Re: [SOSlib-devel] mail for SBML list: variable Compartments in SBML[Scanned]

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

That's better=20

> -----Original Message-----
> From: sbm...@li...=20
> [mailto:sbm...@li...] On=20
> Behalf Of Stefan Mueller
> Sent: 21 June 2006 14:36
> To: sbm...@li...
> Subject: Re: [SOSlib-devel] mail for SBML list: variable=20
> Compartments in SBML[Scanned]
>=20
> rainer,
> there are more mistakes!
> (please see below)
>=20
> > hi,
> >
> > find below a draft for bringing this issue to the SBML list, as=20
> > suggested by Andrew.
> >
> > could you review? is the problem stated clearly and correctly?
> >
> >
> > Dear SBML Community,
> >
> > As we recently wanted to model variable compartments we=20
> realized that=20
> > our tool - SOSlib - actually does not solve models with variable=20
> > compartments correctly.
> >
> > We wonder how other tools approach this topic.
> >
> > In summary:
> >
> > SOSlib constructs ODEs as recommended by the SBML specs, e.g.:
> >
> > species X1 in compartment V1, with concentration x1 =3D X1/V1=20
> species X2=20
> > and X3 in V2, with conc. as above
> >
> > Reactions:
> > X1->X2; k1*X1*V1 	// a translocation, k1 [1/sec]
> > X2->X3; k2*X2*V2    // a unimolecular reaction, k2 [1/sec]
> >
> > Derived ODEs:
> > dx1/dt =3D - ( k1 * X1* V1 ) / V1
> > dx2/dt =3D  ( k1 * X1* V1 - k2 * X2 * V2 ) / V2
> >
> > the kinetic laws are the SBML specific conversion of `classic' rate=20
> > law to substance/time units, instead of concentrations/time=20
> to allow=20
> > for easy software handling of multiple compartment models.
> >
> > If however, the volumes in the model are variable with time, i.e.=20
> > either an assignment rule or a rate rule, these equations=20
> would not be correct.
>=20
> the following section is not very clear and/or wrong:
> (please don't send this to the sbml list!)
>=20
> > A numerical integration routine would start with the initial=20
> > concentration
> > x(0) and add the changes during time t:
> >
> > x(t) =3D x(0) +  dx/dt * t
> >
> > i.e.
> >
> > x(t) =3D X(0)/V(0) + dx/dt * t
> >
> > dx/dt is calculated correctly from above ODE because it=20
> also accounts=20
> > for changing compartments by explicit inclusion of the=20
> volume in the=20
> > kinetic law.
> >
> > However, the change of the initial concentration x(0) is=20
> not accounted=20
> > for anywhere. The solver should rather return:
> >
> > x(t) =3D X(0)/V(t) + dx/dt * t
> >
> > If x is a function of time and of volume V, x(t,V(t)), then the=20
> > correct ODE would actually be
> >
> > dx/dt =3D dx/dt + dx/dV * dV/dt
> >
> > Right?
>=20
> no!
> please use the following math:
> (i already wrote it down in one of my previous mails :) )
>=20
> definitions:
> x(t) ... conc
> X(t) ... substance
> V(t) ... compartment size
>=20
> given a kinetic law for a reaction,
> e.g. X->Y: r*x*V or X+Y->Z: r*x*y*V,
> which explicitly includes the compartment size (!), the=20
> corresponding ode for substance X amounts to:
> dX/dt =3D - r*x*V or - r*x*y*V,
> or replacing conc by substances:
> dX/dt =3D - r*X or - r*X*Y/V
>=20
> 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.
> i.e. we would get a correction term for variable compartment size.
> this is the most important reason for using odes for substances!
>=20
> > We are currently discussing different solutions and their=20
> dangers for=20
> > SOSlib, i.e. how to correctly convert the ODE system to an=20
> ODE system=20
> > in amount/time instead of concentration/time or whether the above=20
> > partial differential equation could or should be=20
> implemented instead.
> >
> > It would be helpful for us to hear how other tools handle variable=20
> > compartments.
> >
> >
> > And BTW, it might be good to indicate it as good practice NOT to=20
> > convert parameters e.g. from [1/sec] to [litre/sec] to=20
> obtain correct=20
> > units for SBML kinetic laws, but to explicitly keep the=20
> volume in the=20
> > formula! This would allow changing the compartment size or=20
> even making=20
> > the variable, at least for tools which do it correctly.
> > E.g. the model in the specs, section 5.6 will not be valid=20
> anymore if=20
> > someone wanted to change the volume sizes!
> >
> > Such rather unconvential volume-dependent rate `constants' can be=20
> > quite dangerous!
> >
> >
> > Rainer
> >
> >
> >
> > Rainer Machne
> > Institute for Theoretical Chemistry
> > University of Vienna
> > Austria
> >
> >
> > _______________________________________________
> > sbmlsolver-devel mailing list
> > sbm...@li...
> > https://lists.sourceforge.net/lists/listinfo/sbmlsolver-devel
>=20
>=20
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>=20