Re: Re: From reactions to differential equations
- To: mathgroup at smc.vnet.net
- Subject: [mg93465] Re: [mg93450] Re: From reactions to differential equations
- From: "Scot T. Martin" <smartin at deas.harvard.edu>
- Date: Sun, 9 Nov 2008 05:26:45 -0500 (EST)
- References: <200811080900.EAA14313@smc.vnet.net>
This link might also be helpful: http://www.mathematica-journal.com/issue/v8i1/features/martin/ On Sat, 8 Nov 2008, Alexei Boulbitch wrote: > Hi, Istvan, > > just to add few words to the previous reply. I learned recently from the = reply of M.Roellig that using Mathematica you can transform chemical equati= ons into differential. This makes sense, if you deal with many tens or even= hundreds of reactions. I rule out the evident problem related to stability= of such a huge system. If one goes this way, he probably have successfully= 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 actuall= y 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 contra= st, the rules of translation a chemical reaction into a kinetic equation ar= e explained in a number of books. Just in case you missed a good one, have = 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 che= mical reactions into differential equations. All the physical sense (chemic= al sense, biological sense - cross out those unnecessary) is hidden exactly= in this step. It is here that you make assumptions and formulate your mode= l. All the rest is some mathematical analysis which will never give you mor= e 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 eligible= 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 > > > >> Hi Istvan, >> >> 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 differen= tial >> >> > >>>> 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 Biology >> >> > >>>> 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 became >> >> > >>>> too cumbersome after a point to deal with indexed variables (without >> >> > >>>> indices it is fairly simple), and I really don't want to invent >> >> > >>>> something that (perhaps) already exists on the field. >> >> > >>>> Any ideas? >> >> > >>>> >> >> > >>>> Istvan Zachar >> >> > > -- > 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. > > > >
- References:
- Re: From reactions to differential equations
- From: Alexei Boulbitch <Alexei.Boulbitch@iee.lu>
- Re: From reactions to differential equations