Population dynamics of a salmonella lytic phage and its host : implications of the host bacterial growth rate in modelling

The prevalence and impact of bacteriophages in the ecology of bacterial communities coupled with their ability to control pathogens turn essential to understand and predict the dynamics between phage and bacteria populations. To achieve this knowledge it is essential to develop mathematical models able to explain and simulate the population dynamics of phage and bacteria. We have developed an unstructured mathematical model using delay-differential equations to predict the interactions between a broad-host-range Salmonella phage and its pathogenic host. The model takes into consideration the main biological parameters that rule phage-bacteria interactions likewise the adsorption rate, latent period, burst size, bacterial growth rate, and substrate uptake rate, among others. The experimental validation of the model was performed with data from phage-interaction studies in a 5 L bioreactor. The key and innovative aspect of the model was the introduction of variations in the latent period and adsorption rate values that are considered as constants in previous developed models. By modelling the latent period as a normal distribution of values and the adsorption rate as a function of the bacterial growth rate it was possible to accurately predict the behaviour of the phage-bacteria population. The model was shown to predict simulated data with a good agreement with the experimental observations and explains how a lytic phage and its host bacteria are able to coexist.Financial support was received through the Strategic Project PEst-OE/EQB/LA0023/2013 from the FCT-Fundacao para a Ciencia e Tecnologia (http://www.fct.pt) and the projects "BioHealth - Biotechnology and Bioengineering approaches to improve health quality'', Ref. NORTE-07-0124 FEDER-000027, co-funded by the Programa Operacional Regional do Norte (ON.2 - O Novo Norte), QREN, FEDER and "Consolidating Research Expertise and Resources on Cellular and Molecular Biotechnology at CEB/IBB'', Ref. FCOMP-01-0124-FEDER-027462. Silvio B. Santos was supported by the grant SFRH/BPD/75311/2010 and Carla Carvalho was supported by the grant SFRH/BPD/79365/2011 both from the FCT-Fundacao para a Ciencia e Tecnologia (http://www.fct.pt). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript