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

[Rainer M. <ra...@tb...>]

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

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' :)

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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