Re: [SOSlib-devel] comments on SBML L2 V2

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

Hi Michael,

This email also goes to the SOSlib developers' email list.

On Mon, 4 Sep 2006, Michael Hucka wrote:

> Andrew recently wrote the following to me in a separate
> message about the L2v2 draft specification:
>
>  afinney> the Example of the translation from
>  afinney> multicompartment models to odes:
>  afinney>
>  afinney> This model is correct as it stands but this type
>  afinney> of translation doesn't work when the compartment
>  afinney> volume varies i.e. is defined by an ODE.  In that
>  afinney> type of system the species odes need to be in
>  afinney> substance/time units.  The species concentrations
>  afinney> can then be computed by simple 'rules' applied to
>  afinney> intermediate species variables in substance
>  afinney> units.  The SOSlib team ran into this issue a
>  afinney> month or 2 ago.  I can't explain the math but we
>  afinney> could probably get them to explain this if you
>  afinney> want real proof.
>  afinney>
>  afinney> Perhaps we can have a variable compartment model
>  afinney> translated into Odes in addition to the existing
>  afinney> model
>  afinney>
>  afinney> either way there needs to some text describing
>  afinney> the limitations of the approach that's used in
>  afinney> the current text.
>
> I think the model in question in the examples section was
> contributed by Nicolas.  I'm afraid I'll run out of time
> to make all the remaining changes to the spec, so could I
> ask for people's help in doing as Andrew suggests above?

The example in section 5.6 has a variable compartment V1:
http://sbml.org/specifications/sbml-level-2/version-1/html/sbml-level-2.html#SECTION00056000000000000000

So I think the given translation to ODEs is wrong in the current state!! 
Or am I wrong? This topic confused me back then. Maybe Stefan or Luki can 
check section 5.6 and the following short explanation:

1) First the constant K3 (and all other Ks) is already corrected for some 
initial volume to convert the kinetic law to substance/time.

K3 = K3original * V1(0)
where K3original was in units [1/time] and K3 is in [volume/time], so 
K3*S3, with S3 as a concentration [substance/volume], yields the required 
[substance/time].

So K3 is actually a volume-dependent variable!!
The equation should rather have an explicit volume term, i.e.

K3original * V1 * S1

The volume corrections in kinetic laws should in general be done 
explicitly and it might be a good thing to note this in the specs 
compartment section.

2) Second the last ODE dS3/dt is wrong. A correct math would require a 
d[S3]/dV term to account for the influence of volume change on the 
concentration.

Imagine an initial concentration of 1 for S3(0) and a Volume V1 that has 
doubled at time t, V1(t) = 2 * V1(0). The ODE given would just add the 
changes by reactions but not changes to this initial condition by the 
volume change which at time t would only be 0.5. A term dS3/dV would 
account for this.

Fortunately there was an easier solution which Andrew mentioned above and 
which is outlined shortly at 
http://www.tbi.univie.ac.at/wiki/index.php/SOSlibDevel#Variable_Compartment_Sizes

1) write ODEs in substance/time, i.e. don't divide by the compartment, the 
left hand side of the ODEs are dXamount/dt rather then dX/dt; the ODE 
solver will the calculate Xamount.
2) write assignment rules for species concentrations which are required at 
the right hand side of ODEs:
X = Xamount / Volume.

Let me know if we can contribute something specific to the new draft.

Rainer



>
> The possible outcomes are as follows, in decreasing value of
> goodness:
>
> 1. Someone writes a 2nd model (and corresponding
>   explanation) that handles the variable volume case.  We
>   add this model as an additional example in the examples
>   section, and also modifies the description of the
>   existing constant-volume model to explain it's a common
>   but special case, it's limited, doesn't handle varying
>   volumes, etc.
>
> 2. Someone modifies the existing model to make it handle
>   varying volumes, and we leave just the one model, because
>   it's the most general case.
>
> 3. We decide we don't have time to create a new general
>   example, and instead only edit the existing
>   constant-volume model to explain its limitations.
>
> 4. I add a sentence to the existing constant-volume model
>   example description mentioning that it's only for
>   constant volumes "and this does not properly handle the
>   more general case".
>
> Let me know if anyone can do something.
>
> MH
>