Team:ETH Zurich/Modeling/Analytical Approximation
From 2011.igem.org
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:
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
In mathematics, the problem posed by general reaction-diffusion systems form is known as the Kolmogorov-Petrovsky-Piskounov Equation. In the case of acetaldehyde as diffusing and reacting molecule, the equation has the following general structure:
Dead Zone Concept
Analytical Solution
References