ENERGY MIGRATION AND THE PHOTOSYNTHETIC UNIT 1289 



estimate by postulating an "intrinsic" fluorescence yield of 10% (the same 

 in vivo as in vitro), and an actual yield of the order of 1%. 



According to Duysens, at an average concentration of 0.1 mole/1, 

 (which is a plausible value for the grana), the average number of energy 

 transfers, during an excitation period of 4 X 10 "^ sec, is about 750. If, 

 before the end of the transfer chain, excitation hits a "reaction center" in 

 which it is utihzed for a photochemical reaction, fluorescence is quenched. 

 Assuming that one such center exists per 200 chlorophyll molecules (in a 

 random, three-dimensional array), the chance of hitting it before the trans- 

 fer chain of 750 links is terminated can be estimated as 0.8; the fluores- 

 cence must then be reduced by 80%— from the "intrinsic" value of 10% 

 to an "actual" value of about 2%. Duysens considered this figure as close 

 to the actual true yield of fluorescence in vivo (about 1%, according to his 

 estimates; c/. chap. 37C, section 7), and the whole calculation as proving 

 that the concept of the photosynthetic unit, with energy exchange by the 

 "slow" resonance transfer mechanism, can be reconciled with the spectro- 

 scopic evidence, if the unit is reduced to about 200 chlorophyll molecules 

 (and the yield of fluorescence in vivo is assumed to be of the order of 1%). 

 About 750 transfers during 4 X 10-^ sec. means an exchange frequency 

 of 2 X 10^^ sec. -^ corresponding to a band shift by only 7 cm. -1 (2 X lO^^V 

 3 X 10^°), which is small compared to the actual red shift in vivo (about 

 200 cm.-i). The vibrational structure of the absorption band wifl be 

 unafi"ected by such slow transfer, and the band shift caused by it will be 

 practically negligible. 



A simplified procedure — similar to that repeatedly used above — would be to set 4 X 

 10-'" sec. as the available migration time (indicated by a 1% fluorescence yield), and to 

 conclude that 200 transfers during this time mean an exchange frequency of 5 X IQii 

 sec.-i, and a visiting time of 2 X IQ-'^ sec— just enough to preserve the coupling with 

 molecular vibrations with frequencies of the order of 10'' sec."'. 



The theoretical migration range is cut to Vs if t is only 1.3 X 10 -» sec. 



The case of energy transfer to a minor constituent of the pigment sys- 

 tem, mixed at random with the main pigment, and having an absorption 

 band in resonance with the fluorescence band of the latter, is clearly 

 analogous to the above-discussed case of energy transfer to a "reaction 

 center" in a photosynthetic unit. Duysens (1952) considered from this 

 point of view the— apparently highly effective— loss of excitation energy of 

 chlorophyll a in red algae by transfer to an unidentified minor pigment 

 (probably, chlorophyll d). To compete effectively with the "reduction 

 centers" as ultimate energy acceptors, the "chlorophyll d" molecules must 

 be present in a similar concentration (one for a few hundred chlorophyll 

 molecules, which is compatible with experimental evidence). This as- 

 sumes eriual probability of transfer to both acceptors; the capacity of 



