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I think this is really neat, well done on an elegant idea.

One thing is bugging me: I'll illustrate by means of an example:
We would be inferring that the set fluxes consists of only the elements
{f1,f2,f3} from the three statements: "f1 in fluxes", "f2 in fluxes", "f3 in
fluxes".
But if fluxes={f1,f2,f3,f4,f5}, that would still be consistent with the
above three "in"/"is an element of" statements.

So, this proposal means that we are kind of hacking the "in" operator to
indicate an imperative action of "now adding this element to this set".
Anything that is not declared to be added to the set in this way is
considered not in the set. Whereas, the true spirit of the "is an element
of" operator is the weaker form, meaning that other elements could also be
in the set.

Perhaps we should just create a construct that unashamedly imperatively adds
the elements to the set. It would be a CellML construct, rather than a
MathML construct. Initial values are done under CellML and smack of an
imperative style rather than a declarative style, and could have been done
under MathML by saying the value of a variable at time t=t0 is such, so it
is not out of the spirit of CellML to break away from the declarative style
when it is pragmatic to do so.

So, I'm proposing removing the "in" statements from the MathML, and
replacing them with CellML statements like <addToSet set="flux_a"
element="flux_a_member1" />

Where flux_a_member1 is defined in the MathML, something like: "declare
flux_a_member1 is lambda(-overallRate)".

Regards,
Randall

> -----Original Message-----
> From: cellml-discussion-bounces at cellml.org [mailto:cellml-discussion-
> bounces at cellml.org] On Behalf Of Andrew Miller
> Sent: Wednesday, 30 January 2008 5:52 p.m.
> To: For those interested in contributing to the development of CellML.
> Subject: [cellml-discussion] Using proposed CellML 1.2 features to
> create more re-usable metabolic models
>
> Hi all,
>
> To aid in working out what features we should include in CellML 1.2, I
> have been looking into one of the major difficulties with creating
> re-usable metabolic models at the moment: that to compute a derivative,
> you need to know all the fluxes, but when a model is extended, new
> fluxes can be added to the model. Ideally, we should be able to define
> CellML 1.2 so that structured types can be leveraged to avoid this
> issue.
>
> I have come up with an example of how this might look in CellML 1.2.
> This is based in part off a discussion that I had earlier with Poul, so
> most of the credit for this goes to him, while most of the blame for
> the
> inelegant parts goes to me.
>
> Note that the lambda constructs without any bound variables are there
> to
> defer interpretation of the fluxes until they are taken from the set.
> The rationale for needing this is that if we had two statements that a
> certain real-valued flux belongs in the set, and two of them happened
> to
> have the same value at a particular point in time, then summing over
> the
> set would only include the flux value once (e.g. saying x is an element
> of N, where N is in the natural numbers, means that the value of x is a
> natural number. Saying x=5, y=5, x in N, y in N does not mean that 5 is
> in the set of natural numbers twice). On the other hand, we can have
> two
> different zero argument lambda functions in a set, which just happen to
> evaluate to the same value. This is consistent with the declarative
> nature of CellML - we are not saying 'add this flux to the set of
> fluxes', but rather, we are making a series of statements about what is
> in the set of fluxes, and the processing software is then summing over
> all fluxes which have been explicitly mentioned. Because we can connect
> the set of fluxes up to an importing model, doing things this way gives
> a great deal of extra flexibility.
>
> Notes:
> 1) In practice, the substance could become an import which is re-used
> many times, and likewise for components representing various general
> types of chemical reactions.
> 2) I have invented a possible way in which we could remove
> directionality from connections. No one has come up with a formal
> proposal to do it this way yet.
> 3) I have followed Randall's earlier suggestion about how to structure
> connections without using component_ref. This again needs a formal
> proposal and discussion.
> 4) The model uses a potential way in which we could get rid of the
> generality of groups, by replacing group and relationship_ref with a
> simple encapsulation element. This again needs to be formally proposed
> and discussed at some point.
>
> <?xml version="1.0" encoding="UTF-8"?>
> <model
> xmlns="http://www.cellml.org/cellml/1.1#";
> xmlns:c11="http://www.cellml.org/cellml/1.1#";
> xmlns:c12="http://www.cellml.org/cellml/1.2#";
> xmlns:m="http://www.w3.org/1998/Math/MathML";
> name="_1_2_example"
> >
> <component name="substance_x">
> <c12:variable name="fluxes" type="set_of_lambda_of_real"
> units="mol_per_litre_per_second"
> public_interface="yes" />
> <c12:variable name="concentration" units="mol_per_litre"
> public_interface="yes" />
> <c12:variable name="time" units="second" public_interface="yes" />
> <m:math>
> <m:apply><m:eq/>
> <m:apply><m:diff/>
> <m:bvar><m:ci>time</m:ci></m:bvar>
> <m:ci>concentration</m:ci>
> </m:apply>
> <m:apply><m:sum />
> <m:bvar><m:ci>f</m:ci></m:bvar>
> <m:condition>
> <m:apply>
> <m:in/>
> <m:ci>f</m:ci>
> <m:ci>fluxes</m:ci>
> </m:apply>
> </m:condition>
> <m:apply>
> <m:ci>f</m:ci>
> </m:apply>
> </m:apply>
> </m:apply>
> </m:math>
> </component>
>
> <component name="substance_a">
> <!-- Identical to substance_x. This would normally be defined once
> and imported.
> -->
> </component>
>
> <component name="substance_b">
> <!-- Identical to substance_x. This would normally be defined once
> and imported.
> -->
> </component>
>
> <component name="substance_y">
> <!-- Identical to substance_x. This would normally be defined once
> and imported.
> -->
> </component>
>
> <!-- Represents a reaction A + B -> X -->
> <component name="reaction_a_b_x">
> <c12:variable name="concentration_a" units="mol_per_litre"
> public_interface="yes" />
> <c12:variable name="concentration_b" units="mol_per_litre"
> public_interface="yes" />
> <c12:variable name="concentration_x" units="mol_per_litre"
> public_interface="yes" />
> <c12:variable name="flux_a"
> public_interface="yes"
> type="set_of_lambda_of_real"
> units="mol_per_litre_per_second" />
> <c12:variable name="flux_b"
> public_interface="yes"
> type="set_of_lambda_of_real"
> units="mol_per_litre_per_second" />
> <c12:variable name="flux_x"
> public_interface="yes"
> type="set_of_lambda_of_real"
> units="mol_per_litre_per_second" />
> <variable name="kf" units="litres_per_mol_per_second"
> initial_value="0.5" />
> <variable name="kb" units="litres_per_mol_per_second"
> initial_value="0.1" />
> <variable name="overall_rate" units="mol_per_litre_per_second" />
> <m:math>
> <m:apply><m:eq/>
> <m:ci>overall_rate</m:ci>
> <!-- First order law of mass action... -->
> <m:apply><m:minus/>
> <m:apply><m:times/>
> <m:ci>kf</m:ci>
> <m:ci>concentration_a</m:ci>
> <m:ci>concentration_b</m:ci>
> </m:apply>
> <m:apply><m:times/>
> <m:ci>kb</m:ci>
> <m:ci>concentration_x</m:ci>
> </m:apply>
> </m:apply>
> </m:apply>
> <m:apply><m:in/>
> <m:lambda>
> <m:apply><m:minus/>
> <m:ci>overall_rate</m:ci>
> </m:apply>
> </m:lambda>
> <m:ci>flux_a</m:ci>
> </m:apply>
> <m:apply><m:in/>
> <m:lambda>
> <m:apply><m:minus/>
> <m:ci>overall_rate</m:ci>
> </m:apply>
> </m:lambda>
> <m:ci>flux_b</m:ci>
> </m:apply>
> <m:apply><m:in/>
> <m:lambda>
> <m:ci>overall_rate</m:ci>
> </m:lambda>
> <m:ci>flux_x</m:ci>
> </m:apply>
> </m:math>
> </component>
>
> <!-- Represents a reaction A + X -> Y -->
> <component name="reaction_a_x_y">
> <c12:variable name="concentration_a" units="mol_per_litre"
> public_interface="yes" />
> <c12:variable name="concentration_y" units="mol_per_litre"
> public_interface="yes" />
> <c12:variable name="concentration_x" units="mol_per_litre"
> public_interface="yes" />
> <c12:variable name="flux_a"
> public_interface="yes"
> type="set_of_lambda_of_real"
> units="mol_per_litre_per_second" />
> <c12:variable name="flux_y"
> public_interface="yes"
> type="set_of_lambda_of_real"
> units="mol_per_litre_per_second" />
> <c12:variable name="flux_x"
> public_interface="yes"
> type="set_of_lambda_of_real"
> units="mol_per_litre_per_second" />
> <variable name="kf" units="litres_per_mol_per_second"
> initial_value="0.5" />
> <variable name="kb" units="litres_per_mol_per_second"
> initial_value="0.1" />
> <variable name="overall_rate" units="mol_per_litre_per_second" />
> <m:math>
> <m:apply><m:eq/>
> <m:ci>overall_rate</m:ci>
> <!-- First order law of mass action... -->
> <m:apply><m:minus/>
> <m:apply><m:times/>
> <m:ci>kf</m:ci>
> <m:ci>concentration_a</m:ci>
> <m:ci>concentration_x</m:ci>
> </m:apply>
> <m:apply><m:times/>
> <m:ci>kb</m:ci>
> <m:ci>concentration_y</m:ci>
> </m:apply>
> </m:apply>
> </m:apply>
> <m:apply><m:in/>
> <m:lambda>
> <m:apply><m:minus/>
> <m:ci>overall_rate</m:ci>
> </m:apply>
> </m:lambda>
> <m:ci>flux_a</m:ci>
> </m:apply>
> <m:apply><m:in/>
> <m:lambda>
> <m:apply><m:minus/>
> <m:ci>overall_rate</m:ci>
> </m:apply>
> </m:lambda>
> <m:ci>flux_x</m:ci>
> </m:apply>
> <m:apply><m:in/>
> <m:lambda>
> <m:ci>overall_rate</m:ci>
> </m:lambda>
> <m:ci>flux_y</m:ci>
> </m:apply>
> </m:math>
> </component>
>
> <component name="abxy_system">
> <c12:variable name="concentration_a" units="mol_per_litre"
> public_interface="yes" />
> <c12:variable name="concentration_b" units="mol_per_litre"
> public_interface="yes" />
> <c12:variable name="concentration_x" units="mol_per_litre"
> public_interface="yes" />
> <c12:variable name="concentration_y" units="mol_per_litre"
> public_interface="yes" />
> <c12:variable name="flux_a"
> public_interface="yes"
> type="set_of_lambda_of_real"
> units="mol_per_litre_per_second" />
> <c12:variable name="flux_b"
> public_interface="yes"
> type="set_of_lambda_of_real"
> units="mol_per_litre_per_second" />
> <c12:variable name="flux_x"
> public_interface="yes"
> type="set_of_lambda_of_real"
> units="mol_per_litre_per_second" />
> <c12:variable name="flux_y"
> public_interface="yes"
> type="set_of_lambda_of_real"
> units="mol_per_litre_per_second" />
> </component>
>
> <c12:connection component_1="substance_a"
> component_2="reaction_a_b_x">
> <variable_ref variable_1="concentration"
> variable_2="concentration_a" />
> <variable_ref variable_1="flux" variable_2="flux_a" />
> </c12:connection>
> <c12:connection component_1="substance_b"
> component_2="reaction_a_b_x">
> <variable_ref variable_1="concentration"
> variable_2="concentration_b" />
> <variable_ref variable_1="flux" variable_2="flux_b" />
> </c12:connection>
> <c12:connection component_1="substance_x"
> component_2="reaction_a_b_x">
> <variable_ref variable_1="concentration"
> variable_2="concentration_x" />
> <variable_ref variable_1="flux" variable_2="flux_x" />
> </c12:connection>
>
> <c12:connection component_1="substance_a"
> component_2="reaction_a_x_y">
> <variable_ref variable_1="concentration"
> variable_2="concentration_a" />
> <variable_ref variable_1="flux" variable_2="flux_a" />
> </c12:connection>
> <c12:connection component_1="substance_x"
> component_2="reaction_a_x_y">
> <variable_ref variable_1="concentration"
> variable_2="concentration_x" />
> <variable_ref variable_1="flux" variable_2="flux_x" />
> </c12:connection>
> <c12:connection component_1="substance_y"
> component_2="reaction_a_x_y">
> <variable_ref variable_1="concentration"
> variable_2="concentration_y" />
> <variable_ref variable_1="flux" variable_2="flux_y" />
> </c12:connection>
>
> <c12:connection component_1="substance_a" component_2="abxy_system">
> <variable_ref variable_1="concentration"
> variable_2="concentration_a" />
> <variable_ref variable_1="flux" variable_2="flux_a" />
> </c12:connection>
> <c12:connection component_1="substance_b" component_2="abxy_system">
> <variable_ref variable_1="concentration"
> variable_2="concentration_b" />
> <variable_ref variable_1="flux" variable_2="flux_b" />
> </c12:connection>
> <c12:connection component_1="substance_x" component_2="abxy_system">
> <variable_ref variable_1="concentration"
> variable_2="concentration_x" />
> <variable_ref variable_1="flux" variable_2="flux_x" />
> </c12:connection>
> <c12:connection component_1="substance_y" component_2="abxy_system">
> <variable_ref variable_1="concentration"
> variable_2="concentration_y" />
> <variable_ref variable_1="flux" variable_2="flux_y" />
> </c12:connection>
>
> <c12:encapsulation>
> <component_ref component="abxy_system">
> <component_ref component="substance_a"/>
> <component_ref component="substance_b"/>
> <component_ref component="substance_x"/>
> <component_ref component="substance_y"/>
> <component_ref component="reaction_a_b_x"/>
> <component_ref component="reaction_a_x_y"/>
> </component_ref>
> </c12:encapsulation>
>
> <!-- Units would also be defined here, as in CellML 1.1... -->
> </model>
>
> _______________________________________________
> cellml-discussion mailing list
> cellml-discussion at cellml.org
> http://www.cellml.org/mailman/listinfo/cellml-discussion

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• [cellml-discussion] Using proposed CellML 1.2 features to create more re-usable metabolic models, Randall Britten, 02/01/2008
  • [cellml-discussion] Using proposed CellML 1.2 features to create more re-usable metabolic models, Justin Marsh, 02/04/2008

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