29. DEOXYRIBONUCLEIC ACIDS AS MACROMOLECULES 5 



second order). However, we cannot in that case make a classification of 

 the molecules as a function of M only, since the value of p can change when 

 V is given. 



3. One may understand that even then it is extremely difficult to go 

 through a complete analysis of the mixture and we shall only consider here 

 the case of a polydispersity of the first order. That is to say that we assume 

 that only one parameter is sufficient to characterize each macromolecule. 

 This would happen, for instance, for ellipsoids of rotation of the same den- 

 sity and elongation. We can then classify the molecular species by the 

 molecular weight M (or by V). 



This polydispersity of the first order in molecular weight is of great in- 

 terest, since it is realized in the very important class of linear macromole- 

 cules (though, very unfortunately, probably not in the case of DNA) and 

 accordingly we shall very rapidly recall some principles. 



The number of macromolecules per milliliter, the weights of which lie 

 between M and M + dM, is 



dn = f(M)dM (6) 



f(M) is called the number distribution function of M. The concentration 

 of these molecules is 



dc = g(M)dM (7) 



g{M) is the weight distribution function of M. Obviously 



g(M) = Mf(M) (8) 



In the case of polydispersed solutions these distribution functions are 

 new unknown quantities which are to be determined. 



Quite generally if one parameter X is sufficient to describe the macro- 

 molecule, the quantities A, B, S, and F are dependent on X and we shall 

 have to consider the distribution functions / or g in number or in weight 

 corresponding to each. 



1. It is generally possible to determine experimentally the function g(S) 

 by means of ultracentrifugation, 2 and with some difficulties the function 

 g(A ) by means of the study of free Brownian diffusion. 



If the relationship between M and S (or A) is known, one or the other 

 experiment gives directly g(M). In this respect, an interesting case may 

 arise. If one observes that the experimental curves g(S) and g(A) can 

 be brought to coincide through a simple change in the scale of the abscissa 

 S or A , it means that S and A for each molecule are uniformly proportional. 



2 J. W. Williams, K. E. van Holde, R. L. Baldwin, and H. Fujita, Chem. Revs. 58, 



716 (1958). 

 3 M. Daune, Thesis, Strasbourg (1958). 



