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Re: From reactions to differential equations

  • To: mathgroup at smc.vnet.net
  • Subject: [mg93423] Re: From reactions to differential equations
  • From: David Bailey <dave at removedbailey.co.uk>
  • Date: Fri, 7 Nov 2008 06:01:09 -0500 (EST)
  • References: <gepb55$skd$1@smc.vnet.net>

zac wrote:
> Dear All,
> 
> from some time now I=E1m working with more and more complex differential
> 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
> 
I think if you give an example of the corresponding differential 
equations that you wish to create, this will not be very hard.

Do you want to use the expression Subscript[a, i] to represent the 
concentration of this reagent, or do you want to represent 
'concentration of' in some way? Also, there are going to be some rate 
constants in her somewhere.


David Bailey
http://www.dbaileyconsultancy.co.uk


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