Re: [SOSlib-devel] variable compartment bug : correction

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

Stefan


> dX/dt = fX() / V0 * V
> that's all!
> of course, via fX the concs enter the odes for substances.


That means we would divide the ODE by the initial volume and multiply 
again by the current volume?

Why that? Why can't be just leave the volumes away?

How to account for different volumes in one ODE, which happens for 
multiple compartment and species involved in transport reactions?

e.g. if
compartment V1 contains A; in substance units, with conc. A/V1 = [A] = a
compartment V2 contains B and C

A->B, would be the transport reaction with a kinetic law:  kt*a*V1

B->C, is an irreversible conversion with kinetic law: kf*b*V2

then our concentration ODE would be

db/dt = (kt*a*V1 - kf*b*V2) / V2

right?

Can't we just leave away the last / V2 to have the correct substance ODE?

dB/dt = kt*a*V1 - kf*b*V2

where V1 and V2 can be variable?

Rainer


On Wed, 14 Jun 2006, Stefan Mueller wrote:

> 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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