Team:Oxford/Model/Supplementary Materials

Appendix 1: How Much Endolysin Needs to be Produced per L. reuteri cell for C. difficile Lysis?

To answer this question, let us first consider the experimentally derived value rate of B. subtilis lysis by CD27L endolysin, as noted in the Resultspage.

Average Lysis Rate /Cells minute-1
$$6.98 \times 10^{-7}$$

Additionally, from literature, we can approximate the population density of C. difficile and L. reuteri in the gut lumen:

Bacteria Approximate Population Density /CFU (g of lumenal content)-1 Reference
C. difficile $$10^8$$ Koenigsknecht, Mark J., et al. “Dynamics and Establishment of Clostridium Difficile Infection in the Murine Gastrointestinal Tract.” Infection and Immunity, vol. 83, no. 3, 2014, pp. 934–941., doi:10.1128/iai.02768-14.
L. reuteri $$10^6$$ Yu, Qing-Hua, et al. “Use of Green Fluorescent Protein to MonitorLactobacillusin the Gastro-Intestinal Tract of Chicken.” FEMS Microbiology Letters, vol. 275, no. 2, 2007, pp. 207–213., doi:10.1111/j.1574-6968.2007.00877.x.

Now consider the following ordinary differential equation describing C. difficile death due to endolysin:

$$\frac {dN}{dt} = - k \times E \times N \ where$$

$$ N = Number \ of \ C. \ difficile \ cells$$

$$ E = Endolysin \ concentration$$

$$k = Killing \ Rate \ of \ C. \ difficile \ due \ to \ endolysin$$

Upon solving this ODE, we obtain $$E = \frac {ln \frac {N_{initial}}{N_{final}}} {k \times (t_{final} - t_{initial})}$$

Let us also assume that the required amount of endolysin must be produced within 10 hours. This is a valid approximation as C. difficile infection generally develops within 24-48 hours.

Thus, the calculation for the total concentration of endolysin required to reduce the initial C. difficile population from 108 CFU at t=0 hrs to the final population of 101 CFU at t=10 hrs is as follows:

$$E = \frac {ln(\frac {10^1}{10^8})}{-6.98 \times 10^{-7} \times 10 \times 60} = 4645 \ M$$

Given that the carrying capacity of L. reuteri in the gut is approximately 106 CFU/(g of lumenal contents), then the required concentration of endolysin per L. reuteri cell = 0.0465 M/CFU

As each cell needs to produce 0.0465 M of endolysin over 10 hrs, the required rate of synthesis = 0.00465 M hr-1