Quantitative models of in vitro bacteriophage-host dynamics and their application to phage therapy

Abstract

Phage therapy is the use of bacteriophages as antimicrobial agents for the control of pathogenic and other problem bacteria. It has previously been argued that successful application of phage therapy requires a good understanding of the non-linear kinetics of phage-bacteria interactions. Here we combine experimental and modelling approaches to make a detailed examination of such kinetics for the important food-borne pathogen Campylobacter jejuni and a suitable virulent phage in an in vitro system. Phage-insensitive populations of C. jejuni arise readily, and as far as we are aware this is the first phage therapy study to test, against in vitro data, models for phage-bacteria interactions incorporating phage-insensitive or resistant bacteria. We find that even an apparently simplistic model fits the data surprisingly well, and we confirm that the so-called inundation and proliferation thresholds are likely to be of considerable practical importance to phage therapy. We fit the model to time series data in order to estimate thresholds and rate constants directly. A comparison of the fit for each culture reveals density-dependent features of phage infectivity that are worthy of further investigation. Our results illustrate how insight from empirical studies can be greatly enhanced by the use of kinetic models: such combined studies of in vitro systems are likely to be an essential precursor to building a meaningful picture of the kinetic properties of in vivo phage therapy.

Figure 1. Phage decay in the culture medium in the absence of hosts.

The plot shows data from one of the three cultures in the phage decay experiment, with observed concentrations in log₁₀ PFU mL⁻¹ (points) and the fitted curve log₁₀ V(t) = log₁₀ V ₀−mt (line). The phage concentration declines linearly on log-linear axes, indicating approximately exponential decay with estimated rate 1.062×10⁻² h⁻¹.

Figure 2. Binding of phages to bacterial hosts and the subsequent release of phage at lysis of infected cells.

The plot shows data from one of the three cultures in the binding assay, with observed concentrations of free phages in log₁₀ PFU mL⁻¹ (points) and the fitted curve V(t) (line), derived from Equation 1. Lysis of infected hosts is well synchronised at approximately 1.3 hours, although this is exaggerated by the fitted curve. The phage concentration does not appear to increase, which is consistent with the low estimate for the burst size (approximately equal to 2 virions).

Figure 3. Data from interaction experiments together with fitted curves obtained by maximum likelihood estimation.

Concentrations of C. jejuni (circles; black) and phage (triangles; red) vary together in a way consistent with the threshold theory of phage-bacterial interactions. Fitted models in which parameters are either common to all (dashed) or allowed to vary between cultures (solid). Panels (A–H) correspond to cultures 1–8, respectively, with fitted parameters as given in Table 2 and Table 3.