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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
>
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