The chemistry of a biological system is fundamentally different from that in the test tubes and in chemical engineering largely due to complexity of the system, non-linearity, feedback loops and the unique roles played by enzymes. The presence of enzymes speeds up the biochemical reactions. This was first realized by L. Michaelis and M.L. Menten in 1913, when they developed a quantitative theory for the enzyme kinetics. Ever since then, Michaelis Menten (MM) Reactions has been used in modelling biological behaviour. Though MM reactions were originated from enzyme kinetics system, they have been used to represent promoter or inhibitor actions in gene regulatory system as well.
In this section, we present the simplest form of MM reactions, which involves four molecular species, namely the enzyme, E, the substrate, S, the product, P and the intermediate heterodimer, ES.
Equation 6-1
The model as shown above has been included in the distribution under the folder “/model repository/michaelisMenten/”. Users can find a project file “michaliesMenten.cwm” and a sbml file “michaelisMenten.sbml” in the folder. Choose to open the project file by clicking on the icon  . The SBML file can be imported by clicking on “file” menu and choose the “import sbml file” item. After which, user should see the similar workspace as shown in Figure 6-1.
After opening the file, proceed to setting up the simulation. In this example, we have moved all the species to the list in the right panel to monitor their progression as shown in Figure 6-2.
Figure 6-1: Michaelis-Menton Reaction Model
Figure 6-2: List of Species to Monitor
After setting up the simulation, the simulation was started by clicking on the “run” button. The results of the simulation are similar to that is shown in Figure 6-3 and the report of the simulation is shown in Figure 6-4.
Figure 6-3: Results of MM Reactions using Gillespie Algorithms
Figure 6-4: Output Report
After the stochastic simulation, the number of particles of the species E and S was changed to 100. Subsequently, using the deterministic algorithm was setup as shown in Figure 6-5 and the corresponding result is shown in Figure 6-6.
Figure 6-5: Simulation Setup for Deterministic Simulation
Figure 6-6: Simulation Results of MM Reactions using Euler Forward
This model provides a basic model for simulation and modelling using Cellware. Users can modify various simulation and modelling parameters to get a better view of the functionality of Cellware.
Users can also choose to estimate the kinetic parameters by clicking on Analysis->Parameter Estimation. Upon clicking on the icon, user can see a windows panel is seen as shown in Figure 6-7.
Figure 6-7: Parameter Estimation Setup Windows
The input data can be found in the folder “examples/michaelisMenten” with the name “inputData.txt”. After setting up the Algorithm, user can proceed to setting up the Parameters Values (Figure 6-8). As shown in the Figure that we selected all three parameters to be estimated and pre-defined the Lower Bounds and Upper Bounds accordingly.
Figure 6-8: Parameter Setup
After the setup, users can click on the “Run” button to start the job. The progress of the job is shown in the Job Manager Panel (Figure 6-9). After the job is completed, users can click on the “View” button to see the results. Figure 6-10 shows the progress of the estimation while Figure 6-11 shows the set of estimated parameters. Clicking on the “Apply to current model” button will apply the estimated parameters to the current model in the workspace.
Figure 6-9: Job Manager Panel
Figure 6-10: Progress of Parameter Estimation
Figure 6-11: Estimated Parameters
|