Bacteriophage therapy and the mutant selection window

Abstract

We use kinetic models to investigate how to design antimicrobial phage therapies to minimize emergence of resistant bacteria. We do this by modifying the "mutant selection window" hypothesis in a way that accounts for the ongoing self-replication of the phage. We show that components of combination phage therapies need to be appropriately matched if treatment is to avoid the emergence of resistant bacteria. Matching of components is more easily achieved when phage dosages are high enough that ongoing phage replication is not needed for the clearance of the bacteria. Theoretical predictions such as ours need to be tested experimentally if applications of phage therapy are to avoid the problems of widespread resistance that have beset chemical antibiotics.

FIG. 1.

A schematic of important thresholds in the PK/PD theory of antibiotic and phage therapies. (A) “Dosing to cure.” Under the MSW hypothesis, the pharmacodynamic properties of antibiotics imply that antibiotic-resistant mutants are selectively enriched when the antibiotic concentration (solid line) is in the MSW between the MIC and the MPC. With a dose-to-cure strategy, the MSW is open as long as the antibiotic is effective (I). (B) “Closing the window.” With higher doses, the antibiotic concentration passes through the MSW quickly (II) and remains above the MPC (III) long enough to ensure that susceptible cells are suppressed, before passing through the MSW once more as it declines (IV). This approach reduces the probability that single-step resistant mutants will acquire additional resistance-conferring mutations. (C) “Passive” phage therapy. At sufficiently high doses, the phage concentration (solid line) rapidly exceeds the IT, and so the treatment will have a therapeutic effect without requiring the phages to replicate (V). The IT for a phage is analogous to the MIC for a chemical antibiotic, and in passive therapy the phage is treated much like a chemical antibiotic. It is unclear whether there must be an analogue of the MPC for phage therapies, but if not then the MSW would be open whenever the phage concentration is above the IT. (D) “Active” phage therapy. Phages can actively proliferate only when the bacterial concentration (dashed line) is at or becomes greater than the PT. Then, even at low doses, a phage (solid line) can grow (VI), eventually exceeding the IT to become effective at suppressing susceptible bacteria (VII).

FIG. 2.

Simulations of active phage therapy of an initially susceptible bacterial strain with a combination of two infective phage strains used in the active mode. (A) A “faster” phage (adsorption rate of 3.0 × 10⁻⁹ [black dashed line]) together with a substantially “slower” phage (adsorption rate of 0.6 × 10⁻⁹ [gray dashed line]). Both phages replicate within the susceptible bacteria (solid line). The faster phage also infects mutants resistant to the slower phage (gray dotted and dashed line), while the slower phage infects mutants resistant to the faster phage (black dotted and dashed line). (B) Better-matched faster (adsorption rate of 1.2 × 10⁻⁹ [black dashed line]) and slower (adsorption rate of 0.87 × 10⁻⁹ [gray dashed line]) phages.

FIG. 3.

Probability (Pr) of multiple resistance arising by a fixed time after phage therapy with a cocktail of two phage strains. (A) Both phages are introduced at the same low concentration so that treatment is principally active, but the adsorption rates are varied. The adsorption rates at the marked ratio (ratio = 5 [dashed line]) are the same as for Fig. 2A and are used again in plots B and C. (B) A cocktail of one “faster” and one “slower” phage is introduced at a fixed, high dose (20 times the average IT of the two strains at time 14 h) so that treatment is passive but the proportion of each strain in the cocktail is varied. Active replication of phage is ignored by assuming that the burst sizes are zero. (C) Alternatively, the same phages are introduced at identical high doses (10 times the average IT) but at different times (14 h and between 11 h and 17 h).

FIG. 4.

Schematic of unoptimized versus optimized combination therapies where at least one component is active phage therapy. (A) When a combination of two active-mode components has not been optimized, the faster phage (solid line) dominates the slower phage (dashed line) until the concentration of faster-phage-resistant mutants grows large enough to support the slower phage. The MSW is open, encouraging the growth of resistant mutants, whenever the concentration of one but not both components is above the IT. (B) Similarly, when an antibiotic or passive phage (gray line) is introduced too early, growth of the active phage (solid line) will be delayed, again leaving the MSW open. (C and D) In either of the above situations, the timing and dosage of components may be adjusted to ensure that the MSW is closed during most of the time in which the treatment has a therapeutic effect.