IGEM:IMPERIAL/2007/Dry Lab/Modelling/ID
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(→Model 1: Steady-state is attained; limitless energy supply ''(link here to derivation)'') |
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<math>\frac{d[LuxR]}{dt} = k_1 + k_3[A] - k2[LuxR][AHL]- \delta_{LuxR}[LuxR]</math> | <math>\frac{d[LuxR]}{dt} = k_1 + k_3[A] - k2[LuxR][AHL]- \delta_{LuxR}[LuxR]</math> | ||
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<math>\frac{d[AHL]}{dt} = k_3[A] - k2[LuxR][AHL]- \delta_{AHL}[AHL]</math> | <math>\frac{d[AHL]}{dt} = k_3[A] - k2[LuxR][AHL]- \delta_{AHL}[AHL]</math> |
Revision as of 19:39, 16 October 2007
Contents |
Model Development for 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
- 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 initial approach assumed that energy would in unlimited supply, and that our system would eventually reach steady-state (Model 1). Experimentation suggested otherwise; our system needed to be amended. This lead to the development of model 2, an energy-dependent network, where the dependence on energy assumed Hill-like dynamics:
Model 1: Steady-state is attained; limitless energy supply (link here to derivation)
Model 2: Equations developed through steady-state analysis; however due to limited energy supply, we operate in the transient regime
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
represents the energy consumption due to gene transcription. It is a function of gene length.
n is the positive co-operativity coefficient (Hill-coefficient)
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.