File: DsmtsDimerization.htm

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<html>
<head>
<title>Dimerization</title>
</head>
<body>
<h1>Dimerization</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: 
dimerization <em>2P &rarr; P2</em> and dissociation
<em>P2 &rarr; 2P</em>, which have rate parameters of
<em>k1 = 0.001</em> and <em>k2 = 0.01</em>, respectively.
</p>

<!------------------------------------------------------------------------>
<h2>dsmts-003-01</h2>

<p>
Use the open button <img src="fileopen.png">&nbsp; in the tool
bar to import the file
<tt>examples/sbml/dsmts31/dsmts-003-01.xml</tt>. The model is imported 
correctly and the reactions are recognized as having 
mass-action kinetics.
Open the file <tt>examples/cain/dsmts31/dsmts-003-01.xml</tt>.
Below are plots of the mean and standard deviation of the species 
populations calculated from 10,000 trajectories.
</p>

<p>
<img src="DsmtsDimerization01Mean.jpg">
</p>

<p>
<img src="DsmtsDimerization01StdDev.jpg">
</p>



<!------------------------------------------------------------------------>
<h2>dsmts-003-02</h2>

<p>
This model is the same as dsmts-003-01, except that the initial amount
of <em>P</em> is 1000, and the rate parameters are <em>k1</em>=0.0002
and <em>k2</em>=0.004.
</p>

<p>
<img src="DsmtsDimerization02Mean.jpg">
</p>

<p>
<img src="DsmtsDimerization02StdDev.jpg">
</p>


<!------------------------------------------------------------------------>
<h2>dsmts-003-03</h2>

<p>
This model is the same as dsmts-003-01, except that there is an event
at time 25 with the assignments <em>P</em> = 100 and
<em>P2</em> = 0. Since Cain does
not import events from SBML files, we need to enter the event in the
time events editor. We generate 100 trajectories and plot the mean
and standard deviation of the populations below.
</p>

<p>
<img src="DsmtsDimerization03Mean.jpg">
</p>

<p>
<img src="DsmtsDimerization03StdDev.jpg">
</p>


<!------------------------------------------------------------------------>
<h2>dsmts-003-04</h2>

<p>
This model is the same as dsmts-003-01, except that there is an event
that is triggered when the amount of P2 exceeds 30. This event
performs the assignments <em>P</em> = 100 and <em>P2</em> = 0.
For this model we must add an event in the trigger events editor.
We generate 100 trajectories and plot the mean
and standard deviation of the populations below.
</p>

<p>
<img src="DsmtsDimerization04Mean.jpg">
</p>

<p>
<img src="DsmtsDimerization04StdDev.jpg">
</p>

<p>
Because of the trigger events, it is difficult to discern the actual
behavior of the proces from a plot of the mean and standard deviation of the
populations. We clear the output and generate 10 trajectories, which
are plotted below.
</p>

<p>
<img src="DsmtsDimerization04Trajectories.jpg">
</p>


<!------------------------------------------------------------------------>
<h2>dsmts-003-05</h2>

<p>
This model is the same as dsmts-003-01, except that <em>P</em> has
been removed from the system using the conservation law
<em>P = 100 - 2 P2</em>. The reaction propensities are correctly
imported. However, if you define a method and launch a simulation with
the compile-and-launch button, you will get the following error:
&quot;P2 is used in the propensity function for a stochastic model, but
is not a reactant. Add P2 as both a reactant and a product.&quot;
</p>

<p>
The problem is that Cain uses the lists of reactants and products to
determine under what circumstances it must recompute the reaction
propensities. The solution is to replace the reaction
<em>0 &rarr; P2</em> with an equivalent reaction
<em>P2 &rarr; 2 P2</em>. We generate 10,000 trajectories and plot the
mean and standard deviation of the populations below.
</p>


<p>
<img src="DsmtsDimerization05Mean.jpg">
</p>

<p>
<img src="DsmtsDimerization05StdDev.jpg">
</p>


<!------------------------------------------------------------------------>
<h2>dsmts-003-06</h2>

<p>
This model is the same as dsmts-003-05, except that the rate law
is written differently. The rate law is imported correctly, but
we need to change the dimerization reaction to 
<em>P2 &rarr; 2 P2</em>.
</p>


<!------------------------------------------------------------------------>
<h2>dsmts-003-07</h2>

<p>
This model is the same as dsmts-003-06, except that the rate law
is written differently.
</p>



</body>
</html>