82 METHODS FOR DETERMINING MOLECULAR SIZE AND SHAPE 



which we shall not discuss here, we obtain curves like those in the right- 

 hand column. The smaller the molecules involved, the faster the curves 

 fall to the even distribution situation in the bottom sketch. The move- 

 ment of the molecules can be computed from the actual distribution of 

 molecular velocities, which is known from physicochemical theory. 



The rate of spreading of the boundary can be related to the so-called 

 diffusion coefficient, D, by the approximate formula 



x 2 = 4Dt, 



where x is the distance between the % and ^4 concentration points at 

 time t seconds after starting. 



This formula is a very handy one for biophysicists. For example, if 

 we introduce a few enzyme molecules into a solution and these are taken 

 up by a 10-micron cell, can these enzyme molecules possibly reach the 

 substrates on which they act, simply by diffusing? In the table below we 

 give typical values of D for spherical molecules of various sizes. 



Molecular weight Diffusion coefficient, D 



A typical enzyme might have a molecular weight of 100,000, and we 

 see that its diffusion coefficient D is therefore about 5 X 10~ 7 cm 2 /sec. 

 Putting this in the formula, we obtain the value of t, the time taken to 

 diffuse just once across the cell: 



, x 2 (1(T 3 ) 2 , „ r 



Thus, this enzyme molecule will diffuse in a waterlike medium so fast 

 that it could travel back and forth across this large cell two times per 

 second, and therefore could well be able to catalyze reactions anywhere 

 in the cell where the substrate happened to be. 



To return to the problem of estimating molecular weights, it is neces- 

 sary to have a connection between the diffusion coefficient and the mass 

 of the molecule. Advanced physical theory gives us the result that 



hTrjr 



