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

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

Andrew

> Intuitively I can't see why this formulae is wrong
> but hey what do I know!
>
> My calculus really isn't up to figuring this out!
> sorry I'm a software engineer.  I guess I should know for SBML and all=20
that b$
>

I'm a biologist, so i really don't know much about this either :)

luckily we have lukas (chemist) and stefan (physicist) to help out.

> I don't have problem in changing SOS to using amount units for the
> species variables.  However you will still have a problem when a model
> contains a rate rule in concentration units.  What happens then?

Mhm ... we will try to figure out on Friday if we can represent variable=20
compartments at all ...

i'm quite confused now :(

Rainer






On Tue, 13 Jun 2006, Andrew Finney wrote:

> Rainer
>
> I think I understand your English argument
>
> my last email was really just a comment on
> how you expressed your argument :-)
>
> I don't exactly understand why the math doesn't work.
> CVODE solves any correctly defined ODE system
> if CVODE produces the wrong results then we've got the formulae wrong. =
 (I'm just restating the issue slightly differently)
>
> given
>
> d[s]/dt =3D f([S])/C         [1]
>
> when
>
> dC/dt =3D g([S])             [2]
>
> Either [1] is the correct formulae or it isn't
> when
> C is varying volume and
> f is a function returning substance/time units and
> g is a function returning volume/time units and
> [S] is the set of all concentrations.
>
> Intuitively I can't see why this formulae is wrong
> but hey what do I know!
>
> My calculus really isn't up to figuring this out!
> sorry I'm a software engineer.  I guess I should know for SBML and all =
that but I don't.
>
> Have we got it wrong?
> Perhaps we have.
>
> I don't have problem in changing SOS to using amount units for the=20
species variables.  However you will still have a problem when a model=20
contains a rate rule in concentration units.  What happens then?=20
> (in that case as na=EFve softy I would multiply by the volume!)
>
> yours Andrew
>
>
>
>> -----Original Message-----
>> From: Rainer Machne [mailto:ra...@tb...]
>> Sent: 13 June 2006 15:09
>> To: Andrew Finney
>> Cc: SOSlib Development
>> Subject: RE: [SOSlib-devel] variable compartment bug[Scanned]
>>
>> Andrew
>>
>>
>> I have added a corrected and more clear version of the example file.
>>
>>
>>> 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?
>>
>> Yes, the internal SBML ode model only contains
>> initialConcentrations; initialAmounts from the input model
>> have all been converted by dividing by compartment size.
>>
>>
>>> if S1 is in a compartment with volume C then
>>>
>>> d[S1]/dt =3D (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.
>>
>> Yes, that is what we have.
>>
>>
>>> Why do you need two sets of values?
>>
>> Ok, I'll try to explain in more detail.
>>
>> I change the notation to
>> S ... amount of molecule S
>> s ... concentration, [S] =3D S/v
>> v ... volume
>>
>>
>> Imagine we start with initialConcentration s(0) =3D 1,
>> and integrate from 0 to time 1.
>>
>> What cvode does is to add the concentration increase ds to
>> the initial
>> concentration:
>>
>> s(t) =3D s(0) + ds
>>
>> if the volume is doubled during that time e.g. by a rate
>> rule, ds should
>> correctly include the changing volume because its part of the ODE.
>>
>> However, s(0)=3D1 has never been corrected for the changing volume!
>>
>> If the ODE ds/dt was 0 during this time, e.g. because of a missing
>> activator of the reaction, s(t) would still change to 0.5,
>> because the
>> volume has doubled.
>>
>> This is not reflected in SOSlib!
>>
>> To the example XML:
>>
>>> Note the initial volume of the compartment is not specified
>> in the xml.
>>
>> Sorry, I tried the model with old version which still had the
>> `missing
>> parameter bug' from last week.
>> See the attached corrected file.
>>
>> The compartment volume increases to 11 because of its rate rule
>> d(volume)/dt =3D + 0.1
>>
>> Substance s1 starts with concentration 1 and is totally
>> consumed by the
>> irreversible reaction
>>
>> S1 -> S2; kineticLaw =3D k+S1
>>
>> which moves all molecules to S2.
>>
>> Substance S2 would have a final concentration of 1, if the
>> compartment
>> still had volume 1, but not for a final volume of 11.
>>
>> The final concentration should be 1/11.
>>
>> The totalConcentration in the example file should also
>> decrease to 1/11.
>>
>>
>> SOSlib and the ODE division by volume only corrects the change of
>> concentration but not the initial concentration, or generally
>> spoken, the
>> concentration of the last time step, which also has decreased.
>>
>> The only solution i can think of, is to define ODEs in
>> substance/time and
>> do the division independently of the ODE system.
>>
>> Rainer
>>
>>
>>
>>
>>
>>
>>
>>
>>
>>
>> On Tue, 13 Jun 2006, Andrew Finney wrote:
>>
>>> 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 =3D (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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