The Bio-PEPA Eclipse Plug-inUser Manual: A model of oscillations

8.1 A model of oscillations

The a-b-c.biopepa model (see Figure 24) contains three species $A$ , $B$ and $C$ which are involved in three reactions $\mathit{a1}$ , $\mathit{a2}$ , $\mathit{a3}$ . Each reaction is governed by a kinetic parameter $r1$ , $r2$ and $r3$ respectively, which controls the rate of the reaction. All three parameters $r1$ , $r2$ and $r3$ have been given the constant value 0.01. The rates of the reactions also depend on the available quantity of the species that are involved in them. The kinetic law for the $\mathit{a1}$ reaction is the product of $r1$ , $A$ and $B$ . The kinetic law for the $\mathit{a2}$ reaction is the product of $r2$ , $B$ and $C$ . The kinetic law for the $\mathit{a3}$ reaction is the product of $r1$ , $C$ and $A$ . $A$ is decreased (<<) by the $\mathit{a1}$ reaction and increased (>>) by the $\mathit{a3}$ reaction. $B$ is increased (>>) by the $\mathit{a1}$ reaction and decreased (<<) by the $\mathit{a2}$ reaction. $C$ is decreased (<<) by the $\mathit{a3}$ reaction and increased (>>) by the $\mathit{a2}$ reaction. An alternative description of the model is provided by the Outline view (see Figure 25).

$\includegraphics[scale=0.5]{screenshots/screenshots/abc_model}$

Figure 42: The a-b-c.biopepa model

$\includegraphics[scale=0.5]{screenshots/screenshots/abc_model_outline}$

Figure 43: The a-b-c.biopepa model outline view

As you can see in Figure 42, there are warning signs appearing in the editor. The Problem View informs us that component $A$ affects the rate of reaction $\mathit{a3}$ but is not a reactant. There are similar warnings for components $B$ and $C$ (see Figure 44).

$\includegraphics[scale=0.5]{screenshots/screenshots/abcerrors}$

Figure 44: The Problems View for the a-b-c.biopepa model

These warnings are due to an abstraction in the species component definitions. The full definition of the species components is:

`A`	`=`	`a1 << + a3 >> + a3 (+);`
`B`	`=`	`a2 << + a1 >> + a1 (+);`
`C`	`=`	`a2 >> + a2 (+) + a3 << ;`

Component $A$ acts as an activator for reaction $\mathit{a3}$ and that is why it affects the rate of the reaction despite the fact that it is not a reactant. Similarly, component $B$ is an activator for reaction $\mathit{a1}$ and component $C$ is an activator for $\mathit{a2}$ . However, the Bio-PEPA Eclipse Plug-in syntax does not allow us to specify two roles for a component in the same reaction. This is an example of a warning that alerts us to a potential problem. However, since we understand the cause of the warnings and know that it will not affect the correctness of the analysis we can simply ignore them.