46 J. H. NORTHROP VOL. 12 (1953) 



b. A constant, small fraction of the intracellular P is liberated per unit of time, 



dP FdN 



i.e., — = — or P = FN, where F = fraction of total phage per ml, liberated per unit 



dt dt 



of time. Also N = MB, where M = phage per cell and B = cells/ml. Substituting the 



^ ^^ P ^ dA^ Pd . , dP ,, ^ 

 value of A^ = - and -— = -— m (3) -— = KpP. 

 F dt Fdt dt 



li F or N is known, then the other variable can be calculated. For instance, Lwoff 

 ANj) GuTMAN^ (c/. also Clark AND CowLEs) have found that lysis of B. megatherium 

 in a hanging drop preparation liberates about 100 phage particles per cell. During the 

 log phase the ratio of free phage to cells, P/B, is about 2/1 (Fig. 4). If each cell contains 

 100 phage particles, F = P/MB = 0.02. In the early stages of the reaction where the 

 cells are in the resting state, the ratio of P/B is 1/500. Since F = 0.02 and M = P/FB, 

 M = 0.1, i.e., only one cell in 10 liberates an active phage particle. 



It is immaterial, as far as the derivation of the equation is concerned, whether or 

 not the cells lyse at the time of liberation of the phage. If the fraction of cells liberating 

 phage is constant, the cell concentration-time curve will still be logarithmic. 



It may be noted that, since P = FN, variation in P could be ascribed mathe- 

 matically, to variation in F (or to variation in F x A^), the fraction of phage appearing 

 as extracellular, rather than to variation in A'' alone. Experimentally, however, this 

 appears to be unlikely, as it would be necessary to assume that F increases logarith- 

 mically with time, in the early part of the reaction, and also that even at the end of the 

 reaction it must remain small compared to i, otherwise all the phage would be outside 

 at the end of the experiment and the cell curve would no longer be logarithmic. 



The assumption that F is constant is also indicated by the fact that the lysis time 



of infected megatherium cells is nearly independent of the growth rate or phage content 



of the cells Northrop^. 



A log P 

 If log P is plotted against t, the slope is ^^ — and Kp = 2.3 x slope = growth 



rate. In the first part of the reaction the P has a growth rate of 4.6 (Fig. i), while the 

 cells (or protein) have a growth rate of i.i. The percentage increase in phage is therefore 

 4 times that of the cells. So far this result is the same as that in the phage-sensitive cell 

 system (Northrop) ^ and the relative rates are also about the same in both systems. 

 This relation cannot exist for long, as the cell would soon be all phage and would be 

 destroyed. In the sensitive system, this is what happens and the reaction is stopped by 

 the lysis of the cells (c/. Fig. 5), but in the lysogenic system, the growth constant of the 

 phage suddenly drops to that of the cells, so that after this jwint is reached, the ratio 

 P/B remains constant. 



If the phage particle is formed from a precursor* in the bacterial cell, as suggested 

 by Bordet^^ {cf. also Northrop^^; Krueger and Mundell^^; Krueger, Mecraken 

 ANDSCRiBNERi'*),the result may be predicted, at least qualitatively. Suppose that, in the 



* The assumption that viruses may be derived from precursors has been criticized on the grounds 

 that the nature of the active virus would then be determined by the nature of the host (Topley 

 AND Wilson^'). This is not a necessary corollary of the assumption of a precursor, but it is a probable 

 one. It must be remembered in this connection that there are at present no really accurate means of 

 identifying bacterial viruses so that small changes may be overlooked. On the other hand, recent work 

 of Krueger and Ralston^^, Rountree^" and Bertani and Weigle^^ has shown that such changes 

 in the virus after a change of hosts actually occur. 



References p. 50. 



