Team:ETH Zurich/Modeling/Reaction-diffusion

"What I cannot create I do not understand."
- Richard Feynmann

Reaction-diffusion Models

Introduction

While single-cell models are useful for correctly implementing and debugging chemical reaction models, they are not sufficient to fully understand the real-life functionality of our system. Since an essential part of our system is increasing the perceived concentrations of lactate and AHL through co-localization, it is necessary to model the concentrations the chemical species though a reaction-diffusion system.

3D model

Four cases

To test whether our system acts as an AND gate on our two inputs (higher lactate production and co-localization signals), we combinatorially tested all possible combinations high vs. low lactate production and E. coli co-localization vs. dispersion.

Assumptions

  • Target mammalian cell located in the center of the well
  • Constant rate of lactate production
  • E. coli bound to target cell abstracted into homogeneous layer around target cell
  • Two different forms of unbound E. coli
    • Discrete: single cell of E. coli suspended in the medium
    • Bulk: reactions of the rest of the E. coli simulated in same space as medium
  • Lactate represented as two states: inside and outside E. coli, denoted \(Lac_{int}\) and \(Lac_{ext}\), respectively
    • \(Lac_{int}\) can diffuse freely through medium and membranes, \(Lac_{ext}\) cannot
    • Use to simulate different import and export rates of lactate into E. coli
  • Bulk E. coli grow logistically

Results

1D and 2D models