# Team:Evry/auxin pde

### From 2012.igem.org

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In order to be able to integrate these equations it is mandatory to specify boundary conditions and the geometry of the 3 comparments. In this ideal case, we would use the true geometry of Xenopus, this can be retrieved from histological cuts, various 3D imaging techniques or sometimes by using various plane images. Permeability experiments of the various interfaces are also required to classify them as permeable or not. Boundary conditions being therefore a composition of Dirichlet and Neumann conditions according to the permeability.<br/> | In order to be able to integrate these equations it is mandatory to specify boundary conditions and the geometry of the 3 comparments. In this ideal case, we would use the true geometry of Xenopus, this can be retrieved from histological cuts, various 3D imaging techniques or sometimes by using various plane images. Permeability experiments of the various interfaces are also required to classify them as permeable or not. Boundary conditions being therefore a composition of Dirichlet and Neumann conditions according to the permeability.<br/> | ||

A last requirement is the condition at t=0. Our goal being to have Auxin synthesis induced by an external stimuli (for instance, a pollutant detection) the concentration would be equal to the residual Auxin concentration measured when the biosensor is "off" | A last requirement is the condition at t=0. Our goal being to have Auxin synthesis induced by an external stimuli (for instance, a pollutant detection) the concentration would be equal to the residual Auxin concentration measured when the biosensor is "off" | ||

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+ | <h3>Issues arising from over-modelling</h3> | ||

+ | This ideal model introduces many parameters which would in practice be very difficult to set. Although most of them could be set with very extensive experimentation, such a rigorous PDE approach is definitely excessive. This model has been introduced to explicitly show the idea that a good model is non necessarily one extremely close to reality. Moreover, although already very difficult to deal with this model is makes still very strong assumptions like tissues homogeneity and the possibility to apply diffusion equations straightforwardly. Nevertheless, this diffusion ideal model is more or less | ||

## Revision as of 16:02, 22 September 2012

# From realistic to simplified auxin diffusion model

The main goal of this section is to clearly present our though process in modelling the diffusion and transportation of Auxin between Xenopus' tissues.## An ideal model

Ideally, modelling Auxin's diffusion in tissues and its transportation through blood would require a 4D (3D space + time) PDE representation.Assuming a concentration can be defined, and considering steady state, a powerful representation would use the general Reaction-Diffusion equation from which the famous Fisher-KPP equation is derived. Using this formalism, we propose to consider the 3 compartments of interest : emitter - blood - receiver and to write one PDE for each.

We model Auxin flux according to Fick's law which is an adaptation of Fourier's law for heat transport.

The according equations, using the Nabla operator and using skin as emitter and kidney as receiver are therefore :

### Skin compartment

### Blood compartment

### Kidney compartment

### Limit conditions and geometry

In order to be able to integrate these equations it is mandatory to specify boundary conditions and the geometry of the 3 comparments. In this ideal case, we would use the true geometry of Xenopus, this can be retrieved from histological cuts, various 3D imaging techniques or sometimes by using various plane images. Permeability experiments of the various interfaces are also required to classify them as permeable or not. Boundary conditions being therefore a composition of Dirichlet and Neumann conditions according to the permeability.A last requirement is the condition at t=0. Our goal being to have Auxin synthesis induced by an external stimuli (for instance, a pollutant detection) the concentration would be equal to the residual Auxin concentration measured when the biosensor is "off"