(************** Content-type: application/mathematica ************** CreatedBy='Mathematica 4.2' Mathematica-Compatible Notebook This notebook can be used with any Mathematica-compatible application, such as Mathematica, MathReader or Publicon. The data for the notebook starts with the line containing stars above. To get the notebook into a Mathematica-compatible application, do one of the following: * Save the data starting with the line of stars above into a file with a name ending in .nb, then open the file inside the application; * Copy the data starting with the line of stars above to the clipboard, then use the Paste menu command inside the application. Data for notebooks contains only printable 7-bit ASCII and can be sent directly in email or through ftp in text mode. Newlines can be CR, LF or CRLF (Unix, Macintosh or MS-DOS style). 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You \ serendipitously discoverd that the drug can be easily manufactured in E. coli \ by splicing in a gene that is highly expressed in the pituitary gland of the \ Bonobo. This is represented by the rection Rax in the diagram below. During a \ test run, the yield of X was quite good, but you need it make it even better, \ since your chief financial officer just informed you of her plans to do a \ leveraged buy out of Pfizer.\n\nOne thing you can try is to increase the \ yield of X by adjusting the glucose and oxygen flux rates on the bioreactor, \ which have the symbols O and G in the diagram. Your options range from 0 to \ 60M/kgDW-hr for O, and from 0 to 40M/KgDW-hr for G. By inspecting the diagram \ below, do you think its possible to cut costs without sacrificing yield by \ giving less than the maximum of glucose and/or oxygen? Might too much of \ either actually reduce production of X? Dont worry if you can't right now - \ that's what Flux Balance Analysis is for!\n\nR stands for gRowth, and we \ assume that E. coli is willing and able to optimize the flux(es) going into \ R. The willing part means that we have succeeded in represneting E. coli's \ best interests as the node R in this model of metabolic fluxes. The able part \ means that E. coli has sufficent regulatory control over the set fluxes in \ this model to find the model optimum for R. We can calculate the model \ optimum using the mass balance equations for each reaction, plus additional \ constraints that reflect the fact that metabolites must be conserved over all \ of the reactions. These intra and inter-reaction conservation equations are \ all linear. The optimization function, simply the magnitude of Rar, is also \ linear, thus we can use the Mathematica LinearProgramming function, that is, \ if you have Mathemaica version 4.2. 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The workbook Flux.xls contains the matrix of \ reactions and metabolites shown below, along with some custom worksheet \ functions that create matrix definitions that are needed by the Mathematica \ LinearProgramming function. The matrix represented by the light grey box of \ cells below is called the Stoichiometric matrix. The reaction mass balance \ equations are represented by the columns, and the metabolite balance \ equations are in the rows. The rel, or relation column below can have the \ values (-1, 0, 1), which is what the LinearProgramming function accepts as \ codes for (<, =, >). Notice that the thresh colum contains 0 for all of the \ rows of the Stoichiometric matrix - this is saying that metabolites must be \ conserved across all reactions. 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