Difference between revisions of "IGEM:IMPERIAL/2007/Dry Lab/Modelling/ID"
(→Model 1: Steady-state is attained; limitless energy supply ''(link here to derivation)'') |
(→Model 1: Steady-state is attained; limitless energy supply ''(link here to derivation)'') |
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<math>\frac{d[A]}{dt} = -k_3[A] + k2[LuxR][AHL]- k_4[A][pLux] + k_5[AP]</math> | <math>\frac{d[A]}{dt} = -k_3[A] + k2[LuxR][AHL]- k_4[A][pLux] + k_5[AP]</math> | ||
− | <math>\frac{d[ | + | <math>\frac{d[P]}{dt} = -k_4[A][P] + k_5[P]</math> |
+ | |||
+ | <math>\frac{d[AP]}{dt} = k_4[A][pLux] - k_5[AP]</math> | ||
<math>\frac{d[GFP]}{dt} = k_6[AP] - \delta_{GFP}[GFP]</math> | <math>\frac{d[GFP]}{dt} = k_6[AP] - \delta_{GFP}[GFP]</math> |
Revision as of 16:36, 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.