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

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

Also, i wonder whether and how other software supports variable 
compartments. should we ask on the sbml list?

r

On Tue, 13 Jun 2006, Andrew Finney wrote:

> Rainer
>
> I've talked with people here and this argument is correct but I only
> vaguely understand the maths - I managed to graduate without covering
> PDEs :-(
>
> I suggest you either:
>
> a) figure out with the others if there is away to do the PDE math so
> that we can support any combination rules and reactions.
> This would require I imagine some clever symbolic processing.
>
> or
>
> b) convert CVODE to substance units but then block the combination of
> rate rules for species in concentration units with rate rules for
> compartment volumes
>
> in fact there may still be problems with (b)...
>
> yours Andrew
>
>> -----Original Message-----
>> From: Rainer Machne [mailto:ra...@tb...]
>> Sent: 13 June 2006 15:46
>> To: Andrew Finney
>> Subject: RE: [SOSlib-devel] variable compartment bug[Scanned]
>>
>> Andrew
>>
>>> [S(0)] = S(0)/C(0)
>>>
>>> not
>>>
>>> [S(0)] = S(0)/C(t)
>>
>> Let's say S doesn't change over time for some reason. It
>> might even have an ODE, e.g.
>>
>> dS/dt = ( k * S(t) * activeEnzyme(t) ) / C(t)
>>
>> but during integration activeEnzyme never appears, i.e. its
>> concentrations stays 0. Thus dS/dt is always 0.
>>
>> Then in SOSlib the initialConcentration would not change and
>>
>>   [S(t)] = [S(0)] = S(0) / C(0)
>>
>> while it actually should be
>>
>>   [S(t)] = S(0) / C(t)
>>
>> This is not represented in SOSlib. Stefand and Luki pointed
>> out that the problem might be even more fundamental and that
>> we cannot represent variable compartments at all.
>>
>> if S is a function of time and of volume C, S(t,C(t)), then
>>
>> dS/dt = dS/dt + dS/dC * dC/dt
>>
>> where the d on the right hand side represent the partial
>> differential (as in PDEs).
>>
>> Maybe on Friday, when Stefan is here, we can formulate the
>> problem in more general terms.
>>
>> Rainer
>>
>>
>> On Tue, 13 Jun 2006, Andrew Finney wrote:
>>
>>> Rainer
>>>
>>> You wrote:
>>>
>>>> What cvode does is to add the concentration increase ds to the
>>>> initial
>>>> concentration:
>>>>
>>>> s(t) = 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)=1 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!
>>>
>>> Either I'm missing something big here or...
>>>
>>> An initial concentration is an >initial< concentration
>>>
>>> at any time concentration
>>>
>>> [S] = S/C
>>>
>>> [S(t)] = S(t)/C(t)
>>>
>>> therefore
>>>
>>> [S(0)] = S(0)/C(0)
>>>
>>> not
>>>
>>> [S(0)] = S(0)/C(t)
>>>
>>> How can S(0) ever vary as the volume varies over time?
>>> S(0) is a value at only one point in time.
>>>
>>> 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 = (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] = S/v
>>>> v ... volume
>>>>
>>>>
>>>> Imagine we start with initialConcentration s(0) = 1, and integrate
>>>> from 0 to time 1.
>>>>
>>>> What cvode does is to add the concentration increase ds to the
>>>> initial
>>>> concentration:
>>>>
>>>> s(t) = 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)=1 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 = + 0.1
>>>>
>>>> Substance s1 starts with concentration 1 and is totally
>> consumed by
>>>> the irreversible reaction
>>>>
>>>> S1 -> S2; kineticLaw = 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 = (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
>>>>>>
>>>>>
>>>>
>>>
>>
>