IGEM:IMPERIAL/2007/Projects/Cell by date/Modelling
Cell by Date: Modelling
Summary:
In the design section we outlined which variants of Cell By Date we would like to implement in different Chassis, as shown in the table below.
| Chassis | Level 1 | Level 2 | Level 3 | |
| E.coli | X | |||
| In-Vitro | X | X | X | |
| In-Veso | X | X | X |
In this section we modify the variants of Cell by Date so that they can be implemented advantageously in each chassis. We also model these modified variants in order to understand the behaviour we expect or to tune the system to realise a particular behaviour. This leads us to write up experiments to determine if our system behaves the way our models predict.
Overview of Modelling
Overall our modelling for this project will take the form of
[math]\displaystyle{ \frac{dFP}{dt}=k_{FP}(t)-d_{FP}[FP] }[/math]
- kFP : Function of Temperature. k is based on the promoter used as promoters take time to turn on.
- dFP : Function of System. May be considered to be a function of temperature as proteins degrade faster at higher temperatures.
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
- Calibration curve to determine error in Fluorometer
- Decay Experiment @ Varying temperatures
- Plug Together to find transient response and k
- Find these parameters as a function of Temperature
Construct Specific modelling
For all constitutive promoters (Ptet promoter used as an example):
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.
- 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.
