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