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Re: [SOSlib-devel] variable compartment bug: example
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From: Rainer M. <ra...@tb...> - 2006-06-20 14:25:16
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stefan >> 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. not really. i wasn't planning any conversion of the math, except for: current ODE: d[S1]/dt = f(S1, S2, ...) / V planned ODE: d S1 /dt = f(S1, S2, ...) then we have two data->value arrays, let's say data->odeValues = S1, S2, S3, etc. and data->concValues = [S1], [S2], [S3] etc. The first array `odeValues' corresponds to the SUNDIALS values in NVector y. The second array `concValues' will be used in evaluateAST, for evaluation the math. This would be equivalent of course, with just replacing all [S1] in all math expressions with S1/volume, and only using one array data->odeValues While the latter approach might be easier to implement it has a probably the not so small drawback, that for each species in each math expression the evaluation needs one more operation, i.e. the division, while this division could be done only once for each species whenever data->odeValues is updated (i.e. e.g. in the SOSlib/SUNDIALS funciton f). However, this might still only be correct, if compartments are determined by assignment rules. If they are determined by rate rules, then the replacement S1 -> S1/V would also be required for constructing the jacobi matrix. > 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? See section 4.6.4 here http://sbml.org/specifications/sbml-level-2/version-1/html/sbml-level-2.html#SECTION00046000000000000000 " The units of the species are of the form substance/size units ... The units of the species are used in the following ways: ... * The species identifier has these units when it appears as a numerical quantity in a mathematical formula expressed in MathML (discussed in Section 3.6.3). " So i guess, the units of species in math expressions are always in concentrations! Rainer > > 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. On Tue, 20 Jun 2006, Stefan Mueller wrote: > 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. >>>>> >>>>> _______________________________________________ >>>>> sbmlsolver-devel mailing list >>>>> sbm...@li... >>>>> https://lists.sourceforge.net/lists/listinfo/sbmlsolver-devel >>>> >>>> _______________________________________________ >>>> sbmlsolver-devel mailing list >>>> sbm...@li... >>>> https://lists.sourceforge.net/lists/listinfo/sbmlsolver-devel >>> >>> _______________________________________________ >>> sbmlsolver-devel mailing list >>> sbm...@li... >>> https://lists.sourceforge.net/lists/listinfo/sbmlsolver-devel >> >> _______________________________________________ >> sbmlsolver-devel mailing list >> sbm...@li... >> https://lists.sourceforge.net/lists/listinfo/sbmlsolver-devel > > > _______________________________________________ > sbmlsolver-devel mailing list > sbm...@li... > https://lists.sourceforge.net/lists/listinfo/sbmlsolver-devel > |
