File: DsmtsImmigrationDeath.htm

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<html>
<head>
<title>Immigration-Death</title>
</head>
<body>
<h1>Immigration-Death</h1>

<p>
The models in this section deal with the immigration-death process, which is 
comprised of the immigration reaction <em>0 &rarr; X</em> and the death
reaction <em>X &rarr; 0</em>. 
</p>

<!------------------------------------------------------------------------>
<h2>dsmts-002-01</h2>

<p>
The immigration and death reactions have mass-action kinetic 
laws with rate parameters Alpha = 1 and Mu = 0.1, respectively.
Use the open button <img src="fileopen.png">&nbsp; in the tool bar
to import the file
<tt>examples/sbml/dsmts31/dsmts-002-01.xml</tt>. The model is imported 
correctly and the rate laws are recognized as having 
mass-action kinetics. 
Add a method in the methods list. In the methods editor select
<tt>Time Homogeneous</tt> and <tt>Time Series, Uniform</tt> with 
the default solver and options. Set the recording time to 50 and 
the number of frames to 51. To see the result of these modifications
open the file <tt>examples/cain/dsmts31/dsmts-002-01.xml</tt>.
Below are the plots of the mean and standard deviation of the species 
population calculated from 10,000 trajectories.
</p>

<p>
<img src="DsmtsImmigrationDeath01Mean.jpg">
</p>

<p>
<img src="DsmtsImmigrationDeath01StdDev.jpg">
</p>


<p>
Note that this problem has a steady state solution. Select 
<tt>SteadyState</tt> in the methods list panel. In calculating the steady
state solution, we let the process equilibrate for 100 time units and
then record the state for 100,000 time units. We generate four 
trajectories and plot the steady state histogram, shown below.
</p>

<p>
<img src="DsmtsImmigrationDeath01SteadyState.jpg">
</p>

<p>
With the steady state output selected, click the table button 
<img src="x-office-spreadsheet.png">&nbsp; and then select
<tt>Estimated Error</tt>. The estimated error in the probability
distribution is 0.0045.
</p>


<!------------------------------------------------------------------------>
<h2>dsmts-002-02</h2>

<p>
For this model, the value of the Alpha is changed to 10. Below are plots
of the mean and standard deviation of the species population.
</p>

<p>
<img src="DsmtsImmigrationDeath02Mean.jpg">
</p>

<p>
<img src="DsmtsImmigrationDeath02StdDev.jpg">
</p>


<!------------------------------------------------------------------------>
<h2>dsmts-002-03</h2>

<p>
This model is the same as <tt>dsmts-002-02</tt>, except that the global
parameter Alpha = 10 is overridden by the local parameter Alpha = 5.
Cain does not support overriding global parameters. You will need to
change the value of Alpha in the parameters editor.
</p>


<!------------------------------------------------------------------------>
<h2>dsmts-002-04</h2>

<p>
This model is the same as <tt>dsmts-002-02</tt>, except that 
Alpha = 1,000. This increases the reaction rates and makes the simulation
more expensive. Thus we only generate 1,000 trajectories in calculating
the mean and standard deviation of the species populations.
</p>

<p>
<img src="DsmtsImmigrationDeath04Mean.jpg">
</p>

<p>
<img src="DsmtsImmigrationDeath04StdDev.jpg">
</p>


<!------------------------------------------------------------------------>
<h2>dsmts-002-05</h2>

<p>
This model is the same as <tt>dsmts-002-02</tt>, except that there are 
two additional species Source and Sink, which are both boundary conditions.
Cain does not support boundary conditions.
</p>


<!------------------------------------------------------------------------>
<h2>dsmts-002-06</h2>

<p>
This model is the same as <tt>dsmts-002-05</tt>, except that Sink is 
not a boundary condition.
</p>


<!------------------------------------------------------------------------>
<h2>dsmts-002-07</h2>

<p>
This model is the same as <tt>dsmts-002-05</tt>, except that Sink is 
a constant boundary condition.
</p>


<!------------------------------------------------------------------------>
<h2>dsmts-002-08</h2>

<p>
This model tests parameter loading, which is not supported in Cain.
</p>


<!------------------------------------------------------------------------>
<h2>dsmts-002-09</h2>

<p>
This model is the same as <tt>dsmts-002-01</tt>, except that an event is 
triggered at time 25 which sets the value of <em>X</em> to 50. Although
Cain supports events, it will not parse events in SBML files. Thus one
must enter the events in either the time events editor or the trigger
events panel.
Open the file <tt>examples/cain/dsmts31/dsmts-002-09.xml</tt> to see 
how to enter the appropriate time event. For models that utilize events,
we must use solvers in the <tt>Use Events</tt> category, which are much
slower than the other solvers. Thus we only generate 100 trajectories 
to calculate the mean and standard deviation plotted below.
</p>

<p>
<img src="DsmtsImmigrationDeath09Mean.jpg">
</p>

<p>
<img src="DsmtsImmigrationDeath09StdDev.jpg">
</p>


<!------------------------------------------------------------------------>
<h2>dsmts-002-10</h2>

<p>
This model is the same as <tt>dsmts-002-09</tt>, except that the event is 
triggered at time 22.5 and <em>X</em> is assigned the value 20.
</p>


</body>
</html>