Team:Dundee/Modelling2

How effective is endolysin at killing C. difficile?

Different Endolysin concentrations can have different effects on the survival of C.difficile cells. It is important therefore to understand how much endolysin is required to control C.difficile population and how can this concentration be obtained from our newly engineered E.coli. In this section we present mathematical models and quantative analyses that quantify the effect of Endolysin on a C.difficile population, Models were constructed using data that have been collected over summer, but we have also exploited data from the literature.

First, we used data from “Molecular Characterization of a Clostridium difficile Bacteriophage and Its Cloned Biologically Active Endolysin” where the size of the C.difficile population is measured (optical density, OD) as a function of the Endolysin concentration, E(μg/ml) and the time, t(mins) during which C.difficile is exposed to Endolysin.

Table 1. Level of C.diff at different time points when cultured with three different masses of endolysin

Table 1. presents the data extracted from Molecular Characterization of a Clostridium difficile Bacteriophage and Its Cloned Biologically Active Endolysin. The data shows the response of C.diff to endolysin is delayed by approximately 10 minutes. Similar data in which the C.diff was flash-frozen before the endolysin was added showed no lag phase. It is likely that freezing weakens bacteria defences and, in the later case, the action of endolysin is seen immediately after application. In the following we choose to focus on this stage where lysis is effective.

Can we formulate a relationship between endolysin and the amount of C.diff it kills?

To find a formula that relates the two variables (E and cell number), we have used curve fitting functions (Curve Fitting Tool, MATLAB). We found that exponential functions best describe the data, see Figures 3-5.