       Re: Re: From reactions to differential equations

• To: mathgroup at smc.vnet.net
• Subject: [mg93486] Re: [mg93473] Re: From reactions to differential equations
• From: Daniel Lichtblau <danl at wolfram.com>
• Date: Tue, 11 Nov 2008 07:45:31 -0500 (EST)
• References: <gf3mik\$emm\$1@smc.vnet.net> <200811100830.DAA26365@smc.vnet.net>

```janos wrote:
> 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.
>>  [...]

> 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

That first is available, in Mathematica notebook form, at

http://library.wolfram.com/infocenter/Conferences/4320/

Daniel Lichtblau
Wolfram Research

```

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