658 GROWTH OF PHAGE AND LYSIS 



that is already near a lysis from within will interfere with this process. It is also not 

 quite certain whether those parts of the surface of the bacterium that adsorb the phage 

 will lose their capacity of binding phage immediately upon lysis. In the strains used 

 previously a slow decrease of phage assay after lysis could be ascribed to the continued 

 "adsorption" of phage onto those scattered surface elements. No such decrease of 

 phage assay was ever observed with the new strain. But such observations refer only 

 to inactivation long after lysis and do not tell us whether the adsorbent is instantly 

 destroyed upon lysis. 



We have therefore calculated growth curves on the basis of two extreme assumptions. 



(a) The amount of adsorbent decreases linearly from its initial value to zero during 

 the 16 minutes in which the bacteria are lysed. 



(b) The amount of adsorbent stays constant at its initial value throughout the course 

 of lysis. 



Case (c) is described by the differential equation 



dP/dt = A - kBo (i-t/T) P 

 In case (b) we have 



dP/dt = A - kBaP 



In these equations the first term, A, represents the phage liberation by lysis during 

 the interval T, as determined in the one step growth curves, the second term is the 

 decrease of phage due to adsorption either on the unlysed bacteria only (case a) or on 

 the unlysed bacteria plus the adsorbent from the lysed bacteria (case b). 



These equations can be integrated explicitly. 



We obtain in case (a) 



P = M\/TTe2(r/-)'-i^-')'/-'[G(r/r) - G{[T - t]/r)] 

 with 



T = \/2T/kBo 

 and G(x) the Gaussian integral 



G(x) = 4- f e-'' dx 

 VT Jo 



In case (b), with constant adsorbent, the adsorption rate grows continuously with 

 the free phage concentration. In this case we have therefore no point of inflection 

 but a continuous asymptotic approach to the final titre 



kBo 



Since all required constants are known from independent experiments, the par- 

 ticular solutions applying to our case can be evaluated quantitatively. These have 

 been plotted in Fig. 6. The experimental values fall between the limits set by these 

 two cases. 



We have also plotted the curve obtained in an ordinary one step growth 

 curve, with B in excess (taken from Fig. 4). The difference between this 



72 



