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Skip to main navigation. Skip to secondary navigation. Skip to search. Skip to content. Info This document is not available in the language you requested. It is therefore shown in German. Introduction to Systems Biology - Tutorial 1 Program of the lecture "Introduction to Systems Biology" WS This tutorial for the module "Dynamics" guides you through the tools Model setup as ordinary differential equations and their simulation with the public domain software Copasi.
The predecessor Gepasi had become widely used in academia but is not developed further. In later tutorials we will encounter Copasi again, which besides simulations can also perform metabolic control analysis Tutorial 3 and structural analysis Tutorial 4.
Creation and validation of SBML files describing your model in machine-readable format, and exchange of models between different software. SBML is not a software but a programming language developed by the Sysbio community. A less specialised companion standard is CellML which we will not use here. In case of problems, intermediate results are available for download and restart of the subsequent steps. To download a linked file, hold down the right mouse button and select Save Link As Docu: The documentation of the software is downloadable as pdf but not required for the following.
Copasi is controled by selecting properties from the tree on the left and filling corresponding forms in the window on the right. Today we only need basic features and only use a small fraction of the tree items. Our model will work with most of the default settings but anything could be adjusted or renamed if you wish. Model info and units: Click on Model top item in left tree , then give your model a name and define the physical units time in minutes, volume in milli liters and molecule quantities in milli molar of all the numbers in your model.
Each time when you are ready with such a form, click the Commit button. Tree of model details: Next you need to enter chemical reactions and Copasi will create the corresponding variables. Parameters: Click Parameter Overview in the left tree and check your model. Each reaction starts counting its own parameters with 1,2,.. Then click Commit. Save: You should now save your model by clicking File and Save or the disc icon in the top menu. If the following steps produce unexpected results with your model setup then compare with this reference file after download and Open in Copasi.
You can then reload your file and make corrections. Run simulation: Next we want to simulate the time courses of the concentrations. To do the latter, click on Output major tree item and Plots. Press the button: Add default plot. Then click on Tasks major tree item and Time Course, there press Run. Plot results: A new window with the concentration versus time curves should open.
These are the simulation results. Think about why and where each of the curves moves up or down, use the Zoom click in menu bar and drag with left mouse button, right mouse button brings you back to full scale. Reports: If the simulated data looks interesting, you can save it click save data Each line shows all concentration values separated by tabs. One may import this data into different software e.
MatLab or xmgrace for further analysis and plotting. Alternatively only read this if it was boring so far you can precisely control the structure of the data table by clicking the tree item Reports under Output and then click New.
This creates an output instruction named report, click on the report item under Reports and select time and important concentrations by clicking the Item button and subsequent menu entries. All this is useful if you work with large models and many variables but want to concentrate on a few of them. Once the output instruction report is ready you can click the Report button in the Time Course simulation form and specify a file name for report.
After clicking Run the data will be directly written to the file in the format you specified and with the possibility of subsequently appending data to the same file. Reports may automatically be filled with a lot more information than just the concentration values.
SBML creation: Another way besides data files of communication with other software is to export your model in a defined format or language that most sysbio software understands. The native Copasi format used to save your model under point 9. SBML validation: If you receive SBML files from collaborators and experience problems, the first check is whether the file confirms with the standard and hence whether the problem is yours or that of your collaborator.
There is stable stand-alone validation software but here we use the convenient online service at sbml. Moreover by clicking visualize you can view an automated layout of your reaction network. Additional task that may be skipped: Here is a wrong SBML file for down- and upload which will provoke some warnings. Alternative reaction: Next we add to the existing model a more compact version of the same reactions. As in 4. Also set the same initial conditions as originally.
Then click on the parameter values and enter those values calculated from the 3 rate constants of the original reactions. Simulation: First we have to update the plot instructions if you like also the report instructions since new variables were introduced. Click on ConcentrationPlot under the item Plots under Output.
Click New curve Also let them be plotted with symbols. Then click Run in the Time Course form. The plot should redraw and show more data than originally. Did you expect the new data to look like that? Parameter Change: Click on Plots to add another default plot and inactivate the first plot to preserve its data for comparison.
Switch to symbols for the Michaelis-Menten curves in the new plot. Run the simulation again and you should get another plot that you can compare with the original one. Discover: If you didn't have enough yet, keep playing with the parameters all k1 and k2 at various [E] 0 to get a feeling for the validity of the steady state approximation. You may also try to plot the product formation FLUX versus the substrate concentration and observe Km and V in the saturation curve.
Under Model go down to the compartment form and reduce the volume of the compartment to 1e which reduces the particle numbers down to several thousands. The results should look familiar to you. Now deactivate the concentration plot to freeze the image. Rerun the simulation after selecting the stochastic method which translates the macroscopic rates into reaction probablilities according to Gillespie.
After comparing the results, further decrease the volume under compartment item to 1e and 1e, at each step rerun the stochastic simulation, did the results change?
The continuous, deterministic approach still visible in the frozen window generally assumes large particle numbers.
Click Run and observe the plot, increase the number of repeats to and run again. What does the average of these simulations do, what behaviour of the deviations do you expect for infinitely many runs? MAPK cascade can oscillate and amplify signals cf. Kholodenko in Eur. We can download the model used by him from public model repositories.
If you could not get it then try again here. Simulation: Create a plot and then run a simulation over the same period as in Fig. Stability analysis of steady states: To confirm the oscillatory state, one can check the stability of coexisting steady states.
In the presented results table click to the Stability-tab on the right. How are the in- stability of steady states and the oscillations related to the calculated Eigenvalues? Repeat the Time Course simulations for decreasing values of V1 less and less input from 2. You need to jump between the Time Course and the Parameter Overview. If something look interesting try to explain it in terms of the Stability analysis of steady states which you then would need to run for the respective V1 like above.
Games corner: Those who think they are too fast may read in the documentation of Copasi about sliders and use a slider for V1 in time course simulations. Automated parameter scan for steady states: The steady state turned out to be the dominant attracting solution for low input values as opposed to the oscillations at large input values. Then click Run. You should see a single curve in a new plot.
Compare the form of the curve to the Michaelis-Menten relations that are used for all reactions. The latter are linear for small input values. Repeat the parameter scan up to 2. Copasi can compute the steady states but for the oscillations we need to rerun individual time courses. Bifurcation analysis with XPP-AUT: Specialised bifurcation analysis software like AUTO can follow steady states and their stability for changing parameters like Copasi above but does also calculate simple and complex, stable and unstable oscillations and other asymptotic solutions.
Here we use AUTO with the user-friendly face of XPP in order to better understand the relation between oscillations and in stabilities of coexisting steady states. Next we want to obtain the same oscillation by means of bifurcation analysis of periodic solutions instead of simulation. A new window opens, this is called AUTO. The main window shows the bifurcation diagram with the value of the steady state as a function of the selected parameter V1. The lables 1 and 3 are the start and end of the branch, as limited by the user.
Participants will learn how to set up computer models of biological systems e. Hands-on sessions, lectures and software demonstrations will be included, providing attendees with the necessary skills to access experimental kinetics data from available resources, to assemble computer models with these data, and finally to simulate the generated models using simulation tools. Also handling and exchange of biological models based on existing community standards will be demonstrated along with the basic principles of the underlying standard formats and how they support reproducible and FAIR computational modelling. Attendees are expected to bring their own computer and have the tools pre-installed listed below.
COPASI Video Tutorials
Simulation and modeling is becoming a standard approach to understand complex biochemical processes. Therefore, there is a big need for software tools that allow access to diverse simulation and modeling methods as well as support for the usage of these method. COPASI is an open-source software application for creating and solving mathematical models of biological processes such as metabolic networks, cell-signaling pathways, regulatory networks, infectious diseases, and many others. The project principal investigators are Pedro Mendes and Ursula Kummer. The chief software architects are Stefan Hoops and Sven Sahle.