From 2007.igem.org

Contents 1 The Model 1.1 System network topology 2 Formulation of the problem 3 Approach 4 Simulations 5 Establishing a model 5.1 Approach

The Model

This section describes a preliminary model for...

System network topology

This section outlines a basic model for our system, Infector Detector. We choose to condition the system in a manner holds for both constructs. Essentially construct 2 only differs with respect to absence of pTET constitutive promoter, and where LuxR is introduced into the system in purified form - in other words - LuxR is controllable for construct 2. Figure 2 and 3 illustrate the system, achieved through construct 1 and 2 respectively. Table 1 exhibits the network of chemical reactions which govern its behaviour.

Formulation of the problem

As described earlier, catheter-associated urinary tract infection (CAUTI) in the clinical setting is a prevalent problem with extensive economic impact. The underlying cause of many such infections can be attributed to the formation of biofilm, by aggregating-bacteria on the surface of urinary catheters.

Infector Detector (ID) is a simple biological detector, which serves to expose bacterial biofilm. It functions by exploiting the inherent AHL (Acetyl Homoserine Lactone) production employed by certain types of quorum-sensing bacteria, in the formation of such structures.

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 markers of biofilm: in this case, low levels of AHL production (which represents the bacterial "chatter" of such aggregating bacteria).

In doing so, a complete investigation of the level of sensitivity to AHL concentration needs to be performed - in other words, what is the minimal AHL concentration for appreciable expression of a chosen reporter protein. Furthermore, establish a functional range for possible AHL detection. How does increased AHL concentration impact on the maximal output of reporter protein?
Finally, how can the system performance be tailored, by exploiting possible state variables (e.g. varying initial LuxR concentration and/or concentration of pLux promoters).

The system performance here revolves most importantly around AHL sensitivity; however, the effect on the maximal output of fluorescent reporter protein and response time is, likewise, of great importance.

Approach

A deterministic, continuous approximation is considered.

Simulations

Establishing a model

Approach

At reasonably high molecular concentrations of the state variables, a continuous model can be adopted, which is represented by a system of ordinary differential equations.

It is for this reason that our approach to modelling the system follows a deterministic, continuous approximation. In developing this model, we were interested in the behaviour at steady-state, that is when the system has equilibrated and the concentrations of the state variables remain constant.

We can condition the system in various manners, but for the purposes of our project, we will seek a formulation which is valid for both constructs considered, i.e. the governing equations are a represenation of both constructs.

The only difference is with regards to the parameter k₁, the maximum transcription rate of the constitutive promoter (pTET) in Construct 1.
Thus k₁ = 0 for construct 2 (which lacks pTET).

Furthermore, we generate two models based upon the available system energy:

Model 1: Infinite Energy
Model 2: Limited Energy

The system kinetics are determined by the following coupled-ODEs. For a derivation of the governing equations, please access Model Derivation