IGEM:IMPERIAL/2007/Projects/Cell by date/Modelling

Cell by Date: Modelling

• Introduction
• Specifications
• Design
• Modelling
• Implementation
• Testing/Validation
• Notes
• References

Overview of Modelling

Welcome to our portal page for the modelling of Cell By Date

Cell by date tries to improve on printed cell by date as acting as a thermal exposure device, exploiting the thermal dependance of the rate of expression of a simple reporter system. We are looking at a variety of constructs to realise this behaviour.

Constructs to be Used

GFP Based
RFP Based

As can be seen in the above table all of our constructs have the same general form of a promoter upstream of a reporter. Looking at the rate of Fluorescent Protein (FP) produced :

[math]\displaystyle{ \frac{d[FP]}{dt}=k_{FP}(t)-d_{FP}[FP] }[/math]

1. kFP : Function of Temperature. k is based on the promoter used as promoters take time to turn on.
2. dFP : Function of System. May be considered to be a function of temperature as proteins degrade faster at higher temperatures.

Transient Response of System Image needs to be changed to matlab plot of system Construct 1 - LuxR expressed constitutively	Transfer Function of System Image needs to be changed to matlab plot of system Construct 2 - LuxR not expressed

Performance Specs

With this in mind we will look at two graphs of k vs. time (special pt is kON.) and [FP] vs. time key point is [FP]ss

• Our major problem at the moment is estimating the errors involved with our fluorometer and experimental procedures, most notably pipetting; we hope to address these through calibration curves.

For each experiment we will do the following

1. Calibration curve to determine error in fluorometer
2. Decay Experiment @ varying temperatures
3. Plug together to find transient response and k
4. Find these parameters as a function of temperature(T)

Construct Specific Modelling

For all constitutive promoters (Ptet promoter used as an example):

Construct employing Ptet

1.Apply the above general equation to this specific construct.

[math]\displaystyle{ \frac{d[GFP]}{dt}=k_{Ptet}(t)-d_{GFP}[GFP] }[/math]

2.Calibration curve to determine error in fluorometer - we are trying to get this information from BertholdTech
3.Decay Experiment at varying temperatues:

• This is to determine [math]\displaystyle{ d_{GFP} }[/math]
• The fluorescence of a pure sample of GFP kept at 'constant temperature' will be measured at time intervals. We expect the fluorescence to decay exponentially with time.
• We plan to determine the decay constant in the following way:
  • We cannot measure the decay constant directly; instead we plan to measure/determine the half-life of our reporter. With this done we can calculate the decay constant using the following equation:

[math]\displaystyle{ t_{1/2} = \frac{\ln 2}{\lambda} }[/math]

DecayPage

4.Having found [math]\displaystyle{ d_{GFP} }[/math] we look at transient respone of construct at several constant temperatures to find k at constant temperature
5.Find k & d as functions of temperature:

• This will hopefully have been carried out by interpolation of data from 4. and 3. eg. plots of k vs. temp & d vs. temp
  
  • The problem with this method is that it will not allow us to determine the response time of the promoters eg. the time taken for the promoter to respond to a temperature change.

Otherwise, another plan is as follows:

• This plan has have several temperature slopes as inputs from which we can compare changes in temperature with changes in k to determine the relationship between the two.
  
  • This methods involes comparing rate of temp increase to rate of k change eg. substituting time in k expression for Temp.
    

6.Following on from this we plan to have several pulse inputs, similar to what we'll have in real life eg. taking meat from the supermarket and bringing it back home to put in your fridge. From this we can work out how well our system behaves in real life scenarios, and how well our model performs.