Figure 1.
Evidence of phenotypic resistance.
(Left) Short-term dynamics of E. coli O18:K1:H7 with phage K1-ind(1). This phage does not require the K1 capsule for infection, and although this phage grows well when introduced at low density to a bacterial culture, it and others like it perform poorly in preventing mortality of mice infected with the bacterium [24]–[27]. The assay here grew bacteria 1 hr at 37 in 10 mL LB with aeration, added phage at an MOI of 0.1 (time 0), then plated phage and bacteria from this culture at times shown by dots. Three replicates were performed, each designated with a different color. Cells from the final, 3 hr culture were plated and 5–10 colonies tested for phage sensitivity; most colonies in each replicate were sensitive to the phage [ratios of sensitive to total were (9+1)/10, (6+1)/7, and (5+2)/9, the second number in parentheses indicating intermediate sensitivity]. As the density of phage exceeded that of cells by 3–4 orders of magnitude at the time of plating, we often observed that sensitive colonies were contaminated by low densities of phage, so these numbers should be considered underestimates of sensitivity. (Right) Efficiency of plating (EOP) values of phage F287 on 27 independent colonies of Campylobacter jejuni obtained from a 24 hr culture inoculated from a single colony. The culture has already accumulated considerable variation in phage sensitivity in the absence of phage. EOP is the ratio of number of plaques obtained on the isolate divided by the number of plaques obtained on a standard sensitive strain. In both panels, the vertical axis is log
of the respective quantity.
Figure 2.
Bacteria are exposed to a high initial density of phage, and survivors (uninfected) measured before burst occurs; cells continue adsorbing to phage regardless of how many phage have already adsorbed. The vertical axis represents the natural log of surviving bacterial densities. (Left) Survival curves for homogeneous bacterial populations. The blue curve represents a 100-fold excess of phage to cells (MOI is multiplicity of infection, or the ratio of phage to cells), whereas the gray curve is for only a 10-fold excess; initial phage densities are /mL, adsorption rate constants are
mL/min. The blue and gray curves account for a decay in phage concentration as phage continue adsorbing to bacteria. The green curve is strictly linear for comparison to the blue curve. The plateau of the gray curve is due to nearly all phage having adsorbed after 20–30 min. Note that all three curves are adjusted to start at the same bacterial density for visual comparison of slopes, even though the blue curve should start at a 10-fold lower bacterial density than the gray curve. (Right) Survival curves for two homogenous bacterial populations differing in adsorption rate constants (orange:
mL/min; blue:
mL/min). The red curve is for a mix of 99% cells with a rate constant of
and 1% cells with rate constant
. Thus, despite the small fraction of cells with low adsorption rate in the mixed population, there is a profound effect on the survival curve after just a few minutes of exposure. Initial phage density is
/mL, and cells are at
/mL for each homogenous population and
/mL and
/mL for the two types in the mixed population.
Table 1.
Variables and parameters.
Figure 3.
Iterations of the ‘intrinsic’ model, as given by eqn(15).
The upper left panel represents a run with baseline parameter values (Table 1; the key gives adsorption rate constants), and only those properties differing from this baseline are noted in the other panels. The three other trials differ in one respect from the upper left: partially resistant bacteria are absent (upper right), the adsorption rate constant of the partially resistant bacteria is increased 4-fold (lower left), or the washout rate is halved (lower right). The red curve represents density of the partially resistant cell type, black is of the sensitive type, and light gray is of phage. In the absence of phage, density of the partially resistant bacteria would be 2% of the total, but partially resistant bacteria always comprise the majority when phage are present (the upper right panel is a control run in which partially resistant bacteria are absent, illustrating the typical oscillations). Initial densities were for
,
for
,
for P, 100 for
, and 0 for both types of infected cells. The vertical axis is log
of the respective density.
Figure 4.
Iterations of the ‘dynamic’ or ‘induced’ model of phenotypic resistance, as given by eqn(16).
Only one bacterial type is present. The maximum adsorption rate is in all three panels, but the minimum adsorption rate is
:
in the upper left and lower panels,
in the upper right panel. Collectively these figures illustrate that the magnitude of oscillations is moderately robust to differences in the minimum absorption rate but sensitive to the adsorption rate function (as determined by
). Red (light gray) curves are for bacteria (phage), the blue curve is the adsorption rate multiplied by
, which varies with
. Parameter values are as given in Table 1 except where indicated. Initial densities were
for
,
for P, 100 for
, 100 for
, and 0 for infected cells. The vertical axis is log
of the respective density.