Re: From reactions to differential equations

*To*: mathgroup at smc.vnet.net*Subject*: [mg93473] Re: From reactions to differential equations*From*: janos <janostothmeister at gmail.com>*Date*: Mon, 10 Nov 2008 03:30:55 -0500 (EST)*References*: <gf3mik$emm$1@smc.vnet.net>

On nov. 8, 10:36, Alexei Boulbitch <Alexei.Boulbi... at iee.lu> wrote: > Hi,Istvan, > > just to add few words to the previous reply. I learned recently from t= he reply of M.Roellig that using Mathematica you can transform chemical equ= ations into differential. This makes sense, if you deal with many tens or e= ven hundreds of reactions. I rule out the evident problem related to stabil= ity of such a huge system. If one goes this way, he probably have successfu= lly solved it. > > However, if I understand you right, you asked another question: your prob= lem is just to translate a certain (not too large) system of chemical react= ions into differential equations and to analyze them. Right? > > OK, but in this case it is an easy task, provided chemical reactions (lik= e 2 Subscript[H, 2] + Subscript[O, 2] -> 2 Subscript[H, 2] O) are already e= stablished. > > "...I would like to understand the method how these reactions are actu= ally converted to diff.equations..." > > I believe that your problem is not in Mathematica or any other program= . I doubt that by use of any program one can understand such things. In con= trast, the rules of translation a chemical reaction into a kinetic equation= are explained in a number of books. Just in case you missed a good one, ha= ve a look into > > Segel, L. A. Biological kinetics (eds. Cannings, C., Hoppenstedt, F. C. &= Segel, L. A.) (Cambridge University Press, Cambridge, 1991). > > I myself learned it first from one of Prigogine=B4s books, such as > Prigogine, Ilya (1961). Thermodynamics of Irreversible Processes, 2nd Ed,= New York: Interscience or > Prigogine, Ilya; Nicolis, G. (1977). Self-Organization in Non-Equilibrium= Systems. Wiley. ISBN 0471024015. > > There is of coarse, also a lot of other books on this subject. You need t= o read only few introductory chapters. > > Even more, I would never trust any program to translate instead of me = chemical reactions into differential equations. All the physical sense (che= mical sense, biological sense - cross out those unnecessary) is hidden exac= tly in this step. It is here that you make assumptions and formulate your m= odel. All the rest is some mathematical analysis which will never give you = more than you put into your equations during this step. > > I successfully used Mathematica several times to analyze equations descri= bing chemical kinetics. However, if you have more than two-three non-linear= equations describing your system, Mathematica may be not the best choice. = I have seen at least one other than Mathematica program which was better de= signed for this purpose. But moderator informed me that it is not eligib= le to give here its name. > > Finally, I let myself one philosophic comment to the Community. In the Ma= thGroup I often see questions which originated when the author cannot do so= mething using Mathematica, but are in fact related to some lack of knowledg= e of the author in Mathematics or in some other discipline. So literally th= e answer does not belong to this forum. My attitude is that we should answe= r these questions nevertheless and give hints of where to look for the answ= er. Itself the fact that some question is related to some other field (rath= er than Mathematica) is something to do with Mathematica nevertheless. Just= due to indication of boundaries. > > Success, Alexei > > > > > HiIstvan, > > > the reaction kinetic equations only tell you what is changed into what. > > > But they do not give you the speed (rate constants). But the diff. > > > equation are actually about speeds and you need the rate constants to > > > write them. > > > Further, Subscripts are only optical sugar, but they make programming > > > hard. Therefore do not use it, or at least only for input/output. > > > hope this helps, Daniel > > > zac wrote: > > > > > Dear All, > > > > > from some time now I=E1m working with more and more complex diffe= rential > > > > > equations. > > > > > Is there a package to transform a set of reaction-kinetic equations > > > > > such as: > > > > > { > > > > > Subscript[a, i] + Subscript[b, j] -> Subscript[c, i, j], > > > > > Subscript[a, i] + Subscript[c, i, j] -> 2 Subscript[a, i] + > > > > > Subscript[b, j], > > > > > Subscript[b, i] + Subscript[c, j, i] -> 2 Subscript[b, i] + > > > > > Subscript[c, j] > > > > > } > > > > > to differential equations expressing the growth of a_i, b_i and c_i= ,j, > > > > > regarding > > > > > that I leave the parameters i and j undefined? > > > > > I am fully aware of software packages like COPASI and Systems Biolo= gy > > > > > that are available, but I think they are far more complex than what= is > > > > > needed here, and furthermore I would like to understand the method = how > > > > > these reactions are actually converted to diff.equations. Which I > > > > > completely miss if I'm to rely on a concealed algorithm. > > > > > I've already started to write a parser in Mathematica, but it becam= e > > > > > too cumbersome after a point to deal with indexed variables (withou= t > > > > > indices it is fairly simple), and I really don't want to invent > > > > > something that (perhaps) already exists on the field. > > > > > Any ideas? > > > > >IstvanZachar > > -- > Alexei Boulbitch, Dr., Habil. > Senior Scientist > > IEE S.A. > ZAE Weiergewan > 11, rue Edmond Reuter > L-5326 Contern > Luxembourg > > Phone: +352 2454 2566 > Fax: +352 2454 3566 > > Website:www.iee.lu > > This e-mail may contain trade secrets or privileged, undisclosed or other= wise confidential information. If you are not the intended recipient and ha= ve received this e-mail in error, you are hereby notified that any review, = copying or distribution of it is strictly prohibited. Please inform us imme= diately and destroy the original transmittal from your system. Thank you fo= r your co-operation. One solution together with deretministic and stochastic models: T=F3th, J.: Formal Kinetics with Applications, 6th World Multiconference on Systemics, Cybernetics and Informatics (July 14-18, 2002, Orlando, FL, USA), Vol. XI (Computer Science II) (N. Callaos, M. Morgenstern and B. Sanchez eds.), pp. 573-576. T=F3th, J.; Rospars, J.-P.: Dynamic modelling of biochemical reactions with applications to signal transduction: Principles and tools using Mathematica}, BioSystems, 79 (2005), 33-52. Background material: =C9rdi, P., T=F3th, J.: Mathematical Models of Chemical Reactions. Theory and Applications of Deterministic and Stochastic Models, Manchester University Press, Manchester, Princeton University Press, Princeton, 1989. J=E1nos

**Follow-Ups**:**Re: Re: From reactions to differential equations***From:*Daniel Lichtblau <danl@wolfram.com>