Difference between revisions of "Team:Nottingham/Model"

Introduction

Aim: To model the interaction between bacteria and phage to gain insight into how we can best engineer and deliver phage to be an effective treatment against Clostridium difficile infection.

The diagram above shows the two possible life cycles of phages. Following infection, phages following the lytic life cycle will hijack the host cell machinery to produce multiple copies of the phage proteins. These proteins are then assembled into multiple phage progeny which burst out of the host cell and go on to infect other bacterial cells. In the lysogenic life cycle, phages can integrate their genome into the host cell chromosome upon infection, where they can remain dormant for long periods of time as prophages. When conditions are favourable, usually due to host cell stress, prophage induction can occur. This is where prophages can excise from the host cell chromosome and enter the lytic life cycle leading to the production of progeny phage particles.

Click on the different sections to learn more about our modelling efforts and remember to refer back to the above diagram to help understand how our ODE models reflect the phage life cycles.

Summary

The main analytical result of our modelling work was the derivation of a condition that determines whether effective temperate phage therapy treatment can occur when prophage induction is allowed:

Our estimated parameters satisfy this inequality so provided our antisense RNA and dCas9 contructs are effective at suppressing toxin production in lysogens this should lead to a stable population of non-toxigenic C. difficile and SBRC phage which would help to prevent reinfection. We also noticed with our induction model that initial phage dose is less crucial to effective treatment. This is particularly important since we gathered from Dr Cath Rees that high phage titre, are difficult to produce and would lead to a costly therapy. Therefore, the ability of our phage to be effective at a low initial dose should lead to a more affordable treatment. From these results we decided to allow SBRC phage to undergo prophage induction at its natural rate instead of preventing induction as we had initially planned.

Lytic phage model

Phage therapy that has been used to date has focused on using lytic phage to kill pathogenic bacteria. In this section we based our model of lytic phage-bacteria interaction on the delayed differential equations proposed by Campbell before adapting these equations in order to model a temperate phage.

Click on the link below to see results.

Temperate phage models

Why consider a temperate phage?

One of the biggest issues surrounding Clostridium difficile infection, is that of reinfection. We originally planned on using a temperate phage, modified so that it could not enter the lytic cycle, with the hope that a stable population of non-toxigenic lysogens (see lab pages for how we developed non-toxigenic C. difficile) would be formed that could outcompete toxigenic C.difficile strains [10]. Hence, we wanted to model the interaction between our engineered temperate phage and bacteria to see if a steady state could be reached and what conditions would be necessary for this to occur. We also wanted to see the time difference in effective treatment between a lytic and temperate phage to ensure that we did not sacrifice speed of treatment in order to prevent reinfection. We later decided to see what would happen if we allowed for phage to undergo induction.

Click on the links below to see our results for both models.

Comparison of models

In this section we compare lytic and temperate phage models in order to direct the phage modification strategy employed in the laboratory. We wanted to predict whether it would be beneficial to produce a strictly temperate phage or whether the natural lytic cycle of the phage should be left untouched. The models were compared in terms of the proportion of lysogens to toxigenic bacteria, the speed of action and the potential for phage to remain in the system to prevent reinfection.

Click on the link below to see our model comparison.

Methodology

In this section we focus on finding and classifying equilibrium points for two types of system, one with the ability to induce a lytic life cycle and one which models a strictly temperate phage. This information is important as it allows us to identify the conditions that must be satisfied by a phage in order to lead to a long term population of lysogens and free phage

Click on the link below to see expanded methodology.

Parameters

The utility of a model is strongly dependent upon the parameters used. Some of the parameters used were acquired from relevant literature while others were determined experimentally in the laboratory. One key parameter was that of decay rate which an analysis of phage literature revealed to be strongly positively correlated with burst size. This correlation allowed us to estimate the decay rate from a burst size assay we conduct on our phage phiSBRC.

Click on the link below for details on the parameters used in these models.

Achievements

This section summarises the achievements of the modelling efforts, allowing us to infer some key information which we can integrate into the design of the overall project, such as indicating the strategy which would lead to the most effective and cost efficient means of dosing patients with phage.

Click on the link below to see all key achievements.

References

All scientific literature used in the generation of the model is accredited below.

Click on the link below to see the full list of references.