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

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hi rainer!

> 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!

i said this just to avoid any additional misunderstanding.
the whole topic seems to be quite confusing...

> >> 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?

yes :)

> >> 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

yes.
and that's exactly the same what you are planning,
if you want to use conc ans subst in parallel.
only the point of conversion differs.

i mean, every species is in a well-defined compartment, isn't it?
so you can use the formula [S]=S/V whenever you want...

i would eliminate conc as early as possile, but that's a matter of taste.

> 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.

of course you have to check if the species in your kinetic law have dimension 
conc or substance!
sbml allows the usage of both, doesn't it?

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

this does not matter, for 2 reasons:

1. if the kinetic law is specified correctly (including the compartment size),
e.g. A+B->C: k*V*[A]*[B],
the the compartment size is considered automatically.

2. the conversion [S]=S/V does not depend on reactions, but only on species
(and their 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

to my taste, double book keeping is dangerous and produces overhead.

> 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?

i agree.

> 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. ??

abs errors might change, but that's not an issue.
rel errors should stay the same.
(in one-compartment models everything is just multiplied by the volume.)

> maybe we will have to really implement both in parallel,

i hope not :)

> * ODEs for concentrations/time if no variable compartments are in the
> model
> * ODEs for ammounts/time if any compartment is variable
>
> ?
>
> Rainer

maybe we discuss the next round via telephone :)

cheers, s

> >> 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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> >>
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