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Team:ETH Zurich/Modeling/Analytical Approximation
From 2011.igem.org
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= Gradient Approximation = | = Gradient Approximation = | ||
| + | We derived the gradient formation dynamics analytically already in the [[Team:ETH_Zurich/Modeling/Microfluidics#Model|reaction-diffusion model]]. However, there we only solved the resulting partial differential equation numerically. '''Here, we are going to venture forth and give a suitable analytical approximation!''' | ||
== Kolmogorov-Petrovsky-Piskounov Equation == | == Kolmogorov-Petrovsky-Piskounov Equation == | ||
== Dead Zone Concept == | == Dead Zone Concept == | ||
Revision as of 17:54, 27 October 2011
Contents |
Analytical Approximation
GFP Band: Dimensionless Model
1. Dimensionless Species
We nondimensionalized all species occurring in the equations for the GFP band circuit.
2. Dimensionless Equations
The dimensionless equations for the dynamics of the band-generating system then read
3. Steady State
4. Dimensionless Groupings
The equation system can be simplified by introducing the following dimensionless groupings:
This yields the final equations for steady state:
Gradient Approximation
We derived the gradient formation dynamics analytically already in the reaction-diffusion model. However, there we only solved the resulting partial differential equation numerically. Here, we are going to venture forth and give a suitable analytical approximation!
Kolmogorov-Petrovsky-Piskounov Equation
Dead Zone Concept
Analytical Solution
References
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