non- 

 fluorescent" and (according to Haxo and Blinks, cf. chapter 30, fig. 30.11, 

 and to Duysens 1952) photosynthetically inactive fraction of chlorophyll a, 

 are transferred to — and produce the fluorescence of — a minor pigment 

 component, probably, chlorophyll d (identified in red algae by Manning 

 and Strain, cf. p. 720). The fluorescence peak of this pigment Hes at 725 

 m/x. 



Duysens (1952) made an attempt to interpret all these experimental 

 results cjuantitatively by applying Forster's theory of resonance transfer to 

 mixed solutions of several pigments. He derived from Forster's equations 

 the efficiency, E, of excitation energy transfer, E, from a molecule of type 

 "/' to any of the molecules of type "A;" in such a mixture, as function of con- 

 centration [/c], expressed in terms of a "critical" concentration, [k]^. The 

 latter is the concentration at which the theoretical transfer probability for 

 a single pair (7, k) would be 0.5, if all molecules were arranged in a simple 

 cubic lattice — in other words, the lattice constant were equal to the "criti- 

 cal distance," da, defined by Forster's equation (32.6). Following is Duy- 

 sen's table: 



[k]/{k\f>: 0.05 O.il 0.27 1.00 >1 



E: 0.3 0.5 0.75 0.96* 1 - 0.036 [^j" 



To apply the above table to the calculation of energy transfer in plant 

 cells, Duysens had to make rough estimates of the concentrations of the dif- 

 ferent pigments, their fluorescence yields (which determine the life-times 

 available for transfer) and the "overlap integrals" between the absorption 

 and fluorescence spectra of the several pigment pairs. 



For example, to estimate the probability of energy transfer from chloro- 

 phyll h to chlorophyll a, in vivo, Duysens assumed <p = 0.01 (i. e., 1% yield 

 of fluorescence for chlorophyll b in vivo in the absence of a, cf. chapter 37C, 

 section 7), and calculated [k](, = 0.046 mole/1. Since the actual concentra- 

 tion of chlorophyll a in the grana is >0.046 mole/1., the transfer efficiency 

 from 6 to a should be, according to the table, >96%; the reverse transfer, 

 from a to h, calculated in the same way, turns out (as mentioned on p. 

 1300) to be 300 times less probable, and thus experimentally undetectable. 



* If the transfer probability to a single neighbor is 0.5, that to any neighbor in a 

 cubic lattice is 0.96. 



