In silico infection
Not every experiment can be conducted in the wet lab. Especially in times of Covid-19 where our options were limited, we tried to work as resourcefully as possible and performed in silico considerations to support our project. Read all about it below!
The modeling part supported the request of the wet lab to produce as many phages as possible. These are needed for the characterization experiments and to produce phage DNA for recombination. The phages are produced in bacteria batch cultures. To follow the question, a simple model of bacteria-phage dynamics was done.
A simplified model was developed to determine the ideal time to introduce the phages to the bacterial culture in order to obtain the highest phage concentration possible.
Therefore, first the bacterial growth has to be described. One assumption that needs to be made is the doubling time of the bacteria. Under ideal conditions E. coli splits every 20 minutes. Since the phages are added at a stage where still plenty of nutrients are left, we assume a doubling time of 20 min. for our liquid culture.1
With a starting concentration of 107 cells/ml and an assumed doubling time of 20 min., we end up with 4 * 109 cells/ml after around 6.5 hours. This result corresponds to the measurements that were taken by our wet lab team. In reality, however, the growth would eventually approach zero because the medium is depleted, and the cell density gets too high at some point. Therefore, the carrying capacity measured in the lab is implemented into the model to allow for a maximum cell density of 4 * 109 cells/ml. The resulting growth rate (normalized to 1) looks like this:
Now, to introduce the phages to our model several additional assumptions have to be made:
1. COMPLEX: Superinfections: Both lytic and lysogenic bacteria can be superinfected by many phages at once.
1.1 SIMPLE: Each bacterium, regardless of the phenotype, can be infected with only one phage at a time. No re-infecting!
2. COMPLEX: While bacteria are infected they still might split, possibly resulting in two infected bacteria or some other configuration.
2.1 SIMPLE: Bacteria can't split while infected.
3. COMPLEX: Burst sizes, the number of new phages produced per infection, vary depending on how fast the bacteria dies.
3.1 SIMPLE: The burst size is constant for each lysis, about 100.
4. COMPLEX: Latency times depend on a few state variables within a bacterium.
4.1 SIMPLE: The latency time is constant for every phage-bacterial interaction.
5. COMPLEX: The induction rate of lysogenic bacteria is variable.
5.1 SIMPLE: The induction rate of lysogenic bacteria is constant.
6. COMPLEX: After bursting, new phages die or float around without ever infecting bacteria.
6.1 SIMPLE: After some time, all phages find a new victim; no floating!
Also, some parameters need to be set:
Our model is based on a simple predator-prey relation between bacteria and phages. Numerical approximation of the phage concentrations with different introduction times yields the following result:
According to our model, the highest phage concentration can be achieved when introducing the phages to the bacterial culture 40 – 50 minutes after inoculation.
The source code of the model was written in Julia and can be accessed here.
If your browser does not support embedded PDFs you can open the PDF seperately: Phage Therapy: a light weight modelling
1Liang ST, Ehrenberg M, Dennis P, Bremer H. Decay of rplN and lacZ mRNA in Escherichia coli. J Mol Biol. 1999 May 14 288(4):521-38. p.524
2Shao Y, Wang IN. Effect of late promoter activity on bacteriophage lambda fitness. Genetics. 2009 Apr181(4):1467-75 p.1471
3You L, Suthers PF, Yin J. Effects of Escherichia coli physiology on growth of phage T7 in vivo and in silico. J Bacteriol. 2002;184(7):1888-1894
4Suttle, C. A. and Chen, F. Mechanisms and rates of decay of marine viruses in seawater. Applied and Environmental Microbiology. 1992 58(11), pp. 3721–3729
