Group 10: Modeling the resilience of the immune response against bacterial infections

This project contains spatial model for a bacteria-immunecell system based on a 2D stochastic automaton with an accompanying

By Anton Dolganov, Peter Hajo Groen, Bálint Szarvas and Sacha Gijsbers

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Table of contents

• Model Overview
  • Bacterial Immune Model
  • Visualizer
• Results and data
• Analytical Tools
  • tool_paralelRun.py
  • tool_fit_ODE.py
  • Tool_ODE_batch.py
  • Tool_plot_ODE_batch.py

Model overview

The bacterial immune model consists of two classes found under model.classes, being the model itself, as well as a built in visualizer.

Bacterial Immune model

A simplified 2D spatial model of the local immune system in a sample of tissue with constant introduction of new pathogens. Immune cells attempt to kill bacteria and multiply if succesful, while bacteria attempt to multiply into their direct Moore neighborhood. If there are no bacterial cells in the vicinity of an immune cell and the density of immune cells in one place is bigger than a set amount, the immune cell dies.

Initialization parameters

Parameter	Explaination
length (int)	Length of the lattice.
width (int)	Width of the lattice.
pImmuneKill (float)	Chance an immune cell kills a bacteria cell.
pbacteriaMult (float)	Chance a bacteria cell multiplies every timestep.
pbacteriaSpawn (float)	Chance a normal cell becomes bacteriaous per timestep.

Quick Implementation Guide

If one wants to implement the model into their own project as is, the following steps should be taken.

1. Initialize a new BacteriaImmuneModel object with the above parameters.
2. (optional) Seed the model with an initial population of bacterial cells for the desired amound of cells nCells using BacteriaImmuneModel.seedBacteria(nCells: int)
3. Seed the model with an initial population of immune cells for the desired amount of cells nCells using BacteriaImmuneModel.seedImmune(nCells: int)
4. Call BacteriaImmuneModel.timestep() to update the lattice. The current populations of immunecells and bacterial cells can be obtained using BacteriaImmuneModel.get_nImmuneCells() and BacteriaImmuneModel.get_nbacteriaCells() respectively

for more information, see /model/classes/bacterialImmuneModel.py

Visualizer

A real time visualizer class for the bacterial immune model that shows that displays the 2D lattice of the model, as well as current values for the cell occupancies.

Initialize object, then call Visualizer.run()

Initialization parameters

Parameter	Explaination
model(BacteriaImmuneModel)	The model to be visualized

Example

When the visualizer is ran, two plots are shown, with on the left the lattice visualization and on the right the cell occupancies. The lattice visualization shows immune cells as yellow and bacterial cells as blue, with the blue background representing the other cells of the tissue (See below).

Results and data

You can find the results of the research under the folder results and other plots and outputs under data

Analytical tools

In order to obtain results, some tool programs were developed, which are explained below.

tool_paralelRun.py

Parallel running program for Bacteria immune model.

Usage

To plot an earlier result, run the program like python tools_paralelRun.py p [FILEPATH] [PLOTNAME: optional]

• FILEPATH - Path of the exported CSV file.
• PLOTNAME - Title for the plotted image

To run an experiment with default settings, run the program like python tools_paralelRun.py

To run a new experiment, run the program like python tools_paralelRun.py [RUNS: int] [ITERATIONS: int] [PROCESSES: int] [KWARGS] or as python paralelRun.py [KWARGS]

• RUNS - The amount of runs to take average of
• ITERATIONS - The maximum amount of iterations for a single run
• PROCESSES - The amount of parallel processes to run
• KWARGS - Keyword arguments (see below)

Keyword arguments

Relevant arguments are presented in a list format, where every list item is associated with the same parameter.

case insensitive

["filename", "fn", "name", "n"]=(int)

• Filename for the resultFile

["runs", "r"]=(int)

• The amount of runs to take average of.

["maxiter", "iter", "iterations", "i"]=(int)

• The maximum amount of iterations for a single run.

["processes", "proc", "p"]=(int)

• The amount of parallel processes to run.

["boxl", "boxlen", "bl", "boxlenght"]=(int)

• The length of the modelled square box.

["immunefraction", "fractionimmune","immunefrac", "if", "frac", "f"]=(float)

• The fraction of cells to be occupied by immune cells in the initial state of the model.

["noplot"]=(bool)

• disable plotting of results afterwards

case sensitive model parameters:

pImmuneKill=(float/list[float])

• The chance an immune cell kills a bacteria cell it occupies the same cell as.

pBacteriaMultiply=(float/list[float])

• The chance a bacteria cell multiplies.

pBacteriaSpawn=(float/list[float])

• The chance a bacteria cell spawns on the grid.

A list structure can also be entered, which makes the program loop through all possible combinations of these parameters.

Example data plot

tool_fit_ODE.py

Fits input guess parameters to data from spatial ODE and prints fitted parameters to console.

Partial Differential Equations

$${dI\over dt}= \alpha BI - \beta I^2$$ $${dB\over dt}= \gamma B^2 - \alpha BI + Spawn$$

• $I =$ Immune Cell population
• $B =$ Bacteria Cell population
• $\alpha=$ immunecell killRate
• $\beta =$ immunecell overcrowding
• $\gamma =$ bacterial growthrate
• $Spawn =$ Bacterial spawnrate

Usage

python ./tool_fit_ODE [filename] [xGuess] [plotGuess]

• filename : Filename or filepath to resultfile relative from active user folder.
• xGuess : Guess parameters for ODE fit, formatted like stock python list of four elements between quotes. Example: "[0.1, 0.1, 0.1, 0.1]"
• plotGuess: Bool like string of whether the input guess should be plotted to the input file data without fitting. Example: True, False

Example Plot

tool_ODE_batch.py

Has variable pBacteriaMult, and fixed ImmuneKill and pBacteriaSpawn parameters Places files in ./data/Batch_ODE-fitted_runs/ Creates files for individual runs and a file containing all ODE parameters as function of pBacteriaMult

Does not have input parameters and has to be edited from source.

tool_plot_ODE_batch.py

Quick plotting program for tool_ODE_batch.py data files, for variable multiplication probability only.

Does not have input parameters and has to be edited from source.

Example Plot