Team:Paris Liliane Bettencourt/Project/Population counter/model
From 2010.igem.org
(Difference between revisions)
Line 61: | Line 61: | ||
The reaction between LuxR and AHL gives a chemical equilibrium determined by the constant k<sub>reac</sub>:<br /> | The reaction between LuxR and AHL gives a chemical equilibrium determined by the constant k<sub>reac</sub>:<br /> | ||
<img src="https://static.igem.org/mediawiki/2010/b/bc/Eq_luxR2.jpg" alt="Eq_luxR2" title="Stability equation of LuxR" align="center" height="35"/><br /> | <img src="https://static.igem.org/mediawiki/2010/b/bc/Eq_luxR2.jpg" alt="Eq_luxR2" title="Stability equation of LuxR" align="center" height="35"/><br /> | ||
+ | |||
+ | so at the equilibrium:<br /> | ||
+ | <img src="https://static.igem.org/mediawiki/2010/7/78/Eq_luxR3.jpg" alt="Eq_luxR3" title="concentration equilibrium of LuxR" align="center" height="30"/><br /> | ||
</li> | </li> |
Revision as of 18:32, 24 October 2010
Population counter : Modelling
Introduction
We aim at setting up a biological device counting random events occuring in a microfluidic device (see figure 1). These events are recombinations in the cells of the device, stimulated by pulses of arabinose coming from the tunnel. Once a certain number of pulses have been triggered, we expect our device to start shining. First, we shall describe the dynamics of the population of bacteria in our device as well as its recombinations, which further lead to the rise of the concentration of produced AHL. AHL is a molecule such that, once a certain concentration threshold is reached, make all the cells start producing GFP, alerting us of the end of the experiment. Determining the role of a few parameters in a model we shall describe in the following should allow us to count how many recombinations (so how many events) had to happen before the whole device starts shining.The process
Here we will give the bigger picture, discussing how every component of the process reacts and interacts with the other molecules. First, we send a pulse of arabinose through the tunnel. The bacteria are then expected to react in a way that is described in the next section. Those bacteria that recombinated start producing LuxI, which in turns promotes the production of AHL. This AHL will play two roles:- it can bind with LuxR in the cell. LuxR is a protein produced so that its concentration inside the cell will be considered as constant. We call it LuxRf as long as it is free from AHL, LuxR* otherwise;
- it can cross the cell membrane to bind with LuxR of other bacteria in the device.
![Scheme of the microfluidic device Mf device](https://static.igem.org/mediawiki/2010/4/40/Mf_device.jpg)
Model
We can develop the information we gave in a system of equations:- In a first approach, we will consider that the dynamics of production of LuxI is represented by a step function: [LuxI] is 0 before the recombination, and 1 after. If the time between the two states cannot be neglected, which is probably the case (since it is roughly 20 minutes, close to the expected time of a cell recombinating, and larger than the diffusion significant times), compared to the average time between two recombinations, we may reconsider this simple model.
- Let's call R the constant concentration (how "constant" is it?} of LuxR in a cell. Some of it binded with AHL and we called it LuxR*, so this gives:
The reaction between LuxR and AHL gives a chemical equilibrium determined by the constant kreac:
so at the equilibrium:
![Diffusion equation, AHL AHL](https://static.igem.org/mediawiki/2010/5/51/Eq_AHL.jpg)