Code: Cost calculation of an altruistic act for the plasmids-in-bacteria system through probabilistic simulations

Bachelor of science (physics) thesis - Universidad de los Andes. Bogotá, Colombia

Author: María Alejandra Ramírez

Supervisor: Prof. Dr. Juan Manuel Pedraza

Text available at: https://repositorio.uniandes.edu.co/bitstream/handle/1992/49156/u833901.pdf?sequence=1

• Code and results to calculate the cost of an altruistic act for the system of plasmids in bacteria

The code for this simulation consists on 4 main parts.

1. Stabilization

On the folder Stabilization, the script code_stable.py can be found. This script runs the simulation for the evolution of a single plasmid type, in order to obtain its steady-state. The results are recorded on CSV files and are graphed, when indicated, in folders like h3.

The script fit_KyN.py can be also found in this folder. This script graphs the steady-states in function of the repression coefficient (K) for each Hill coefficient (h) considered. Afterwards, it performs a fit to obtain the relationship between the steady-state and K. These results are located in the folder StableGraphs. Similarly, the relationship between the parameters of the previous fit and the Hill coefficient was obtained via fit_KyN.py and its results can be also found in the folder StableGraphs.

In particular, the steady-state is the main quantity that determines the initial amount of plasmids in each competition between plasmid types.

2. Total

The quantity NT used to calculate the cost of an altruistic act is obtained with the script TotalN.py. The main goal of this script is to run one-on-one competitions of different plasmid types to record the general total population size (NT). The corresponding results are recorded in the folder Total via CSV files and graphs, such graphs are organized in different folders according to the Hill coefficient of the plasmid types.

3. Simulation

The whole simulation of the one-one-competitions of different plasmid types is performed by the script simu.py. In this case, the results of the simulation are relative population growth graphs from which the cost of an altruistic act can be graphically calculated. The demonstration of the mathematical expression used to find the cost is explained on the document related to this bachelor's thesis.

In general, the graphical results of the population growth graphs are located in the folder SimulationGraphs and are organized according to the Hill coefficient of the plasmid types.

Furthermore, in the script simu.py the calculation of the cost is performed. The results of the cost can be found in the folder Results. That folder contains the following results: filled contour plots representing the cost related to each one-on-one competition, txt files with the cost results, filled contour plots illustrating the variance associated with the linear fits performed on the previous graphs and txt files with such information.

4. Fit

The fit performed on the cost results was done through the script fit_contour.py. Therefore, this script takes the results from the previous subsection and carries out the corresponding fit to find the relationship between the cost, KA and KB. The results of the fits are located in the folder Results/Fit. Particularly, the visual representations of the fits are saved as PNG files and the results of the fit parameters are recorded in a CSV files, along with the variance related to those fits (in separate files).

Finally, through the script fit_contour.py the relationship between the fit parameters previously found and the Hill coefficient was determined. Such relation is documented in the file Cte_Fit.png.

Note: the files Log_#.txt are used to record information about the progress of the simulations.

• Overall, to run a competition between plasmid types the scripts should be run in the following order to calculate the cost:

1. code_stable.py
2. TotalN.py
3. simu.py

This order should be followed, because code_stable.py establishes the initial amount of plasmids in the competitions by calculating the steady-states. Subsequently, TotalN.py computes NT, a quantity that is necessary to determine the cost via the calculation perfomed in simu.py.

It should be noted that the competitions take place between pairs of plasmid types, which means that this fact should be taken into account while running the code.

The scripts fit_KyN.py and fit_contour.py are not needed to run a competition, since they are mainly used to establish mathematical relationships among variables.

For further information about this research, please contact:

Author: María Alejandra Ramírez

Supervisor: Juan Manuel Pedraza - Professor at Universidad de los Andes