IGEM:IMPERIAL/2007/Dry Lab/Modelling/ID
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==Formulation of the problem== | ==Formulation of the problem== | ||
As described earlier, Infector Detector (ID) is a simple biological detector, which serves to expose bacterial biofilm. It functions by exploiting the inherent AHL production employed by the quorum-sensing bacteria, in the formation of such structures.<br> | As described earlier, Infector Detector (ID) is a simple biological detector, which serves to expose bacterial biofilm. It functions by exploiting the inherent AHL production employed by the quorum-sensing bacteria, in the formation of such structures.<br> | ||
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+ | <font color = red>~~Insert diagram illustrating this phenomenon </font><br> | ||
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Our project attempts to improve where previous methods of biofilm detection have proven ineffective: first and foremost, by focussing on the sensitivity of the system, to low levels of AHL production (bacterial chatter). | Our project attempts to improve where previous methods of biofilm detection have proven ineffective: first and foremost, by focussing on the sensitivity of the system, to low levels of AHL production (bacterial chatter). | ||
In doing so, a complete investigation of the level of sensitivity to [AHL] needs to be performed - in other words, what is the minimal [AHL] for appreciable expression of reporter protein. Furthermore, establish a functional range for AHL detection. How does increased [AHL] impact on maximal output of reporter protein?<br> | In doing so, a complete investigation of the level of sensitivity to [AHL] needs to be performed - in other words, what is the minimal [AHL] for appreciable expression of reporter protein. Furthermore, establish a functional range for AHL detection. How does increased [AHL] impact on maximal output of reporter protein?<br> | ||
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*Construct 2 - simpler in nature, lacks pTET; LuxR is introduced in purified form here.<br> | *Construct 2 - simpler in nature, lacks pTET; LuxR is introduced in purified form here.<br> | ||
- | ~~Here explain briefly why Construct 2 was selected. | + | <font color = red>~~Here explain briefly why Construct 2 was selected, i.e. we were concerned with the time the system would take to reach steady-state (that is before energy-dependence was considered) - due to almost negligible <math> \delta_{LuxR}</math>, etc </font>. |
==Selection of model structure== | ==Selection of model structure== |
Revision as of 07:49, 20 October 2007
Contents |
Model Development for Infector Detector
Formulation of the problem
As described earlier, Infector Detector (ID) is a simple biological detector, which serves to expose bacterial biofilm. It functions by exploiting the inherent AHL production employed by the quorum-sensing bacteria, in the formation of such structures.
~~Insert diagram illustrating this phenomenon
Our project attempts to improve where previous methods of biofilm detection have proven ineffective: first and foremost, by focussing on the sensitivity of the system, to low levels of AHL production (bacterial chatter).
In doing so, a complete investigation of the level of sensitivity to [AHL] needs to be performed - in other words, what is the minimal [AHL] for appreciable expression of reporter protein. Furthermore, establish a functional range for AHL detection. How does increased [AHL] impact on maximal output of reporter protein?
Also, how can the system performance be tailored, by exploiting the remaining state variables (e.g. varying initial [LuxR] and/or [pLux]).
The system performance here revolves most importantly around AHL sensitivity; however, the effect on, maximal output of fluorescent reporter protein and/or response time is, likewise, of great importance.
Our approach, involves the proposal of two simple constructs, varying with respect to the manner in which LuxR is introduced into the system:
- Construct 1 - represented by T9002, incorporates constitutive expression of LuxR by pTET.
- Construct 2 - simpler in nature, lacks pTET; LuxR is introduced in purified form here.
~~Here explain briefly why Construct 2 was selected, i.e. we were concerned with the time the system would take to reach steady-state (that is before energy-dependence was considered) - due to almost negligible δ_{LuxR}, etc .
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 be 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.