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Hi Herb,

It seems the notion of modifier is underspecified. Here is one
consistent interpretation. Let's call it the "implicit OR"
interpretation:

A list of modifiers is anything that participates in the catalysis of
the reaction. Each modifier is capable of independently catalyzing
the reaction. (implicit OR)
If all modifier concentrations are zero, then the reaction cannot be
catalyzed.

To deal with stoichiometries of modifiers, if two species are subunits
of a complex that catalyzes the reaction, then this should be
represented as a separate binding reaction:
So, for your example:

2A + B -> 2A + C,

you would specify this with two reactions. The first is the binding
reaction:
2 A -> A_homodimer

The second is the biochemical conversion:
A_homodimer + B -> A_homodimer + C

This would be represented in the SBML fragment below:

<listOfSpecies>
<species id="A"/>
<species id="A_homodimer"/>
<species id="B"/>
<species id="C"/>
</listOfSpecies>
<listOfReactions>
<reaction id="binding_rxn" name="2 A -> A_dimer">
<listOfReactants>
<speciesRef species="A" stoichiometry="2"/>
</listOfReactants>
<listOfProducts>
<speciesRef species="A_homodimer"/>
</listOfProducts>
</reaction>
<reaction id="biochemicalConversion_rxn" name="2A + B -> 2A + C">
<listOfReactants>
<speciesRef species="B"/>
</listOfReactants>
<listOfProducts>
<speciesRef species="C"/>
</listOfProducts>
<listOfmodifiers>
<speciesRef species="A_homodimer"/>
</listOfModifiers>
</reaction>
</listOfReactions>


If you wanted to specify isozymes of a reaction:

2A + B -> 2A + C
and
D + B -> D + C
Then this could be represented by placing both modifiers in the
listOfModifiers of the B->C biochemical conversion.

<listOfSpecies>
<species id="A"/>
<species id="A_homodimer"/>
<species id="B"/>
<species id="C"/>
<species id="D"/>
</listOfSpecies>
<listOfReactions>
<reaction id="binding_rxn" name="2 A -> A_dimer">
<listOfReactants>
<speciesRef species="A" stoichiometry="2"/>
</listOfReactants>
<listOfProducts>
<speciesRef species="A_homodimer"/>
</listOfProducts>
</reaction>
<reaction id="biochemicalConversion_rxn" name="2A + B -> 2A + C">
<listOfReactants>
<speciesRef species="B"/>
</listOfReactants>
<listOfProducts>
<speciesRef species="C"/>
</listOfProducts>
<listOfModifiers>
<speciesRef species="A_homodimer"/>
<speciesRef species="D"/>
</listOfModifiers>
</reaction>
</listOfReactions>


This interpretation is consistent with the BioPAX concepts of
BiochemicalConversion, ComplexFormation, and Catalysis.
If one wanted to represent cofactors of a reaction, (such as
Magnesium), one would represent the cofactor as a modifier of the
binding reaction:


<listOfSpecies>
<species id="A"/>
<species id="A_homodimer"/>
<species id="B"/>
<species id="C"/>
<species id="D"/>
<species id="Mg"/>
</listOfSpecies>
<listOfReactions>
<reaction id="binding_rxn" name="2 A -> A_dimer">
<listOfReactants>
<speciesRef species="A" stoichiometry="2"/>
</listOfReactants>
<listOfProducts>
<speciesRef species="A_homodimer"/>
</listOfProducts>
<listOfModifiers>
<modifierspeciesRef species="Mg"/>
</listOfModifiers>
</reaction>
<reaction id="biochemicalConversion_rxn" name="2A + B -> 2A + C">
<listOfReactants>
<speciesRef species="B"/>
</listOfReactants>
<listOfProducts>
<speciesRef species="C"/>
</listOfProducts>
<listOfModifiers>
<speciesRef species="A_homodimer"/>
<speciesRef species="D"/>
</listOfModifiers>
</reaction>
</listOfReactions>

It gets trickier if you want to specify that 3 Mg's are required for
the formation of the A_homodimer. In that case, you are best off
representing
the Enzyme-cofactor complex as an additional species.

2 A + 3 Mg -> A_Mg_homodimer


<listOfSpecies>
<species id="A"/>
<species id="A_Mg_homodimer"/>
<species id="B"/>
<species id="C"/>
<species id="D"/>
<species id="Mg"/>
</listOfSpecies>
<listOfReactions>
<reaction id="enzyme_cofactor_complex" name="2 A+ 3 Mg->A_Mg_homodimer">
<listOfReactants>
<speciesRef species="A" stoichiometry="2"/>
<speciesRef species="Mg" stoichiometry="3"/>
</listOfReactants>
<listOfProducts>
<speciesRef species="A_Mg_homodimer"/>
</listOfProducts>
</reaction>
<reaction id="biochemicalConversion_rxn" name="2A + B -> 2A + C">
<listOfReactants>
<speciesRef species="B"/>
</listOfReactants>
<listOfProducts>
<speciesRef species="C"/>
</listOfProducts>
<listOfModifiers>
<speciesRef species="A_Mg_homodimer"/>
<speciesRef species="D"/>
</listOfModifiers>
</reaction>
</listOfReactions>


Of course, these distinctions are much clearer in the BioPAX ontology.
I will show the representation in a follow-up email.

Jeremy





On Apr 25, 2005, at 5:40 PM, Herbert Sauro wrote:

>
> I too am curious how a modifier can have a stoichiometry, that is a
> true
> modifier not a molecule that is explicitly described as a binding
> reaction, eg a WMC model of an allosteric enzyme.
>
> Herbert
>
> -----Original Message-----
> From: Pedro Mendes [mailto:mendes@vbi.vt.edu]
> Sent: Monday, April 25, 2005 12:40 PM
> To: sbml-discuss@caltech.edu
> Subject: Re: [sbml-discuss] stoichiometries of modifiers
>
> I'm rather intrigued by this "modifier stoichiometry". Modifiers do not
> even have to bind anything, so I don't think the concept of
> stoichiometry applies here. The way in which a modifier modifies the
> rate of reaction is explicit on the rate law.
>
> Pedro
>
> On Monday 25 April 2005 12:56 pm, Hiroyuki Kuwahara wrote:
>> Hi,
>>
>> I'd just like to know why SBML does not support stoichiometries of
>> modifiers. This is fine for ODE simulation, but not for discrete
>> stochastic simulation. The workaround, of course, is to express a
>> modifier as both a reactant and a product with an appropriate
>> stoichiometry. But if this is how it's supposed to be, then we don't
>> even need a modifier field.
>>
>> Thanks,
>>
>> Hiro
>
> --
> Pedro Mendes
> Research Associate Professor
> Virginia Bioinformatics Institute,
> Virginia Tech, Washington St.,
> Blacksburg, VA 24061-0477, USA
> http://mendes.vbi.vt.edu fax:+1-540-231-2606
>
>
Jeremy Zucker
Bioinformatics Specialist
Dana-Farber Cancer Institute
url: http://research.dfci.harvard.edu
email: zucker@research.dfci.harvard.edu
work: 617-632-6852
cell: 617-833-3196