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

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

rainer!

> Yes you are right. my mistake. We only need the
> * additional assignment rules for all species x = x.amount,

that would be too easy! :)
x = x.amount / V

> * formulate ODEs for new variables x.amount and leave away the  ... /
> volume from current ODEs
>
> and everything, incl. the jacobian, should be fine ( i hope ).

yes, that's easy!
before the symbolic differentiations (for the jacobian) are done,
all conc have to be eliminated from the rhs of the odes. 
(via the above formula.)
but this is done anyway, isn't it?

> of course we haven't considered the `hasSubstanceUnits-species' ...
>
> wow :) such an easy conclusion for such a long and confusing discussion. i
> am really not a `formula-person' :)

for me as a formula person :), the most difficult problem was to understand 
which odes remain valid in the case of variable compartments:
the odes for conc or the odes for substances?
with hindsight, it seems clear: the odes for substances!

anyway, there exist correct odes for both conc and substances.
(with a correction term for the former.)
as a consequence, the implementation of the latter is simpler!

cheers,
s

> rainer
>
> > I don't think you need to actually substitute the x.amount/volume into
> > the
> > ODEs if you have the assignment rules.  In SOSlib
>
> On Fri, 23 Jun 2006, Andrew Finney wrote:
> > 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 = x2.amount/volume
> > dx1.amount/dt = k * x2
> > dx2.amount/dt = ???
> >
> > should be equivalent to:
> >
> > dx1.amount/dt = k * (x2.amount/volume)
> > dx2.amount/dt = ???
> >
> > 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...
> >> [mailto:sbm...@li...] On
> >> Behalf Of Stefan Mueller
> >> Sent: 21 June 2006 16:51
> >> To: sbm...@li...
> >> Subject: Re: [SOSlib-devel] implementing variable
> >> compartments[Scanned]
> >>
> >> rainer
> >>
> >>> 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=X/V:
> >>>> dx/dt = (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)
> >>> expressions for all reactions where X is a
> >>
> >> product/reactant, i.e. it
> >>
> >>> is a function of concentrations x, y, z ...
> >>>
> >>> Right? (If not forget, the rest ...)
> >>
> >> right.
> >>
> >>> So actually, the first part of this equation (dX/dt)/V is
> >>
> >> the current
> >>
> >>> form of ODEs in SOSlib!
> >>>
> >>> Could the implementation of variable compartments in SOSlib
> >>
> >> would be
> >>
> >>> as easy as:
> >>>
> >>> 1) add the expression " - x*(dV/dt)/V "
> >>> to the concentration ODEs for species in a variable compartment?
> >>
> >> yes.
> >>
> >>> 2a) if the compartment is defined by a rate rule, this rate
> >>
> >> rule could
> >>
> >>> be appended to all ODEs directly, i.e.
> >>>
> >>> newODE = currentODE - (x/V) * rateRule
> >>
> >> yes.
> >>
> >>> 2b) if the compartment is defined by an assignment rule, we
> >>
> >> would have
> >>
> >>> differentiate it towards time? For this we need to convert the
> >>> assignment rule to a form, where differentiateAST recognizes time
> >>> dependent variables that are in the assignment rule, e.g.
> >>
> >> x(t), which
> >>
> >>> appears only as ASTNode "x". Is this possible/easy?
> >>
> >> possible.
> >> easy? differentiateAST has to extended.
> >> there must be differentiation with respect to time, but only
> >> 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...
> >>
> >>> 2c) if the compartment is changed by events, we don't need
> >>
> >> to append
> >>
> >>> anything but just recalculate concentrations and re-initialize the
> >>> solver, just as we do now for events.
> >>>
> >>>
> >>> If above is right - but i guess it might just not be that easy - we
> >>> would have extracted two alternatives:
> >>>
> >>> A) use ODEs in substance/time, write assignment rules for
> >>
> >> x.amount = x
> >>
> >>> / volume and replace all x by x.amount in ODEs, as Andrew suggested
> >>
> >> you mean: x = x.amount / volume !?
> >>
> >>> or
> >>>
> >>> B) use above approach.
> >>>
> >>> Is that it?
> >>
> >> yes.
> >> i vote for alternative A :)
> >>
> >> reason:
> >> (i) in alternative B you have to do point 1 and 2a, the
> >> volume correction, for each ode.
> >> (ii) in alternative B you have to do point 2b, the additional
> >> differentiation.
> >> (iii) the use of assignment rules x = x.amount / volume are
> >> not a criterion.
> >> they can be used in both alternatives.
> >>
> >> cheers, s
> >>
> >>> Rainer
> >>> _______________________________________________
> >>> sbmlsolver-devel mailing list
> >>> sbm...@li...
> >>> https://lists.sourceforge.net/lists/listinfo/sbmlsolver-devel
> >>
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