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Team:Evry/ODE model
From 2012.igem.org
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Each compartment is modeled by a differential equation representing the evolution of the auxin quantity as a function of the time. | Each compartment is modeled by a differential equation representing the evolution of the auxin quantity as a function of the time. | ||
| - | Each equations are composed of two kinds of terms: creation and degradation. The creation term can represent either a creation of auxin in the compartment or an arriving quantity of auxin from another one. In the same way, the degradation term can either represent a natural degradation of molecules or a quantity leaving the compartment. | + | Each equations are composed of two kinds of terms: creation and degradation. The creation term can represent either a creation of auxin in the compartment or an arriving quantity of auxin from another one. In the same way, the degradation term can either represent a natural degradation of molecules or a quantity leaving the compartment.<br/> |
<center> | <center> | ||
<img src="https://static.igem.org/mediawiki/2012/2/25/Ode-syst.png" alt="ODE system" /> | <img src="https://static.igem.org/mediawiki/2012/2/25/Ode-syst.png" alt="ODE system" /> | ||
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| + | In this system, the J terms represent the fluxes between the different compartments. We made them depend on the concentrations of both the in and out compartments as explained in hypothesis 2. Their mathematical formulation is the following:<br/> | ||
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Revision as of 14:58, 17 September 2012
Model using Ordinary Differential Equations(ODE)
Overview
The first model we developed represents the tadpole as a three compartment system:- The skin that produces (or receives) auxins;
- The blood that transport auxins to the organs;
- The organs (called receptors) that interacts with auxin molecules.
The parallel with (electrical) engineering is made easy: the skin represents a generator that will add a quantity to the system; The blood represents wires, that convey this quantity throughout the system; Finally the organs are the sinks that use the quantity to work.
This very idealized view of the tadpoles allows to make some interesting simplifications: The processes happening in the system can be approximated using Ordinary Differential Equations (ODE), one of the simplest form of differential equations; Plus, the organs repartition and shape are not taken into account.
This over-simplication of the problem causes the model to give very imprecise quantitative results but its strength is in allowing us to make some qualitative predictions about the success or failure of some experiments.
Hypothesis
There are the different hypothesis we were constrained to make in order to model the system:- The auxin concentration inside a compartment is homogeneous This condition is inherent to this kind of modeling.
- No auxins can go from the skin directly to the organs. We have chosen to neglect the exchanges between the skin and the other organs. This hypothesis is supported by the fact that... #[FIXME?]
- The auxin flow follows the concentration gradient between compartments. This hypothesis is based on the fact that a small capillary is nothing more than a hole in a cell layer. So the exchanges between the surrounding cells and the capillary are mutual.
Model description
Equations
Each compartment is modeled by a differential equation representing the evolution of the auxin quantity as a function of the time. Each equations are composed of two kinds of terms: creation and degradation. The creation term can represent either a creation of auxin in the compartment or an arriving quantity of auxin from another one. In the same way, the degradation term can either represent a natural degradation of molecules or a quantity leaving the compartment.
Calibration
Results
Conclusion
References
References:
Other possible topologies
With auxin in the external medium:
With a specific receptor organ:
