Tutorial Page 12
Applying perturbations to the model and environment parameters is an extremely powerful tool, allowing the simulation of almost any experiment. In the last tutorial we applied a simple one-off perturbation to switch on a gene at a defined time. This time we are going to see how easy it is to apply multiple perturbations at defined times. Say you wished to simulate the effect of an external factor other than the environment on the circadian system, for example a hormone or an artificial drug. First you must decide how this factor's presence will affect the model. Generally this will be by altering one of the model parameters, for example a drug that switched on a gene could raise the parameter representing its maximum transcription rate, or a drug that binds to a protein and prevents it from doing its job could set the appropriate parameters to zero. It would be very easy to simulate a single application in a similar experiment to the last tutorial, but an interesting experiment might then be to see if the system can be entrained by repeated regular application of this external factor.
The first thing we will do is create a suitable environment file for this simulation. Click the "Environment" tab and open the file "Default". As we are entraining our model with perturbations, we don't want the light-dark cycle interfering. Set both "On" and "Off" values to zero to create DD. The bar should then turn all black. Set the number of days to five. Now click the "Insert Copy" button which is just above the tab saying "Regime 1". You will see that another tab "Regime 2" has appeared. What this means is that after the five days defined in regime one are applied, then the days defined here will be applied. This is the period when we will begin to apply our perturbations. Click "Insert Copy" again to create a third regime. This time however, change the cycle period to 28 hours. We'll see why in a minute.
The concept of multiple regimes allows us to apply as complex an environment cycle as we wish. We can simulate almost any combination of light-dark values. Most commonly we will want to apply an LD cycle which then switches to constant conditions. We are not doing this here though, as all our regimes are DD. What we are doing is using the environment to provide us with reference points in time for applying out repeated perturbation.
Save the file as "Multi Regimes" and close the form.
Now we must create a suitable perturbations file. Click on the "Perturbations" tab. Right click on the file view area and select
Newfrom the popup menu to launch the perturbations dialogue box. We have already looked at perturbing parameters, so lets imagine our external factor causes an immediate boost levels of TOC1 mRNA and we can look at perturbing model states.
Select the "States" tab and select "cTm Level of TOC1 mRNA" from the drop down list.
Set the other controls as shown here.
There are three ways to define the size of a perturbation: setting to an absolute value, adding a value to the existing value, or multiplying the existing value by a factor. In the case of a state we cannot know what the existing value will be at the moment of the perturbation of course. Set the "Perturb its value by" list to "Adding" and leave the value to add as "1". (It is possible to add a negative value to remove some RNA or protein , but the equation solver ensures that its level never falls below zero of course.)
Set "At" to "0" and "hours from start" to "Light-Dark cycle" Regime "2" Cycle "1". This defines the time of the perturbation as being at the start of the first day of the second regime.
Now to cause the perturbation to be repeated. Check the "Repeat at" box and set the drop down list to "same time in subsequent LD cycles". Set the max repeat number to "10". This will cause the perturbation to be repeated at time zero on every subsequent new cycle, up to a maximum of ten times if the simulation is long enough. Remember that we changed the length of the cycle at the start of Regime 3, and so the frequency of our perturbations will alter at this point. Thus we will investigate if it is possible to entrain the system to this different period.
There is another option, to repeat perturbations at the same ZT time each cycle. This is slightly different as it depends on the time of lights on rather than the start of the cycle, but we won't use this option here.
Now click "Add" and the details should appear in the grid as shown. Save the file as "TOC1 boost" and close the form.
We are now ready to run the simulation. Click the
Experiments->Time Series->Simplemenu item. This will produce the dialogue box that requests us to select parameters and environment files. Change the environment file to "Multi Regimes", enter a name for the workbook, and click "Next".This brings up the form we have ignored before.
Here you are asked to choose a perturbations file to use in the experiment. Select "TOC1 boost" from the drop down list and select the "States" tab. You should then see all the calculated times when the perturbations will be applied.
Note how the first six from 120 to 240 hours are applied at 24 hour intervals, but after this the interval becomes 28 hours.
Click "Next" to bring up the outputs form. Select "1 Level of LHY mRNA" and "4 Level of TOC1 mRNA" and click "Next".
This brings up the integration form. We won't integrate this time so just click "Finish" to launch the simulation and wait for it to complete.