CHAPTER 



7 



Methods for Determining 

 Molecular Size and Shape 



INTRODUCTION 



1 . A survey 



One of the important aspects of biological studies is the determination 

 of the size, shape, and molecular weight of molecules associated with 

 various biological functions. Until the advent of the electron microscope, 

 these properties could be determined directly only if the molecules were 

 larger than, say, 0.4 micron, so that they could be studied in the light 

 microscope. As a result, indirect methods of determining particle size 

 and shape were developed. Even now that the electron microscope has 

 made it possible to obtain visual images of particles as small as 1 to 5 m/x, 

 there are still many instances in which the less direct methods are more 

 practical than electron microscopy. And there are still other instances in 

 which the indirect methods are the only ones which can give the desired 

 information. Furthermore, some of these indirect methods operate on a 

 fineness of structure still inaccessible to the electron microscope. For all 

 these reasons, therefore, it is advisable and worth while to present a sur- 

 vey of such biophysical methods. After presenting these surveys, several 

 of the methods will be presented in more detail. 



(a) Kinetic methods 



Diffusion. If a particle moves through a liquid, its movement will de- 

 pend on its size, shape, and mass. Therefore, by following the movement, 

 deductions may be made about these properties. If there is no net force 

 acting on the particle, it moves only by thermal agitation in a random 

 fashion. The bigger it is, the less mobile it will be. Therefore the average 

 displacement of such particles will be a measure of the size and shape. 

 If the shape chances to be spherical, it can be shown that the actual 

 diameter can be deduced. If the shape is other than spherical, the obser- 

 vation of the displacement must be coupled with some other measurement 

 to enable the investigator to deduce the actual size and shape. 



For a spherical particle, the relationship that is used is ^* - «^^ 



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