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Revision as of 22:26, 17 September 2012

Plasmid splitting

Overview

The idea of this model is to better understand the consequences of our experimental method
Our protocol consists in injecting a large amount of plasmid at the 1-cell stage, directly into the cytoplasm. When cells divide, the initial quantity of plasmid is split between daughter cells. Only a very infinitesimal proportion of plasmid will be integrated in the nucleus so most of the "effective" plasmids containing our constructs comes directly from this first injection.
This model has been created in order to answer critical questions about our experimental protocol :

• What is the average amount of plasmid we can expect to find in a cell at a given time?
• How uniform is the plasmid repartition among cells?
• Which known mechanisms in morphogenesis could play a role in the plasmid repartition?

Hypothesis

There are the different hypothesis we were constrained to make in order to model the system:

1. The auxin concentration inside a compartment is homogeneous
This condition is inherent to this kind of modeling.
2. 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?]
3. 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.


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:


Where:

• S in m^2, represents the area of the exchange surface between the two compartments.
• P in m^2, represents the permeability of the membrane between the specified compartments.
• C in [quantity] / m^3, represents the concentration of auxin in the specified compartment

These flow equations are based on Newton's law of cooling where the difference between the concentrations of the two compartments gives the direction and magnitude of the flow. This allows us to model in a single equations the two opposite flows between the compartments.

Calibration

Results

Conclusion

References

Other possible topologies

With auxin in the external medium:

With a specific receptor organ: