       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=

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

```

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