Team:NTU-Singapore/Modeling
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*Single solvable equation for the unknown C | *Single solvable equation for the unknown C | ||
*Simple, unique solution available with I.C | *Simple, unique solution available with I.C | ||
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+ | ==Phosphorylation and Dephosphorylation== | ||
+ | Assumptions: | ||
+ | *Linear kintic rate laws apply only if XT is much less than the Michaelis constants of both kinase and phosphotase | ||
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+ | *Modeled after simple linear kinetics | ||
+ | *Gives a hyperbolic signal response curve when X plotted vs S | ||
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Revision as of 01:43, 25 June 2008
Contents |
Introduction
The use of models to describe synthetic biology has its merits. Synthetic biology investigates the use of different biological parts to put together and assemble devices that carry out specific functions. Good mathematical models to describe each part would greatly help not only in the characterization of a part but also facilitate the use of the part by other people when they choose to use the part within their devices or systems.
Simulations based on modeling can give a first insight on how the system would turn out and provide a rough guide of the system’s behaviour.
System
The system can be viewed as two parts. The first part comprises of lactose induced production of colicin E7 and the immunity protein. The second part comprises of a detection mechanism that produces the lysis protein upon the detection of both Iron ions and Ai-2 ( Autoinducer 2).
ODEs used in modeling
The following equations shows the break down of the different equations that will be used in this modeling exercise. By understanding this section, it would make the understanding of the system of ODEs used
Constant synthesis & Linear Synthesis
- Simple ode to describe constant synthesis
- Gives an explicit analytical solution
- Unique solution once a IC is posed
Linear Degradation
- Rate of degradation is proportional to how much of the molecule is present
- Gives an explicit analytical solution
- Constant half life
Simple Forward Reaction
This equation ignores the fact that dissociation of the complex occurs. We can do so if the dissociation is much slower than the formation.
- Single solvable equation for the unknown C
- Simple, unique solution available with I.C
Phosphorylation and Dephosphorylation
Assumptions:
- Linear kintic rate laws apply only if XT is much less than the Michaelis constants of both kinase and phosphotase
- Modeled after simple linear kinetics
- Gives a hyperbolic signal response curve when X plotted vs S
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