Adsorption of Bacteriophages to Homologous Bacteria 



phage particles n, replace Jdt by the decrease —dn of the number of free phages 

 which occurs in the time dt, and bear in mind that for the adsorption process there 

 is available not one but simultaneously h adsorbing bacteria (referring our entire 

 consideration to the unit of volume), then we can write 



— dn = ^TzDRhndt. 



If we compare this expression with the differential equation on which equation (1) 

 was based 



— dn = kbndt 

 then it follows that 



k = 4tDR or Z) = -A^ . 

 ■iirK 



the desired relation between adsorption velocity and diffusion constant of the 

 bacteriophage. Now it will be recalled that the values of the velocity constant 

 for adsorption to living and dead bacteria are not the same, since k for living 

 bacteria is 2.6 times greater than k for dead bacteria. The reduced adsorption 

 velocity for heat-killed bacteria evidently implies that a smaller fraction of the 

 contacts leads to adsorption, since the collision frequency is the same whether the 

 bacteria are living or dead. The assumption that every collision leads to fixation 

 can therefore be excluded a priori for dead bacteria, while it could still be valid 

 for living bacteria. In the latter case, the number of collisions is probably greater 

 than that estimated since the motion of the coli cell was neglected in the calcu- 

 lations. Nevertheless, the relatively slow motion of the bacteria is insufficient to 

 explain the entire difference between the adsorption velocity to dead and to living 

 bacteria, since the movement of the cells could hardly triple the collision fre- 

 quency. Therefore, our comparison of the D values for living and dead 

 bacteria will be based on our calculations of their respective k values. 



For the purpose of our calculations we shall equate R to the radius of that 

 sphere whose surface is equal to the surface of a cylmder of 1.2 /x length and 0.5 m 

 width, in which case R is equal to 4.3 X 10~^. The diffusion coefficient of the 

 phage at the experimental temperature of 37° thus is 



^ 4 X 4.3 X 10-^ ^-^ ^ ^^ 



if the time is reckoned in seconds, as in the calculation of k. If this value is 

 reduced to the unit of time generally used in diffusion experiments, i.e., the day, 

 it follows that D is equal to 0.0055. On the basis of this value of the diffusion 

 coefficient, one estimates from Einstein's formula^ a diameter of the bacterio- 



^This formula is 



CT 



'^ GirNnD 



where p is the particle radius, C the gas constant (8.32 X 10'' erg/degree), T the absolute 

 temperature, A^ Avogadro's number (60.7 X 1022), and n the viscosity. It thus follows that 



8.32 X lOT (273 + 37) 



'^ Qw X 60.7 X 1022 X 0.007 X 6.3 X IQ-* 

 or that the diameter is 102 m^. 



33 



= 5.1 X 106 cm 



