IGEM:IMPERIAL/2007/Dry Lab/Modelling/ID
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==Formulation of the problem== | ==Formulation of the problem== | ||
- | + | Questions to be answered with the approach | |
+ | *Level of sensitivity of system to [AHL] - what is the minimal [AHL] for appreciable expression of reporter protein | ||
+ | #Effect of range of [AHL] upon system - does continued increase in [AHL] increase output? | ||
+ | #If saturating behaviour is exhibited, is there a point at which greater [AHL] actually supresses output | ||
+ | *Can sensitivity to AHL, be tailored by varying initial [LuxR] | ||
+ | *Can sensitivity to AHL, be tailored by introducing increased [pLux] - in other words increasing [DNA] | ||
+ | *Description of response times - for construct 1 and contruct 2 | ||
+ | <br><br> | ||
*Verbal statement of background | *Verbal statement of background | ||
*What does the problem entail? | *What does the problem entail? |
Revision as of 21:07, 16 October 2007
Contents |
Model Development for Infector Detector
Formulation of the problem
Questions to be answered with the approach
- Level of sensitivity of system to [AHL] - what is the minimal [AHL] for appreciable expression of reporter protein
- Effect of range of [AHL] upon system - does continued increase in [AHL] increase output?
- If saturating behaviour is exhibited, is there a point at which greater [AHL] actually supresses output
- Can sensitivity to AHL, be tailored by varying initial [LuxR]
- Can sensitivity to AHL, be tailored by introducing increased [pLux] - in other words increasing [DNA]
- Description of response times - for construct 1 and contruct 2
- 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
Assumptions
- Ignore spatial information of the system; we ignore molecular dynamics of the system.
- Keep track of number of molecules of each type - concentrations of these state variables.
- Thus assume that the system is homogeneous - well-stirred, so that the molecules of each type are spread uniformly throughout spatial domain. *assume thermal equilibrium
- assume constant volume of spatial domain
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.