[SOSlib-devel] variable compartment bug : correction

[Stefan M. <ste...@oe...>]

andrew, lukas, rainer!

sorry guys, the problem of compartments is so difficult :)
that i made an error, too.

given the law for concentrations dx/dt = k*y*z for a fixed volume V,
the "law" for substances X=x*V is correct even for a time-dependent volume:
dX/dt = (k*V)*y*z = (k/V)*Y*Z
whereas the law for concentrations has to be corrected:
dx/dt = k*y*z - x (dV/dt) / V

if we write down odes for substances instead of concs, we can calculate V 
either by an ode or by an assignment rule.
if we used odes for concs this would be more complicated.

so with the sbml definition of a kinetic law for a fixed volume V0
dX/dt_V0 = V0*dx/dt = V0*k*x*y = fX(concs)
the odes for substances can be written as:
dX/dt = fX() / V0 * V
that's all!
of course, via fX the concs enter the odes for substances.

so. i hope that was the last error.
anyway, let's discuss it on friday!

cheers,
stefan.


Am Dienstag 13 Juni 2006 19:01 schrieb Stefan Mueller:
> andrew, lukas, rainer!
>
> the problem of compartments (multiple or even variable) is not that easy.
>
> the definition of kinetic laws in sbml is conceptionally bad.
> ok. the sbml people wanted to ease the treatment of multiple compartments.
> and it's working...
> but among other things, it complicates the treatment of variable
> compartments. anyway, we can "work around" the current definition. (see
> below.)
>
> first, how should it be:
> in chemistry, rate laws are defined for concs,
> e.g. dx/dt=k*x*y.
> and there is a reason for this: the law is independent of the volume V!
> if you formulate "laws" for substances X=x*V,
> you get dX/dt=(k*V)*x*y=(k/V)*X*Y.
> this is not a law of chemistry, but depends also on the volume V.
> moreover, for time-dependent V the above "law" is wrong!
>
> having this in mind (?), sbml people specified dX/dt for a given volume V0,
> let's call it dX/dt_V0=(k*V0)*x*y.
> by simple calculus, we can derive dX/dt from X=x*V:
> ----------------------------------------------------
> dX/dt = dX/dt_V0 / V0 * V + X * dV/dt / V
> ----------------------------------------------------
> dV/dt can be given explicitly or derived (!) from an assignment rule.
> as rainer already suspected, we have to use odes for substances to allow
> for variable compartments. (although the kinetic laws still depend on
> concs).
>
> i hope i clarified the situation a little bit.
>
> cheers,
> stefan.
>
> Am Dienstag 13 Juni 2006 15:25 schrieb Andrew Finney:
> > Rainer
> >
> > Slow down!!
> >
> > I don't actually understand the argument:
> > why can't you have the ODEs as ODEs of concentrations:
> >
> > if S1 is in a compartment with volume C then
> >
> > d[S1]/dt = (f1() + f2() + ... fn()) / C
> >
> > f1..fn are the reaction rates which are
> > expressions that have units substance/time
> >
> > f1...fn are functions of the concentrations of the
> > species [S1]..[Sn]
> >
> > I thought that's what we'd implemented.
> >
> > Why do you need two sets of values?
> >
> > I would strongly urge we go for the approach is having
> > one set of values and carefully converting the units as is appropriate.
> >
> > fundamentally what's the problem?
> >
> > In the SBML you sent the only fly in the ointment
> > is that the initial value for the species is
> > expressed in substance units via the initialAmount attribute rather than
> > the initialConcentration
> > attribute which is in concentration units.
> >
> > All you need to do is ensure that the initialAmount
> > values are used to calculate the initialConcentration values again by
> > dividing by the volume.  Have
> > we implemented that?
> >
> > Note the initial volume of the compartment is not specified in the xml.
> >
> > yours Andrew
> >
> > > -----Original Message-----
> > > From: sbm...@li...
> > > [mailto:sbm...@li...] On
> > > Behalf Of Rainer Machne
> > > Sent: 13 June 2006 11:42
> > > To: SOSlib Development
> > > Subject: [SOSlib-devel] variable compartment bug[Scanned]
> > >
> > > Folks
> > >
> > > Lukas has identified another serious bug!
> > >
> > > SOSlib doesn't support variable compartments.
> > >
> > > We initialize sundials with ODEs for concentrations d[A]/dt,
> > > and sundials calculates [A] + (d[A]/dt)*h, where h is a small
> > > time step and [A] is the initial condition or the current value.
> > >
> > > If we have a variable, e.g time-dependent compartment, then
> > > d[A]/dt will change with changing compartment because the
> > > compartment size is part of the right hand side.
> > >
> > > However, not only d[A]/dt is dependent on the volume, but
> > > also [A], i.e.
> > > the current value in data->value!
> > >
> > > The attached example file exemplifies this.
> > >
> > > So we actually should use an ODE system in amount/time
> > > instead of concentration/time, and have a second data->value
> > > array for concentrations to be used in formula evaluation.
> > >
> > > Didn't we discuss this once? I remember that I had started to
> > > do this (ODEs in amount/time), but then it got more
> > > complicated then I thought and something else came up.
> > >
> > > Can you think of any problems we will run into? Andrew, how
> > > about the compiling version?
> > >
> > > Rainer
> >
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