Tutorial on Doing Parameter Estimation Using PET

(Email Rajat Singhania at rsinghan@vt.edu for any questions.)

This document is intended to help you use the parameter estimator within PET.  It assumes you have already installed PET and have read the release notes.

0.)Warning: Keep saving the file every now and then...remember, this software is still Alpha!! See the last step for instructions on how to do so.

1.) Download the file testModel.sbml to your Desktop by right-clicking on the name of the file and choosing the Save option. Then run PET, and click on the "Import SBML" button indicated below by the red arrow to load the testModel.sbml file you just saved.  If you wish, you can verify that the SBML file has been loaded by clicking on the "View SBML" button.

2.) Click on the "Edit Basals" tab in order to create a Basal Set. 

3.) Type "Set 1" below where the red arrow is, and click "Add".

4.) New instructions should now be displayed on the right-hand section. Click on "Import" in the box entitled “Current SBML” (as shown by the red arrow below) - this will import parameters and initial conditions from the file testModel.sbml.

5.) Add another set, "Set 2", just as you had previously added "Set 1" in Step 3, and then follow the rest of the instructions just like above in Step 4.

NOTE: Make sure that in the left-hand column in the window, the boxes next to both "Set 1" and "Set 2" are checked.  Clicking on "Set 1" brings the pane where you can enter the Initial Conditions and Parameters for "Set 1" - same thing for "Set 2".

6.) After clicking on "Set 1", enter the Initial Conditions and Parameters as: M = 0, k2 = 1 & k1 = 1. The values of Mp = 1 and Ct = 1 should already be there, as imported from the file testModel.sbml.  You can click on the button "Commit Changes" underneath if you wish to do so. Make sure the box next to “Step 1” remains checked.

7.) Repeat Step 6 by clicking on "Set 2" first, and then entering: M = 0, k2 = 0.8 & k1 = 1.25. Again, the values of Mp = 1 and Ct = 1 should already be there, as imported from the file testModel.sbml.  You can commit the changes if you wish to do so. Make sure the box next to “Step 2” remains checked.

8.) Create a Simulation. Select the "Edit Simulations" tab, type in "Sim 1" where the red arrow is, and click "Add". 

      Make sure that the resulting box next to the words "Sim 1" is checked.

9.) From the drop-down menu under the word "Parameters", choose Ct.  In the next field that is blank, type in "1" and click on "Set."

10.) Now click on the "Edit Data" tab.  Click on "Sim 1".  Then in the drop-down menu next to the word "Type:", choose "Time Series".

11.) This is the data-entering step.  The first column is for the Time and the second column is for the concentration of a particular Species.  This is the “experimental data” that the model will be trying to fit! From the drop-down menu under the words "Species", choose "M".

12.) Enter the first new row with Time = 0.25 and Species = 0.2. Remember that the first column is for the Time and the second column is for the Species concentration.

13.) Insert the rest of the rows in the same way as in Step 12; the data to be inserted after [0.25, 0.2] is: [Time: 0.5, Species: 0.3], [0.75, 0.4], [1, 0.43] & [1.5, 0.48]. The final display should now look like the image below.

14.) Now click on the "Estimator Settings" tab.  Note that the window is divided into three parts as shown in the figure below: (1) In the left-third, parameter properties are displayed [henceforth referred to as "Section A"]; (2) In the middle-third, the experimental data to be matched is displayed ["Section B"]; (3) In the right-third, the available settings are displayed ["Section C"].

15.) In Section A, each row corresponds to a parameter. Checking a box in the "Fixed" column specifies that that parameter's value is to remain fixed throughout parameter estimation.  Make sure that the box for Ct is checked.  Min, Max and Initial specify the desired minimun, maximum, and initial values of a parameter. 

NOTE: Min specifies the lower bound on the value of a parameter while it is being estimated.  Similarly, Max specifies the upper bound on the value of a parameter while it is being estimated.  Both the Min and Max values can be edited by clicking on them; "Inf" stands for Infinity.    We shall soon see how to set the Initial values.

16.) In Section B, the experimental data we stored earlier, under the tab "Edit Data" (Steps 10 to 13), can be seen by clicking on the arrow next to the experiment name, "Sim 1".

17.) In Section C, make sure that "ODRPACK95 (Local)" is selected.  In the "Initial Guess" drop-down menu, choose "Set 2" (which has k2 = 0.8 and k1 = 1.25 - these are the parameters which are being estimated, hence they are NOT fixed in Section A as compared to the parameter Ct).  Now notice that in Section A, the "Initial" column is filled with the above initial-guess values of the corresponding parameters as specified by "Set 2", as they were input in Step 7. The final display should now look like the image above.

18.) Now we are ready to do parameter estimation!  Click on the "Estimate" button in the upper right-hand corner.  A new window entitled "Estimator Status" should open up.  After the status is displayed as "done", you can click on "Show ODRPACK95 Report" for a detailed report.  To get the returned estimated parameter values, go to the "Edit Basals" tab in the original PET window, and click on the newly created "Estimated" Basal Set.  The returned estimated values of the parameters "k1" and "k2" are now displayed. You should obtain the value of "k1" as "0.972228075" and the value of "k1" as "0.936163089" ("Ct" should be "1.0"). These values can be off by small amounts (10^-4) depending on the machine you are using.

In case your values are way off, check the values that you input for the two basal sets and for the data points in the “Edit Basals” tab. Also make sure that “Ct” is checked to be a fixed parameter as described in Step 15.

19.) Now we will do a Simulation to see how well our model fits the data. Click on the “Simulator Settings” tab and fill in the first box with the value of “5” to simulate for 5 time units. Leave the number of output points as blank – this will use the default value of 200 output points. Note that the default number of time units is 500.

20.) Go back to the “Edit Basals” tab and uncheck the box next to the words “Set 1.” Only checked basal sets are simulated – in this case, we are interested in only “Set 2” and “Estimated” since we want to compare how good our initial guess of the parameters was (with “Set 2”) and how well the parameters returned by the Estimator (basal set “Estimated”) help the model fit the data.

21.) Now click on the “Simulate” button near the upper right-hand corner. You should get the following window:

Note how well the parameters from the “Estimated” basal set help the model fit the data points, as compared to our initial guess with basal set “Set 2”!!

22.) MAKE SURE that you save the file!!  Click on File->Save, name the file "myTutorial.pet", and save it in the same directory as the file testModel.sbml.

Errata: The “View SBML” button in the main window has been renamed to “Edit SBML”!!!