470 



S. S. Brody and M. Brody 



properties which accompany greening, result solely from changes in the size 

 of the aggregate, and that the geometry of the aggregate (R and a) remains 

 constant. 



Equation 1 will be re-written in terms of emission, since the data which 

 are available for the aggregate in vivo are for emission rather than absorp- 

 tion. To accomplish this we take the wave number difference, 6, between 

 the absorption and emission maxima of the monomer and set it equal to the 

 wave number difference bet^ween the absorption and emission maxima of the 

 aggregate, i. e. 



V -V =6 = v -V 



A F A2 F, N 



In this expression subscripts A and F denote absorption and fluorescence, 

 respectively, and primes and double primes denote monomer and aggregate, 

 respectively. Assuming there is symmetrical splitting of the monomer 

 absorption band upon aggregation, it can be shown that Eq. 1 may be re- 

 written in terms of emission maxima, in the following way: 



^" rr ^T =~'ip - 2 {N-l)m^ (1 + cos^a)/NhcR^ Eq. (2) 



F, N F 



A pictorial representation of our notation is shown below. 



8 



( ^ 



111 II 



8 



The long wavelength emission maximum- which is observed at low temper- 

 atures with Euglena exposed to light for only a few hours,- is assumed to arise 

 from the smallest possible aggregate - namely, a dimer {N=2). Using this 

 value for'vp j^, the term m^ (l + cos2a)/hcR-' in Eq. 2 can be eliminated to 

 yield our working equation: 



G' ^ -~"^ ^) = 2(~'^ -~"^ ^)(l -1/N) = A(l-1/N) Eq. (3) 



in which 'v ^ and'x? „ ^ are constants. 

 F F, 2 



Since we are dealing with a distribution of molecular aggregates, it should 

 be recognized that the emission maximum Cv r- ivt) determined experiment- 

 ally is an average value, which can be represented by the following express- 

 tion: — 00 ,, =0 , 



~FN = ^ ~FN^^^/^ [N]=~ -A{l-[1/N]], 

 ' N = 2 ' N = 2 



where [N ] is the concentration of aggregates of S ize N , and A is as defined 

 in Eq. 3. An effective size for the aggregate l/[l/N] (slightly greater than 

 the true average size N) can be calculated with the aid of Eq. 3. For con- 

 venience, let 1/[1/N] = lO . To determine A the following data obtained 



