Fig 1.
This model is an extension of our original model presented in [28], with the inclusion of antibiotic effects. Each bacteria strain (BE resistant to erythromycin, BT resistant to tetracycline, or BET resistant to both) can replicate (purple). The lytic phage (PL) multiply by infecting a bacterium and bursting it to release new phage (gold). This process can create transducing phage (PE or PT) carrying a resistance gene (ermB or tetK respectively) taken from the infected bacterium (dashed, green). These transducing phage can then generate new double-resistant progeny (BET) by infecting the bacteria strain carrying the other resistance gene (solid, green). The antibiotics, erythromycin (CE) and tetracycline (CT), decrease the growth rate of each bacteria strain to varying extents, depending on their concentration and the resistance level of the strain (dotted, red and orange). Phage and antibiotics can decay at a fixed rate (dotted, grey and black).
Table 1.
Parameters with no units are dimensionless. All estimates were obtained by fitting the model to in vitro data, except those marked with a * which are assumed.
Fig 2.
Growth curves of NE201KT7 (tetracycline-resistant, left), NE327 (erythromycin-resistant, middle) and DRPET1 (double-resistant, right), exposed to varying concentrations of erythromycin (top) or tetracycline (bottom). Solid lines show in vitro data, with error bars indicating mean +/- standard deviation, from 3 replicates. Dashed lines show model output after fitting. Values indicate the percentage of model points that fall within the range of the corresponding in vitro data point +/- standard deviation. cfu: colony-forming units. Note that cfu per mL are shown on a log-scale.
Fig 3.
a) Model-predicted dynamics with two single-resistant strains starting at carrying capacity (109 colony-forming units (cfu)/mL), in the presence of no antibiotics (1st column), erythromycin only (2nd column), tetracycline only (3rd column), or both erythromycin and tetracycline (4th column), combined with either no phage (top row), phage incapable of transduction (middle row), or phage capable of generalised transduction (bottom row). The starting strains are either erythromycin-resistant (BE) or tetracycline-resistant (BT). Antibiotics and/or phage (PL) are present at the start of the simulation, at concentrations of 1 mg/L (4 x MIC for susceptible strains) and 109 plaque-forming units (pfu)/mL respectively. Double-resistant bacteria (BET) can be initially generated by generalised transduction only, and then by replication of existing BET. Dashed line indicates the detection threshold of 1 cfu or pfu/mL. b) Change in bacteria (single-resistant to erythromycin, single-resistant to tetracycline, or double-resistant) and phage numbers depending on the antibiotic exposure, in the presence of phage capable of generalised transduction. Dashed line indicates the detection threshold of 1 cfu or pfu/mL.
Fig 4.
a) Model-predicted dynamics with one single-resistant strains starting at carrying capacity (109 colony-forming units (cfu)/mL) and the second in minority (106 cfu/mL), in the presence of no antibiotics (1st column), erythromycin only (2nd column), tetracycline only (3rd column), or both erythromycin and tetracycline (4th column), combined with either no phage (top row), phage incapable of transduction (middle row), or phage capable of generalised transduction (bottom row). Erythromycin-resistant bacteria (BE) are initially present at a concentration of 109 cfu/mL, and tetracycline-resistant bacteria (BT) at 106 cfu/mL. Antibiotics and/or phage (PL) are present at the start of the simulation, at concentrations of 1 mg/L (4 x MIC for susceptible strains) and 109 plaque-forming units (pfu)/mL respectively. Double-resistant bacteria (BET) can initially be generated by generalised transduction only, and then by replication of existing BET. Dashed line indicates the detection threshold of 1 cfu or pfu/mL. b) Change in bacteria (single-resistant to erythromycin, single-resistant to tetracycline, or double-resistant) and phage numbers depending on the antibiotic exposure, in the presence of phage capable of generalised transduction. Dashed line indicates the detection threshold of 1 cfu or pfu/mL.
Fig 5.
a-b) Varying timing (x-axis) and dose of antibiotic and phage (y-axis) affects total bacterial count after 48h (top), maximum concentration of double-resistant bacteria (BET) (middle), and time when the concentration of BET is greater than 1 colony-forming unit (cfu) per mL (bottom). a) Adding 108 plaque-forming units (pfu) per mL of phage, and between 0.2 and 2.2 mg/L of both erythromycin and tetracycline. b) Adding 1 mg/L of both erythromycin and tetracycline, and between 105 and 1010 pfu/mL of phage. The x-axis indicates the time when antibiotics were added, relative to when phage were added. For example, the value “4” indicates that phage were present at the start of the simulation, and antibiotics were introduced 4h later. The segments with black borders correspond to the dynamics shown in c). c) Phage and bacteria dynamics over 48h for 4 conditions taken from panel b. In all 4 conditions, indicated by the black rectangles, phage are initially present at a concentration of 108 pfu/mL, while erythromycin and tetracycline are both introduced at concentrations of 1 mg/L after either 0h, 3h, 5h or 15h, stated on the plots, with the timing indicated by the vertical dashed lines. Horizontal dotted lines indicate bacteria remaining after 48h (corresponding to the top row of a-b) and maximum double-resistant bacteria (BET) concentration (middle row of a-b). Solid line indicates the detection threshold of 1 cfu or pfu/mL. The concentrations of single-resistant bacteria (BE, blue, and BT, green) overlap and cannot be distinguished.
Fig 6.
Sensitivity of phage-bacteria dynamics to changes in model parameters.
Effect of varying the transduction probability between 10−10 and 10−6 when a) antibiotics and phage are present at the start of the simulation, b) phage are present at the start, antibiotics are introduced 10h later, and c) antibiotics are present at the start, phage are added 10h later. Transduction probability is defined as the probability that a transducing phage carrying an AMR gene is released instead of a lytic phage during bacterial burst. The dashed lines for single-resistant bacteria overlap and cannot be distinguished. Vertical dashed lines indicate timing of addition of antibiotics or phage. cfu/mL: colony-forming units per mL. d) Partial rank correlation between model parameters, and remaining bacteria after 48h (pink) or maximum double-resistant bacteria (BET) concentration (blue). Information on the parameter ranges investigated can be found in Table 1. β: adsorption rate, P50: phage concentration at half saturation, δmax: burst size, τ: latent period, α: transduction probability, γP: phage decay, γE: erythromycin decay, γT: tetracycline decay, μmaxE: BE growth rate, μmaxT: BT growth rate, μmaxET: BET growth rate.