A.5 Species Components

The species component definition, lists all the reactions a particular species is allowed to participate in and in what role. The list of actions are separated by the choice operator $(+)$. The concrete syntax, as accepted by the plug-in, is as follows [14]:

$ \begin{array}{r} ID = S; \end{array} $

where $S = action \; | \; S+S$
 
and where an $action$ is defined as:

$ \begin{array}{r} action \;  = \;  (rateID, \;  stoichiometry) \;  op \;  speciesID; \; | \; rateID \;  op \;  speciesID; \; |\;  \\ (\; rateID\; [\; locationID \;  op’ \;  locationID\; ], \;  stoichiometry\; ) \;  (.) \;  ID; \; |\;  \\ rateID\; [\; locationID \;  op’ \;  locationID\; ] \;  (.) \;  ID; \end{array} $

with

$ \begin{array}{r} op \in \{ >>, <<, (+), (−), (.)\}  \end{array} $

and

$op’ \in \{ ->, <->\} $.

The first $ID$ refers to a species, but in this particular definition is labelled as an $ID$ to make it distinct from the the other species identifiers expected within a single species component definition. This identifier must take the first $speciesID$ form of just the species name with no location. Thus, each global species can have at most one definition, with the $speciesID$ used to allow control over where a particular action is permissible. In the case of non-transport definitions, i.e. the first two in the action definition, the $speciesID$ can take any of the previously defined forms. Thus a single reaction can be defined as occurring in the global sense for the species, in a single location, or in a subset of the locations where the species is present [14]. If a reaction occurs in the global sense for the species, then the $speciesID$ identifier may be ommited. For example, in the species components definitions of the a-b-c.biopepa model (see Figure 42), the $speciesID$ identifier after the operation symbol has been ommited in all of the reactions, as they occur in the global sense :

A = a1 << + a3 >> ;

This is equivalent to:

A = a1 << A + a3 >> A;

The identifiers labelled $rateID$ must refer to a previously defined functional rate. Additionally, $stoichiometry$ is the stoichiometric coefficient for the species in this reaction($stoichiometry \in N^{\star }$). If a statement does not specify a stoichiometric coefficient, the default value of one is used. The definition for $action$ shows the syntax for including the stoichiometric coefficient and the abbreviated form for when the stoichiometry is one, these being the first two forms shown in the action definition above [14]. For example, in the species components definitions of the a-b-c.biopepa model (see Figure 42), the stoichiometric coefficient has been omitted, since it has the value of 1 in all cases:

A = a1 << + a3 >> ;

This is equivalent to:

A = (a1,1) << + (a3,1) >> ;

And also equivalent to:

A = (a1,1) << A + (a3,1) >> A;

Transportation represents the movement of a single species between two adjacent locations within the model, as described in [10]. In the defined syntax above (third and fourth action definitions) it requires two $locationIDs$, the first acting as the source and the second as the target and must refer to locations that this particular species resides in. As the locations are embedded within the transportation action, the identifier is simply the species name. The general modifier operator ((.)) is used for transportation as, while the levels of the species in the two locations change, the overall amount does not. Transportation can either be in a single direction or in both directions (unidirectional or bidirectional transportation respectively) [14]. For an example of the unidirectional and the bidirectional transportation see section A.9 and section A.10, respectively.

For the Bio-PEPA Eclipse Plug-in user’s convenience, many of the original Bio-PEPA mathematical symbols have been replaced with textual representations that are available on every keyboard. Table 1 contains the Bio-PEPA symbols and their ASCII representations in the Bio-PEPA Eclipse Plug-in [14]:

Behaviour

BioPEPA symbol

ASCII representation

reactant

$\uparrow $

<<

product

$\downarrow $

>>

activator

$\oplus $

(+)

inhibitor

$\ominus $

(-)

modifier

$\odot $

(.)

unidirectional transportation

$\rightarrow $

->

bidirectional transportation

$\leftrightarrow $

<->

Table 1: Bio-PEPA mathematical symbols and Bio-PEPA Eclipse Plug-in symbol representation