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

[Stefan M. <ste...@oe...>]

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.