User:Johnsy/SB Mini iGEM
The Model
In this section, we present a mathematical model of the system we are trying to develop. To simplify the system, we split the system into three components:
- The Cell Free System
- The Xenopus Oocyte ACh Receptors
- Voltage-Gated Ion Channel Response
The Cell Free System
We have decided to use microfludic devices and use a cell free system because parameters in such a system are more controllable than in a normal E. coli system. To design a good model, we must first understand the biochemistry behind the system which is outlined in previous sections and summarized here.
Our input of AHL activates a LuxR promoter which then allows transcription of the enzyme PEMT, the rate limiting step of the synthesis of ACh. Although there are several more enzymes invovled in this pathway and they are all under the control of the LuxR promoter, we have decided only consider the transcription and expression of PEMT and assume that the production of all other enzyems are on the same order of time and the rate of production of ACh is only dependent upon the activity of PEMT.
The enzyme PEMT itself can be modelled with Michaelis-Menten kinetics whose parameters are well publicized. With these biochemical systems in mind, we can come up with the following system of differential equations to model our system.
[math]\displaystyle{ \frac{d[mRNA]}{dt} = \frac{k_1[AHL]^n}{K_{m1}^n+[AHL]^n} - d_1[mRNA] }[/math]
