130 LIGHT AND LIFE 



analogue captures, in effect, all of the excitation energy from 6 

 tryptophan residues, or 80 per cent of the excitation from each of 

 the 7 that occur within a domain. 



What is the line of demarcation that prevents energy transfer be- 

 tween domains if the protein does not dissociate? Energy transfer of 

 the type being considered is a quantum effect arising from an elec- 

 trical dipole interaction. Forster has calculated the general expres- 

 sion for the rate constants of such transfers and has expressed the 

 results in terms of a distance, R,„ between excited donor and acceptor 

 at which the donor transfers the energy with the same probability 

 that it emits a quantum of light. 



^ 9 (In \OycrJ, 



where c is the velocity of light; /?, the refractive index of the medium 

 (in this case of the protein) ; 77, the lifetime of the excited state of 

 the donor; A'^', Avogadro's number divided by 1000; ,-„, the frequency 

 of the pure electronic transition; and /)/, the overlap of the emission 

 band of the donor and the absorption band of the acceptor. ]v may 

 be determined graphically as mentioned earlier, or analytically from 

 the integral 



Jv = / e.i(j')ez>(2j'o — v) div (3) 



where e.i (1) is the absorption coefficient of the acceptor as a function 

 of wave number, and en (2i'„-i') is the emission band of the donor set 

 up as the mirror image of the absorption band around j-o- The factor 

 x~ is a mutual orientation factor and has the value 



A- = (cos ^ — 3 cos a cos h)~ (4) 



where is the angle between the two dipolcs, and (i and b are the 

 angles each makes with the line connecting their centers. 



Rg, calculated from the above relations for tryptophan and DPNH 

 in free solution, is 25 A (M) . This is at best an approximation and 

 is qualitatively in accord with experiment. From its hydrodynamic 

 properties LDH may be treated as a rod of axial ratio 2/1 and dimen- 

 sions of the order of 92 X ^6 X 46 A. The R„ value for APNH and 

 tryptophan is a little larger than 25 A but the dimensions of a quar- 

 ter of the LDH molecule are large for the observed eighty per cent 

 transfer of excitation energy unless the average tryptophan residue 



