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<html>
<head>
<title>Reaction Editor</title>
</head>
<body>
<h1>Reaction Editor</h1>
<p align="center">
<img src="ReactionEditor.png">
</p>
<p>
The identifier and name for a reaction are analogous to those for a
species. By default the name field is hidden.
Specify the reactants and products by typing the species
identifiers preceded by their stoichiometries. For example: "s1",
"s1 + s2", "2 s2", or
"2 s1 + s2 + 2 s3". The stoichiometries must be positive
integers. A reaction may have an empty set of reactants or an empty
set of products, but not both. (A "reaction" without
reactants or products has no effect on the system.)
The <tt>MA</tt> field indicates if the equation has mass-action kinetics.
In the
<tt>Propensity</tt> field you can either enter a propensity factor for
use in a mass-action kinetic law or you can enter an arbitrary
propensity function. The reactions editor has the same tool bar as
the species editor. Again, you will be informed of any bad input when
you try to launch a simulation.
</p>
<p>
If the <tt>MA</tt> field is checked, a reaction will use a mass-action
kinetics law. For this case you can enter a number or a Python
expression that evaluates to a number in the <tt>Propensity</tt>
field. This non-negative number will be used as the propensity factor
in the reaction's propensity function. Below are some examples of
reactions and their propensity functions for a propensity factor of
<em>k</em>. [X] indicates the population of species X. The population
is measured in substance units, for example number of molecules, and
not in concentration units. (In the table
below 0 indicates the empty set; either no reactants or no products.)
</p>
<!--CONTINUE: Tables are not currently rendered correctly.
<table border="1">
<tr><th>Reaction<th>Propensity Function
<tr><td>0 → X<td>k
<tr><td>X → Y<td>k [X]
<tr><td>X + Y → Z<td>k [X] [Y]
<tr><td>2 X → Y<td>k [X] ([X] - 1)/ 2
</table>
-->
<pre><b>
Reaction Propensity Function</b>
-------------------------------
0 → X k
X → Y k [X]
X + Y → Z k [X] [Y]
2 X → Y k [X] ([X] - 1)/ 2
</pre>
<p>
If the <tt>MA</tt> field is not checked the <tt>Propensity</tt> field
is used as the propensity function. For example, you might
to use a
<a href="http://en.wikipedia.org/wiki/Michaelis_menten">Michaelis-Menten</a>
kinetic law. Use the species identifiers
to indicate the species populations. You can use any model parameters
in defining the function. The format of the function must be
a C++ expression. (Don't worry if you don't know C++. Just remember to use
* for multiplication instead of a space. Also, if you divide by a number use a
decimal point in it. For example, write "5/2." or "5/2.0" instead of "5/2".
<a href="http://en.wikipedia.org/wiki/Integer_division#Division_of_integers">
Integer division</a> instead of floating point division will be used in the
third expression resulting in 2 instead of 2.5.)
Below are
some examples of valid expressions for propensity functions. Assume that
the species identifiers are s1, s2, ...
</p>
<!--CONTINUE: Tables are not currently rendered correctly.
<table border="1">
<tr><th>C++ Expression<th>Propensity Function
<tr><td>2.5<td>2.5
<tr><td>5*pow(s1, 2)<td>5 [s1]<sup>2</sup>
<tr><td>1e5*s2<td> 100000 [s2]
<tr><td>P*s1*s2/(4+s2)<td> P [s1] [s2] / (4 + [s2])
<tr><td>log(Q)*sqrt(s1)<td> log(Q) √[s1]
</table>
-->
<pre><b>
C++ Expression Propensity Function</b>
------------------------------------
2.5 2.5
5*pow(s1, 2) 5 [s1]<sup>2</sup>
1e5*s2 100000 [s2]
P*s1*s2/(4+s2) P [s1] [s2] / (4 + [s2])
log(Q)*sqrt(s1) log(Q) √[s1]
</pre>
<p>
Here we assume that <tt>P</tt> and <tt>Q</tt> have been defined as parameters.
Note that you do not have to use the <tt>std</tt> namespace qualification
with the standard math functions like <tt>sqrt</tt>, <tt>log</tt>, and
<tt>exp</tt>. The expressions will be evaluated in a function with a
<tt>using namespace std;</tt> declaration.
</p>
<p>
Most of the stochastic simulation methods store the values of the
propensity functions and recompute them only when the values
change. (This innovation was introduced with the
<a href=SimulationNext.htm>next reaction method</a>.) If firing a
certain reaction modifies a species <em>X</em> then any propensity
that depends on <em>X</em> must be recomputed. For mass-action
kinetic laws, the propensity function depends on the reactants. Thus
we use the reactants to determine the reaction dependencies.
</p>
<p>
There is a technical issue with custom propensities when simulating a
model with a stochastic method: If one uses a species
population in the propensity function, then that species must appear as a
reactant. Otherwise the reaction dependencies will not be determined correctly.
For example consider a system with two species <em>X</em> and <em>Y</em>.
Suppose one had the reaction <em>0 → X</em> with the custom propensity
<em>Y</em>. Of course the propensity does not make physical sense, but that
is beside the point. Cain will not allow this reaction. Attempting to launch
a stochastic simulation will produce an error message.
(One can, however, run a deterministic simulation.)
To ammend the reaction one must
add <em>Y</em> as a reactant (and as a product so as to leave the kinetics
unchanged). The reaction <em>Y → X + Y</em> is allowed.
Physically speaking, <em>Y</em> is a substrate.
</p>
</body>
</html>
|
