VOL. 12 (1953) GROWTH AND PHAGE PRODUCTION OF B. megatherium IV 45 



DISCUSSION 



1. The growth curve. The curves shown in Fig. i consist, as usual, of three more or 

 less overlapping parts : the lag period during which the medium remains nearly constant, 

 but the cell composition changes; the log growth period when both medium and cells 

 remain nearly constant in composition; and the terminal lag period or stationary phase, 

 in which the composition of both medium and cells is changing. These various stages 

 of the growth cycle have been discussed in detail by Hinshelwood-'', and the present 

 discussion applies principally to the log growth or steady state phase. 



The decrease in rate towards the end of the reaction is due to depletion of the 

 medium, in this case*. The usual method of correcting for this effect is to write the 



equation as — = K^ x [Xg — .r) where x = x^ when — = o; i.e., when the reaction 

 d/ dt 



stops. This equation lits nearly 90% of the cell growth curve, whereas the simple log 



equation holds for about 50%. This is a surprisingly good fit, when it is recalled that 



almost all "simple" enzyme reactions show as great or greater discrepancies, when 



compared to simple kinetic theory. In the case of enzymes, also, it is the substrate term 



(corresponding to {x^ — x) in the present instance) which causes the difficulty**. 



2. Relation between free phage concentration and phage growth rate. The growth rate 

 of the phage for the first two hours is accurately described by the autocatalytic equation 



dP 



— = Kp • P, where P is the free phage formed during the experiment. It does not hold if 

 d^ 



the free phage is added from an outside source (Fig. 2). It follows that the free phage 



formed during the experiment must be proportional to the catalyst, but added free phage 



is not. 



Exactly the same peculiarity occurs during the autocatalytic formation of trypsin 



from trypsinogen (Kunitz^). In this reaction trypsin, and also an inert protein, are 



formed from trypsinogen and the time curves of the reactions are accurately predicted 



d/ ^, ^ . , dTr r- ^ ■ 1 r 



bv the equations — = Kjl trypsmogen and = -'^rr-' ^ trypsmogen, where 1 = con- 



dt dt 



centration of inert protein and Tr — concentration of trypsin. 



The inert protein, however, is not the catalyst (although it appears as such in the 



equation) since addition of more inert protein has no effect on the reaction rate just as 



the addition of phage has no effect on the reaction rate in the present example. The 



explanation is that, in the trypsinogen experiment, the concentration of inert protein 



is proportional at all times to the concentration of trypsin which is the true catalyst. 



The kinetics of the phage reaction may be accounted for by the following assumptions : 



a. The rate of formation of the phage is proportional to the concentration of intra- 



diV 

 cellular phage; i.e., — = KpN, where iV is the intracellular P/ml. (3) 



d^ 



* The decrease in P/ml at the end of the reaction is due to some cellular activity, possibly the 

 formation of an inhibitor (Burnet^^) since the decrease does not occur in the supernatant from the 

 culture, at this time. 



** In this form the reaction is bimolecular and the rate of the reaction depends on the product 

 of the concentrations of x and {x^ — x) . Diluting the system, therefore, will slow the rate in direct 

 proportion. As a result, if a cell is disintegrated in a relatively large volume of media, all the auto- 

 catalytic reactions must decrease enormously in rate. 



This effect may account, in part, for the difficulty of causing such reactions to take place in vitro 



References p. ^o. 



