Cocktail, a Computer Program for Modelling Bacteriophage Infection Kinetics

Abstract

Cocktail is an easy-to-use computer program for mathematical modelling of bacteriophage (phage) infection kinetics in a chemostat. The infection of bacteria by phages results in complicated dynamic processes as both have the ability to multiply and change during the course of an infection. There is a need for a simple way to visualise these processes, not least due to the increased interest in phage therapy. Cocktail is completely self-contained and runs on a Windows 64-bit operating system. By changing the publicly available source code, the program can be developed in the directions that users see fit. Cocktail's models consist of coupled differential equations that describe the infection of a bacterium in a vessel by one or two (interfering) phages. In the models, the bacterial population can be controlled by sixteen parameters, for example, through different growth rates, phage resistance, metabolically inactive cells or biofilm formation. The phages can be controlled by eight parameters each, such as different adsorption rates or latency periods. As the models in Cocktail describe the infection kinetics of phages in vitro, the program is primarily intended to generate hypotheses, but the results can however be indicative in the application of phage therapy.

Keywords: bacteriophage; computer program; infection kinetics; mathematical modelling; phage therapy.

Figure 1

The Cocktail user interface.

Figure 2

Example output graphs from the Cocktail program: (A) Escherichia coli bacteria infected with phage T4 in a chemostat where both the bacteria and the phage titre fluctuate under certain conditions. The parameter settings were as in [26] with the exception of the resource density being set to 1.0 instead of 0.5 mg/L (µg/mL) in the chemostat, and the time step size set to 1 min instead of 3 min. The run was for the first 200 h of the original chemostat experiment (before development of bacterial phage resistance). Complete parameter settings can be found in the file Bohannan_Lenski_1997_Fig 3B.ctl in the Supplementary Materials. (B) Oscillations of bacterial and phage can theoretically exist even at higher titres as shown by Lenski [19]. Bacteria in a titre of 10⁶ cell forming units is infected with virulent phages with a burst size of 100 and in a titre of 10⁸. The stability of the system depends on a low concentration of nutrients, 25 µg/mL. The parameter settings can be found in the Supplementary Materials file Lenski_1988_Fig_2a.ctl. (C) As the concentration of nutrients increases four times, the titres of both bacteria and phages shift. This results in increasingly large oscillations where bacterial titres are reduced to a few cells every cycle, but they never become extinct. The settings are from the file Lenski_1988_Fig_2b.ctl. in the Supplementary Materials. (D) An example of bacteria at high titres simultaneously infected by two phages with different infection characteristics. Bacteria that mutate and become resistant to either one of the phages are eventually lost and non-resistant bacteria slowly become extinct but replaced by bacteria resistant to both phages. See text for more details. Settings from the file Fig_2D.ctl in the Supplementary Materials.