File: DsmtsDimerisation.htm

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<html>
<head>
<title>Dimerisation</title>
</head>
<body>
<h1>Dimerisation</h1>

<p>
The dimerisation process has two species <em>P</em> and <em>P2</em>
with initial amounts of 100 and 0, respectively.
There are two reactions which both have mass-action kinetics: 
<em>2P &rarr; P2</em> and <em>P2 &rarr; 2P</em>
and two reactions
</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 <tt>File&rarr;Import SBML</tt> to import the file
<tt>examples/sbml/dsmts31/dsmts-001-01.xml</tt>. The model is imported 
correctly, however the reactions are not recognized as having 
mass-action kinetics. Edit the reactions to reflect this.
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 is the plot of the mean and standard deviation of the species 
population calculated from 10,000 trajectories. (We have set the lower
bound on the Y axis to 0 in the plot configuration window.)
</p>

<img src="DsmtsImmigrationDeath01MeanStdDev.jpg">


<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>

<img src="DsmtsImmigrationDeath01SteadyState.jpg">

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



</body>
</html>