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

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stefan

>> Currently the ODE would be:
>>
>> d[S1]/dt = k1 * [S1] / V1
>
> this is not valid for variable compartments.

i said that it's invalid for variable compartments some lines below:

>> which is only valid for constant compartments V1 and V2.

> please don't use it for comparison!

it's not used for comparison, but it is the current implementation in 
SOSlib!

>> At least for the second ODE, depending in two different volumes,
>> the conversion to ODEs depending on substance instead of concentration is
>> not as simple as
>>
>>> dS1/dt = k * [S1] * [S2] / V(0) * V = k/V(0) * S1 * S2 / V
>
> why dou you refer to this law for a reaction of order 2?
>

sorry, at first i wanted to make the second reaction in V2 of 2nd order, 
e.g.,

in V2:
S2 + S3 -> P: k2*[S2]*[S3]

>> as your example before,
>> but for S2 I get:
>>
>> dS2/dt = k1/V1(0) * S1/V1 * V2  -  k2/V2(0) * S2
>>
>> Right?
>
> no!
> dS2/dt = k1/V1(0) * S1 - k2/V2(0) * S2
> it's as simple as that!
> (since dS2/dt = -dS1/dt as far as reaction S1->S2 is concerned.)
> that's the advantage of kinetic laws (and consequently odes) for substances!

of course! sorry, i got quite confused obviously.

and for the above second order reaction in V2 it would be:

  dS2/dt = k1/V1(0) * S1 - k2/V2(0) * S1 * S3 / V2

Right this time?

>
>> Thus I would really have to check the type of reaction and edit a lot of
>> kinetic laws before constructing the ODEs.
>
> the above example shows that this is not necessary.
> maybe there are other examples...

so you say, we could convert kinetic laws that don't explicitly contain 
the volume by simply differentiating these three cases and

>>> order 1:
>>> S1->junk: k*[S1]
>>> dS1/dt = k * [S1] / V(0) * V = k/V(0) * S1
>>>

divide k by V(0) for 1st order reactions

>>> order 2:
>>> S1+S2->bla: k*[S1]*[S2]
>>> dS1/dt = k * [S1] * [S2] / V(0) * V = k/V(0) * S1 * S2 / V

divide k by V(0) and the whole kinetic law again by V^2 for 2nd order 
reactions

>>>
>>> order 3:
>>> S1+S2+S3->wow: k*[S1]*[S2]*[S3]
>>> dS1/dt = k * [S1] * [S2] * [S3] / V(0) * V = k/V(0) * S1 * S2 * S3 / 
V^2

divide k by V(0) and the whole kinetic law again by V^2 for 2nd order
reactions

but there are also enzymatic reactions, with in often quite complex 
kinetic laws. we would really have to do unit checking, recognizing the 
implemented reaction mechanisms etc.

also, we don't really know in which compartment reactions happen, but 
could just try to get this information from the reactants' compartments.

so i guess, it would be much easier to

a) use ODEs for substances but dependent on concentrations, here the only 
thing we need to do is to leave out the compartment division at the end of 
Species_odeFromReactions and have a double bookkeeping of amounts and 
concentrations

and

b) just ignore WRONG models that have a variable compartment but don't 
have the compartment explicitly in their kinetic laws
(or check for such cases and issue an error);

isn't it an issue of correct model writing rather then correct model 
solving?

However, another problem might be that to calculate in amounts rather then 
in concentrations also changes the use of absolute errors and maybe 
also the general the performance of the integrator, i guess. ??

maybe we will have to really implement both in parallel,
* ODEs for concentrations/time if no variable compartments are in the 
model 
* ODEs for ammounts/time if any compartment is variable

?

Rainer

>> Thus I think it just doesn't work with kinetic laws that don't
>> include the compartment explicitly!
>
> i don't know exactly what you mean.
> of course kinetic laws with explicit compartment are "nicer",
> but you can always transform any kinetic law to a "nice" one...
>
>> But if they include the compartment we can write ODEs for substances but
>> have concentrations in the right hand side of the ODEs. We then just need
>> to a second array for the concentrations, as discussed before.
>
> if we still use concentrations is a separate problem,
> independent of which we discussed until now.
> it's a matter of taste, if we eliminate the concentrations  from the kinetic
> laws and get a (possibly nonlinear) dependence on the compartments OR
> if we keep concentrations and always have linear dependence on the comp.
>
>> Rainer
>
> cheers,
> stefan.
>
>
>> On Mon, 19 Jun 2006, Stefan Mueller wrote:
>>> let me summarize:
>>> kinetic laws have units substance/time,
>>> and they depend on concentrations or substances.
>>>
>>> we SHOULD write down odes for substances,
>>> and we COULD eliminate concs completely.
>>> (of course, we would have to convert initial concs to substances.)
>>>
>>> in any case, odes for substances depend on the compartment size
>>> (linearly or according to the order of the reaction):
>>>
>>> order 1:
>>> S1->junk: k*[S1]
>>> dS1/dt = k * [S1] / V(0) * V = k/V(0) * S1
>>>
>>> order 2:
>>> S1+S2->bla: k*[S1]*[S2]
>>> dS1/dt = k * [S1] * [S2] / V(0) * V = k/V(0) * S1 * S2 / V
>>>
>>> order 3:
>>> S1+S2+S3->wow: k*[S1]*[S2]*[S3]
>>> dS1/dt = k * [S1] * [S2] * [S3] / V(0) * V = k/V(0) * S1 * S2 * S3 / V^2
>>>
>>> ...
>>>
>>> if the kinetic laws included the compartment explicitly (which is
>>> desirable), we would have the following situation:
>>>
>>> order 1:
>>> S1->junk: r*[S1]*V
>>> dS1/dt =  r * [S1] * V= r * S1
>>>
>>> order 2:
>>> S1+S2->bla: r*[S1]*[S2]*V
>>> dS1/dt = r * [S1] * [S2] * V= r * S1 * S2 / V
>>>
>>> order 3:
>>> S1+S2+S3->wow: r*[S1]*[S2]*[S3]*V
>>> dS1/dt = r * [S1] * [S2] * [S3] * V = r * S1 * S2 * S3 / V^2
>>>
>>> as stated earlier, odes for substances have got another advantage. for
>>> the compartment size we could use either a rate rule or an assignment
>>> rule: dV/dt = f(t, V, ...)
>>> or
>>> V= f(t, V, ...)
>>>
>>> cheers,
>>> stefan.
>>>
>>> Am Montag 19 Juni 2006 11:17 schrieb Stefan Mueller:
>>>> andrew:
>>>>
>>>> for the SBML system
>>>> 	S1 in C
>>>> 	S1->junk : k * [S1]
>>>> 	dC/dt = 1
>>>>
>>>> the right math is:
>>>> 	dS1/dt = k * [S1] / C(0) * C
>>>> 	dC/dt = 1
>>>> with initial cond:
>>>> 	S1(0) = [S1](0) * C(0)
>>>> 	C(0)
>>>>
>>>> notation:
>>>> 	S1 ... substance
>>>> 	[S1] ... conc
>>>>
>>>> the "proposed solution" (who proposed this?) has the right units,
>>>> but is wrong otherwise... :)
>>>>
>>>> as rainer and me already discussed, everything would be much clearer,
>>>> if the kinetic law included the compartment explicitly:
>>>> 	S1 in C
>>>> 	S1->junk : C * r * [S1]
>>>> 	dC/dt = 1
>>>>
>>>> with:
>>>> 	r ... the "real" chemical rate constant.
>>>>
>>>> rainer:
>>>>
>>>> chemists always knew that rate constants are not constant with respect
>>>> to pH, T, ... as a physicist i have to be fair! :)
>>>>
>>>> to conclude: the math is not really tricky.
>>>> odes for substances are better suited to handle both multiple and
>>>> variable compartments. of course, we have to take care of many
>>>> implementation details...
>>>>
>>>> cheers,
>>>> stefan.
>>>
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