IGEM:IMPERIAL/2007/Dry Lab/Modelling/ID: Difference between revisions
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=Analysis of the Model of the Infector Detector= | =Analysis of the Model of the Infector Detector= | ||
==Formulation of the problem== | |||
*Questions to be answered with the approach | |||
*Verbal statement of background | |||
*What does the problem entail? | |||
*Hypotheses employed | |||
==Selection of model structure== | ==Selection of model structure== | ||
*Present general type of model | |||
#is the level of description macro- or microscopic | |||
#choice of a deterministic or stochastic (!) approach | |||
#use of discrete or continuous variables | |||
#choice of steady-state, temporal, or spatio-temporal description | |||
*determinants for system behaviour? - external influences, internal structure... | |||
*assign system variables | |||
==Our models== | ==Our models== |
Revision as of 17:14, 16 October 2007
Analysis of the Model of the Infector Detector
Formulation of the problem
- Questions to be answered with the approach
- Verbal statement of background
- What does the problem entail?
- Hypotheses employed
Selection of model structure
- Present general type of model
- is the level of description macro- or microscopic
- choice of a deterministic or stochastic (!) approach
- use of discrete or continuous variables
- choice of steady-state, temporal, or spatio-temporal description
- determinants for system behaviour? - external influences, internal structure...
- assign system variables
Our models
Model 1: Steady-state is attained; limitless energy supply
Model 2: Equations developed through steady-state analysis; however due to limited energy supply, we operate in the transient regime
Generalities of the Model
- Introduction
We can condition the system in various manners, but for the purposes of our project, Infector Detector, we will seek a formulation which is valid for both constructs considered. Our system can thus be modellied by the following Dynamical System:
[math]\displaystyle{ \frac{d[LuxR]}{dt} = k_1\bigg(\frac{[E]^n}{K_E^n + [E]^n}\bigg) + k_3[A] - k_2[LuxR][AHL]- \delta_{LuxR}[LuxR] }[/math]
[math]\displaystyle{ \frac{d[AHL]}{dt} = k_3[A] - k_2[LuxR][AHL]- \delta_{AHL}[AHL] }[/math]
[math]\displaystyle{ \frac{d[A]}{dt} = -k_3[A] + k_2[LuxR][AHL]- k_4[A][P] + k_5[AP] }[/math]
[math]\displaystyle{ \frac{d[P]}{dt} = -k_4[A][P] + k_5[P] }[/math]
[math]\displaystyle{ \frac{d[AP]}{dt} = k_4[A][P] - k_5[AP] }[/math]
[math]\displaystyle{ \frac{d[GFP]}{dt} = k_6[AP]\bigg(\frac{[E]^n}{K_E^n + [E]^n}\bigg) - \delta_{GFP}[GFP] }[/math]
[math]\displaystyle{ \frac{d[E]}{dt} = -\alpha_{1}k_1\bigg(\frac{[E]^n}{K_E^n + [E]^n}\bigg) - \alpha_{2}k_6[AP]\bigg(\frac{[E]^n}{K_E^n + [E]^n}\bigg) }[/math]
where:
[A] represents the concentration of AHL-LuxR complex
[P] represents the concentration of pLux promoters
[AP] represents the concentration of A-Promoter complex
k1, k2, k3, k4, k5, k6 are the rate constants associated with the relevant forward and backward reactions
[math]\displaystyle{ \alpha_i \ }[/math] represents the energy consumption due to gene transcription. It is a function of gene length.
n is the positive co-operativity coefficient (Hill-coefficient)
[math]\displaystyle{ K_E \ }[/math] the half-saturation coefficient
The system of equations for the two constructs varies strictly with respect to the value of the parameter k1. Construct 1 possesses a non-zero k1 rate constant, whereas for construct 2, a zero value is assumed.