THE KINETICS OF THE BACTERIUM-BACTERIOPHAGE REACTION
Authors: Krueger Albert P. , Northrop John H. 
Published: May 2004

The above data relating to the reaction between 16 hour cultures of S. aureus and antistaphylococcus bacteriophage in nutrient broth of pH 7.6 at 36°C. and with mechanical shaking to maintain a uniform B suspension, bring out the following points:
(a) B growth in P-B mixtures does not differ from growth in controls without P except in the case of a very high initial P/B ratio as noted below. There is no evidence that lytic destruction of B begins shortly after mixing P and B nor that B growth is stimulated by P, for the B growth curves in the presence of ordinary [P]'s and in controls are identical. Only at the sudden onset of the rapid lytic process does the B curve of a P-B mixture deviate from the control curve.
(b) B growth is an essential conditioning factor for P formation.
(c) Both B growth and P production exhibit short lags. During this time P diffuses into or becomes adsorbed to B so rapidly that by the end of the lag period only 10 to 30 per cent of the total P present is extracellular, the remainder being associated with the B.
(d) During the logarithmic B growth phase, P formation is also logarithmic but proceeds at a much faster rate. That is, d P/d t is proportional to a power of d B/d t. Consequently the statement that each time a B divides a certain amount of P is formed is not correct.
(e) As B growth enters the phase of positive acceleration equilibrium between the extracellular and intracellular P fractions becomes established and is maintained up to the onset of lysis, extracellular [P] representing a small constant percentage of total [P]. The distribution of P on a constant percentage basis suggests the manner in which a relatively simple chemical compound would be distributed and is not at all typical of the distribution one would expect if P were a complex organized parasite.
(f) When the value of log P/B = 2.1 lysis begins. Obviously, this limiting value for any initial [B] is reached sooner the higher the initial [P]. When log P/B at the time of mixing P and B is already 2.1 or greater, there is no growth of B and lysis soon occurs.
(g) While there is good evidence that lysis is brought about by the attainment of a particular [P] per B and not by a certain [P] per ml., it is not clear at this time which of the ratios intracellular P/B, extracellular P/B or total P/B is the major conditioning factor for B lysis.
(h) Experimentally the maximal [P]'s of lysates made by mixing a constant initial [B] with widely varying Po's fall within a relatively narrow range. This fact is explained by the large value of d log P/d t as compared to d log B/d t. That is, the loci of points at which log P = 2.1 + log B (maxima-lysis begins) on the curves of log P against t originating in various [Po]'s will lie at a nearly constant level above the abscissa. Because of this same relationship the maximal [P]'s of such a series will be in the reverse order of magnitude of the Po's, i.e., the larger the Po the smaller will be the maximal [P] attained during the reaction (cf. Fig, 16).
(i) The lytic destruction of B is logarithmic with time, in this respect being similar to most death rate processes. The value -d log B/d t for a particular initial [B] is constant for various initial values of [P]. There is good evidence that cells need not be growing in order to undergo lysis.
(j) During B lysis a considerable percentage of the total maximal P formed is destroyed, the chief loss probably occurring in the intracellular fraction. The major portion (70 to 90 per cent) of the final P present after the completion of bacteriophagy is set free during the brief phase of bacterial dissolution.
(k) When the entire process of bacteriophagy is completed the lysates are left with certain [P]'s determined by the foregone P-B reaction. The destruction of P during lysis is sufficiently regular to maintain the relationship established at the maximal [P]'s. Therefore the final [P]'s have the same points in common that were noted in "h" as applying to the maximal [P]'s. That is, they all are grouped within a narrow range of [P] values, those having been made with high Po's being of lower titre than those made with low initial [P]'s.
(1) There is a significant difference in the temperature coefficients of P and B formation. Further, the temperature coefficients of P and B destruction during lysis differ in almost the same ratio. Consequently, while all experimental evidence postulates B growth as an essential conditioning factor for P formation, the temperature coefficient data suggest that the two processes are basically separate reactions. A similar interpretation holds in the case of B dissolution and P inactivation.
(m) The major events in the complete process of "bacteriophagy" are mathematically predictable. The [B] at which lysis occurs under certain standard conditions for given values of Bo and Po may be calculated from the equation:
See PDF for Equation
Substitution of this value for log B in the equation:
See PDF for Equation
gives satisfactory agreement with observed values for t(lysis).
(n) The kinetic analysis of the P-B reaction predicts that the values of log Po plotted against t(lysis) for a constant Bo will give a straight line. This plot is employed in a method for the quantitative estimation of P described in an earlier paper on the basis of experimental observation alone. Its use is made more rational by the facts given above.