Re: [SOSlib-devel] implementing variable compartments[Scanned]

[Andrew F. <af...@ph...>]

Folks

So what your suggesting is pretty simple:
for any SBML system always transform the system to
create ODEs of rates of substance change
and assignment rules that derive concentrations from substance.

That's pretty straightforward I think.  I'm happy.

Note:

I don't think you need to actually substitute the x.amount/volume into
the
ODEs if you have the assignment rules.  In SOSlib

x2 =3D x2.amount/volume
dx1.amount/dt =3D k * x2
dx2.amount/dt =3D ???

should be equivalent to:

dx1.amount/dt =3D k * (x2.amount/volume)
dx2.amount/dt =3D ???

This works because the relevant assignment rules are evaluated in the
CVODE rhs function
before evaluating the ODEs themselves.

Or am I missing something? An issue with the jacobian???

If the above isn't true then the way assignment rules work
in the general case is wrong too.

yours Andrew

> -----Original Message-----
> From: sbm...@li...=20
> [mailto:sbm...@li...] On=20
> Behalf Of Stefan Mueller
> Sent: 21 June 2006 16:51
> To: sbm...@li...
> Subject: Re: [SOSlib-devel] implementing variable=20
> compartments[Scanned]
>=20
> rainer
>=20
> > Stefan, thanks for the clarification in your last email.
> >
> > i think i got it now :)
> >
> > you wrote:
> > > the ode for conc can be derived by differentiating x=3DX/V:
> > > dx/dt =3D (dX/dt)/V - x*(dV/dt)/V
> > > where dX/dt is given by the kinetic law above.
> >
> > dX/dt is just the sum of the +/- (stoichiometry*kineticLaw)=20
> > expressions for all reactions where X is a=20
> product/reactant, i.e. it=20
> > is a function of concentrations x, y, z ...
> >
> > Right? (If not forget, the rest ...)
>=20
> right.
>=20
> > So actually, the first part of this equation (dX/dt)/V is=20
> the current=20
> > form of ODEs in SOSlib!
> >
> > Could the implementation of variable compartments in SOSlib=20
> would be=20
> > as easy as:
> >
> > 1) add the expression " - x*(dV/dt)/V "
> > to the concentration ODEs for species in a variable compartment?
>=20
> yes.
>=20
> > 2a) if the compartment is defined by a rate rule, this rate=20
> rule could=20
> > be appended to all ODEs directly, i.e.
> >
> > newODE =3D currentODE - (x/V) * rateRule
>=20
> yes.
>=20
> > 2b) if the compartment is defined by an assignment rule, we=20
> would have=20
> > differentiate it towards time? For this we need to convert the=20
> > assignment rule to a form, where differentiateAST recognizes time=20
> > dependent variables that are in the assignment rule, e.g.=20
> x(t), which=20
> > appears only as ASTNode "x". Is this possible/easy?
>=20
> possible.
> easy? differentiateAST has to extended.
> there must be differentiation with respect to time, but only=20
> variables for which there is an ode are differentiated.
> (and the rhs of the ode is the result.)
> the chain rule does the rest of the work...
>=20
> > 2c) if the compartment is changed by events, we don't need=20
> to append=20
> > anything but just recalculate concentrations and re-initialize the=20
> > solver, just as we do now for events.
> >
> >
> > If above is right - but i guess it might just not be that easy - we=20
> > would have extracted two alternatives:
> >
> > A) use ODEs in substance/time, write assignment rules for=20
> x.amount =3D x=20
> > / volume and replace all x by x.amount in ODEs, as Andrew suggested
>=20
> you mean: x =3D x.amount / volume !?
>=20
> > or
> >
> > B) use above approach.
> >
> > Is that it?
>=20
> yes.
> i vote for alternative A :)
>=20
> reason:
> (i) in alternative B you have to do point 1 and 2a, the=20
> volume correction, for each ode.
> (ii) in alternative B you have to do point 2b, the additional=20
> differentiation.
> (iii) the use of assignment rules x =3D x.amount / volume are=20
> not a criterion.
> they can be used in both alternatives.
>=20
> cheers, s
>=20
>=20
> > Rainer
> > _______________________________________________
> > sbmlsolver-devel mailing list
> > sbm...@li...
> > https://lists.sourceforge.net/lists/listinfo/sbmlsolver-devel
>=20
>=20
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>=20