29. deoxyribonucleic acids as macromolecules 3 



1. Hydrodynamical Methods 



a. Monodispersed Solutions 



Let us first assume that we have to deal with a solution containing only 

 one type of macromolecule. It is possible then by proper operations to ob- 

 tain, among many other data, the following ones: the Brownian diffusion 

 constants of the macromolecules (^4 for translation, B for rotation); their 

 velocity v of sedimentation in an external field 7 (produced, for instance, 

 by ultracentrifugation); the intrinsic viscosity [77] of the solution, which is 

 the limiting value of (77 - ifo)/i7cC (where 770 = viscosity of the solvent, 

 77 = viscosity of the solution at the concentration c in grams per milliliter) 

 when c decreases to zero. 



These data are related to the macromolecular parameters in the follow- 

 ing way: 



1. The constants of diffusion obey the general laws 



A = kT/f (1) 



B = kT/C (2) 



where k is the Boltzmann constant, T the absolute temperature of the 

 solution, / and C the unitary coefficients of the viscous friction respectively 

 exerted by the solvent on the particle when it moves with a constant 

 velocity of translation or of rotation along a given axis. 



The coefficients / and C do not depend on the molecular weight M of the 

 particle, but they are obviously functions of its shape and dimensions. 



2. When the permanent state is attained, the velocity of sedimentation 

 in the field of inertia 7 is given by the equation 



v/y = M(l - F spPo )/3l/ (3) 



where V sp is the partial specific volume of the particle, p the density of the 

 solvent, and 91 the Avogadro number. The sedimentation constant S is 

 given by S = v/y. 



3. The relative increase of viscosity (or specific viscosity), tj 3P = (77 — 

 770) /t?o : is proportional at very large dilutions to the number, cOl/M of par- 

 ticles per unit of volume. It can be shown that T7 3p = (cVl/M) F or, accord- 

 ing to the definitions of [77], 



[7,] = aiF/ilf (4) 



In these equations F is a factor which depends only on the shape and di- 

 mensions of the macromolecule. 



