Hi Andrew, This looks quite intriguing. As you mention later in this thread I currently take the approach of adding an extra real scalar term and exposing that as a way to hook future (in my case) currents into ion concentration rate equations. Such and approach works well when I only have three ion concentrations to deal with, but gets overwhelming when considering many different species, such as happens when adding metabolic processes to an electrophysiology model.
Just to try and better understand your proposal by use of an example closer to my own work and perhaps to also check that this approach is not limited to metabolic models... Using this method, I would be able to say that each calcium membrane current is in the set of calcium fluxes and then formulate the time derivative of intracellular calcium concentration to be a sum over all fluxes in that set. Then as I extend the model I simply specify any new calcium currents as being in the set of calcium fluxes and the intracellular calcium concentration automatically has them included. Have I got that right? Assuming I have understood this, how hard do you expect it to be to implement support for such set summation techniques in the current Auckland API implementation? I would guess this falls into the code generation services rather than the core API implementation? Andre. Andrew Miller wrote: > 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 > [email protected] > http://www.cellml.org/mailman/listinfo/cellml-discussion -- David Nickerson, PhD Research Fellow Division of Bioengineering Faculty of Engineering National University of Singapore Email: [EMAIL PROTECTED] _______________________________________________ cellml-discussion mailing list [email protected] http://www.cellml.org/mailman/listinfo/cellml-discussion
