216 A. GAREN AND L. M. KOZLOFF 



F. Rate of Attachment 



It was first proposed by Schlesinger (1932) that the phage attachment 

 reaction could be treated theoretically in terms of diffusion equations pre- 

 viously developed to describe coagulation of colloidal particles. Schlesinger 

 defined a velocity constant k by the equations: 



k 



P + C-> PC 



velocity of attachment = — ; — = ; = h{P){C) 



at at 



where P is unattachtd phage, C is the cell, and PC is attached phage. 



and obtained accurate measurements of k under various experimental condi- 

 tions. These values were compared to the maximum theoretical value of k 

 to be expected if every contact between a phage and a cell, arising from 

 random diffusion of the phage particles, resulted in attachment. The theo- 

 retical value was estimated by assuming that a cell provides a stationary 

 surface which acts as a perfect phage absorber; since every phage particle 

 reaching the cell surface attaches, the phage concentration of unattached 

 phage at the cell surface wiU be zero (Delbriick, 1940a). A concentration 

 gradient of phage particles wall then arise in the near vicinity of the cell 

 surface, which wiU bring about a net flow (by diffusion) of particles towards 

 the cell. The velocity of flow will be determined by the concentration 

 gradient and the diffusion constant of the phage. The maximum value of k, 

 as calculated theoretically in this manner, is close to the maximum experi- 

 mental values obtained with several phages; this result has led to the con- 

 clusion that essentially every "collision" (i.e., surface contact) between a 

 phage and a cell leads to attachment (Puck et al., 1951; Stent and WoUman, 

 1952; Tohnach, 1957). 



This conclusion must be reconciled with the requirement that a collision 

 between a phage particle and a cell can result in attachment only if the phage 

 tail is brought into juxtaposition with an attachment site on the cell. This 

 requirement should limit the chance that a random collision will be effective, 

 since collisions should not invariably occur at an attachment site or in a 

 tail-first orientation. These steric considerations make it unlikely that the 

 attachment reaction can achieve perfect efficiency, but it is not clear to what 

 extent they limit the maximum attainable efficiency, since there also are 

 compensating factors. For one thing, there are at least several hundred 

 separate sites on an individual cell for binding a particular phage (Watson, 

 1950; Garen, 1954), and for another, probably a significant fraction of collision 

 orientations enable the tail fibers of the phage to come into contact with the 

 cell surface, especially since the fibers appear to be unwound to a large 

 extent (Fig. 7). 



