# What did our model achieve?

We achieved two main goals;

We designed a mathematical model for phage-bacteria interaction. This work expands upon existing models to encompass variation in lysis timing of phages.

We applied our mathematical model to our chemostat system and determined ideal parameters for our experimental project. We then utilized these parameters when implementing our physical system (see results below).

All our code is available on our Wiki. Se functions.cpp, classes.cpp, header.h and main.cpp.

# Modelling phages

Phages are infectious viruses that kill certain bacteria. When a phage finds a bacterium to infect, it attaches and inserts itself into the bacterium, and hijacks the bacterium’s cellular machinery to create lots of copies of itself. After a short period, the new phage particles will burst out of the now dead bacterium (lysis), ready to infect new bacteria. We used existing mathematical models of this interaction, and expanded upon them.

# Modelling chemostats

Our motivation for modelling phage-bacteria interactions is to provide our wet lab with appropriate parameters for accomplishing our goal. That is, using our chemostat system to evolve a phage capable of killing a select strain of bacteria. We described our system mathematically and wrote a C++ program to numerically solve the system of integro-differential equations. Matlab was used for plotting. Using this, we determined parameters to optimally evolve a capable phage and test out project.

# Applied results:

We used our mathematical model and numerical simulations to maximize the efficiency of our wetlab system. We determined the optimal exchange rate of a chemostat to maximize various desired qualities, and utilized our results in implementing our physical project.

# Constants list

The constants we used for modelling were chosen by a mix of reviewing previous research, empirical observations, and considerations of what our system was physically capable of. Some of the constants are not tested as thoroughly as we would have liked due to time limitations. A more thorough exploration of how these constants are interconnected and influence our simulations would be an interesting topic of further research.

# References

1. Cairns, Timms, Jansen, Connerton, Payne; “Quantitative Models of In Vitro Bacteriophage–Host Dynamics and Their Application to Phage Therapy”, PLOS pathogens, published Jan. 2, 2009. http://journals.plos.org/plospathogens/article?id=10.1371/journal.ppat.1000253, accessed 01/11/17

2. Schule, Lipe; “Relationship between substrate concentration, growth rate, and respiration rate of Escherichia coli in continuous culture”, Archives of microbiology, March 1964, Issue 1, pp 1-20.

3. Shao, Wang; “Bacteriophage Adsorption Rate and Optimal Lysis Time”, Genetics, 2008 Sep; 180(1): 471–482.