Difference between revisions of "Team:ETH Zurich/Modeling/Reaction-diffusion"
m |
m |
||
| Line 12: | Line 12: | ||
<p> | <p> | ||
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 <i>E. coli</i> co-localization vs. dispersion. | 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 <i>E. coli</i> co-localization vs. dispersion. | ||
| + | </p> | ||
| + | <h3>Lactate diffusion</h3> | ||
| + | <p> | ||
| + | Under alkaline conditions, <i>E. coli</i> actively import lactate via a proton-motive symporter. Thus, a cross-membrane transport reaction had to be implemented. Since this is not possible directly in COMSOL, we had to model lactate in two states. Suppose our reference is the subspace of the interiors of the <i>E. coli</i>. We then defined the two states \(Lac_\text{int}\) and \(Lac_\text{ext}\), denoting intracellular and extracellular lactate, respectively. \(Lac_\text{ext}\) is produced by the target cell and can diffuse freely though the medium and all membranes. \(Lac_\text{int}\) is produced through first-order production dependent on the intracellular concentration of \(Lac_\text{ext}\) and only \(Lac_\text{int}\) can react with the other chemical species in the <i>E. coli</i>. | ||
</p> | </p> | ||
<h3>Assumptions</h3> | <h3>Assumptions</h3> | ||
| Line 23: | Line 27: | ||
<li>Bulk: reactions of the rest of the <i>E. coli</i> simulated in same space as medium</li> | <li>Bulk: reactions of the rest of the <i>E. coli</i> simulated in same space as medium</li> | ||
</ul> | </ul> | ||
| − | <li>Lactate represented as two states: inside and outside <i>E. coli</i>, denoted \(Lac_{int}\) and \(Lac_{ext}\), respectively</li> | + | <li>Lactate represented as two states: inside and outside <i>E. coli</i>, denoted \(Lac_\text{int}\) and \(Lac_\text{ext}\), respectively</li> |
<ul> | <ul> | ||
| − | <li>\(Lac_{int}\) can diffuse freely through medium and membranes, \(Lac_{ext}\) cannot</li> | + | <li>\(Lac_\text{int}\) can diffuse freely through medium and membranes, \(Lac_\text{ext}\) cannot</li> |
<li>Use to simulate different import and export rates of lactate into <i>E. coli</i></li> | <li>Use to simulate different import and export rates of lactate into <i>E. coli</i></li> | ||
</ul> | </ul> | ||
Revision as of 15:18, 20 August 2015
- Project
- Modeling
- Lab
- Human
Practices - Parts
- About Us
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.
Lactate diffusion
Under alkaline conditions, E. coli actively import lactate via a proton-motive symporter. Thus, a cross-membrane transport reaction had to be implemented. Since this is not possible directly in COMSOL, we had to model lactate in two states. Suppose our reference is the subspace of the interiors of the E. coli. We then defined the two states \(Lac_\text{int}\) and \(Lac_\text{ext}\), denoting intracellular and extracellular lactate, respectively. \(Lac_\text{ext}\) is produced by the target cell and can diffuse freely though the medium and all membranes. \(Lac_\text{int}\) is produced through first-order production dependent on the intracellular concentration of \(Lac_\text{ext}\) and only \(Lac_\text{int}\) can react with the other chemical species in the E. coli.
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 \(Lac_\text{int}\) and \(Lac_\text{ext}\), respectively
- \(Lac_\text{int}\) can diffuse freely through medium and membranes, \(Lac_\text{ext}\) cannot
- Use to simulate different import and export rates of lactate into E. coli
- Bulk E. coli grow logistically