29. DEOXYRIBONUCLEIC ACIDS AS MACROMOLECULES 21 



it will be better to begin with the first; after all, the nonreproducibility of 

 physical properties can be judged from a comparison of numerical data. 



a. Light Scattering at Small Angles 



We have seen [Eqs. (11) and (20)] that the values of M w and R 2 were, 

 respectively, calculated from the intercept of the c/K function of 9 with 

 the axis of ordinates, and from its initial slope. It is then necessary to ob- 

 tain from the experimental determination a set of values of c/K which really 

 can be extrapolated to 6 = 0. This, as we shall see, requires discussion. In 

 fact, in all experimental devices now in use, it is quite impossible to make 

 practically any measurement under a certain limiting value 6; of 6. In 

 general, sin (6^/2) is of the order of x /±. 



There exists, then, a practical limiting value hi of h, and a minimum 

 value h t L of the parameter hL which, as we have seen, is the true variable 

 in the c/K function. But the larger L is, the larger hiL is; and it may happen 

 that for very large particles this value is so large that we are far away from 

 the region where it is possible to represent the experimental curve P(6) — 

 that is P(hL) — by its limited development as it has been given in Eq. (20). 

 If this is so, it is to be feared that the extrapolation to 6 = of the experi- 

 mental curve P(6) leads to erroneous results. 



For instance, let us consider a rod-shaped particle. At the limit, when it 

 is very long, K/c depends only on M/L (Eq. 31) and not on M (or on L). 

 Then no extrapolation of the experimental curve, when it is practically 

 identical to its asymptote, can be used for the determination of M (or of 

 L). 



Unfortunately, this situation seems — to a certain extent — to apply to 

 the particles of DNA as illustrated in Fig. 9A, where we have represented 

 as a function of sin 6/2 (full points) the values of (K/c) c =o as they have 

 been measured in a solution of sample CV71 in 1 molar NaCl. 



It is obvious that the experimental points lie on the "tail" of the K/c 

 curve and that no safe extrapolation is possible, as shown by continuous 

 curves 1 to 5 which have been calculated from theoretical equations for 

 rods of different radii of gyration (or lengths) (Fig. 9A). 



However, in the representation of c/K as a function of sin (6/2) accord- 

 ing to Zimm's procedure, the extrapolation seems straightforward (Fig. 

 9B). Unfortunately, this is a mere appearance due to the use of sin (6/2) 

 and c/K as abscissas and ordinates. For large values of M — as in the case 

 of the DNA particles — a slight deviation in the extrapolation produces a 

 large error in the determination of l/M, and the use of the square of sin" 

 (6/2) contracting the scale of the abscissa in the region of the small values 

 of 6, gives still a much greater uncertainty to the extrapolation. 



It seems that we cannot avoid the conclusion that the values of M w , 

 which have been determined from light-scattering data, must be suspected 



