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

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rainer

> Stefan
>
> i guess it might be different if we have to consider multiple
> compartments
>
> S1 is in V1;
> S2 and S3 are in V2;
>
> S1->S2: k1*[S1]

well, this is not a chemical reaction, but a transport process,
but let's see...

> S2->S3: k2*[S2]
>
> [S1] = S1 / V1
> [S2] = S2 / V2
> [S3] = S3 / V3
>
> Thus the two parameters include two different initial volumes, i.e.:
> k1 [volume/sec] = r1 * V1(0)
> k2 [volume/sec] = r2 * V2(0)
>
> Currently the ODE would be:
>
> d[S1]/dt = k1 * [S1] / V1

this is not valid for variable compartments.
please don't use it for comparison!
btw, this ode is missing a minus :)

> d[S2]/dt = ( k1*[S1] - k2*[S2] ) / V2
> d[S3]/dt  k2*[S2]*[S3] / V3
>
> which is only valid for constant compartments V1 and V2.
>
> 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?

> (all the ODEs in your email are missing a minus, BTW!)
>
> It should probably be something like:
>
> dS1/dt = - k1 * [S1] / V1(0) * V1 = - k1/V1(0) * S1

yes, this is the right one!
(of order 1)

> 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!

> 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...

> 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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> > sbm...@li...
> > https://lists.sourceforge.net/lists/listinfo/sbmlsolver-devel
>
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