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Stoichiometric

# Stoichiometric - Stoichiometric Analysis Reading and...

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Stoichiometric Analysis

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Reading and Software Textbook section: 5.2 Palsson Paper: Am looking for a newer tutorial paper For the best explanation that I have ever seen on the relationship of subspaces, least squares estimation, and the singular value decomposition, please read this paper by Gilbert Strang, “The Fundamental Theorem of Linear Algebra,” The American Mathematical Monthly, Vol 100, No 9, 848-855, 1993. Strang Paper CellNetAnalyzer / FluxAnalyzer has been developed by Steffen Klamt in the Systems Biology group of Prof. Ernst Dieter Gilles at the Max Planck Insitute for Dynamics of Complex Technical Systems in Magdeburg. Academic use: free academic license. Current version is 9.2. The requirements for using CellNetAnalyzer are: MATLAB version 7.0 or higher some functions require the optimization toolbox of MATLAB (or/and GLPKMEX with GLPK library)
Next week Tools CellNetAnalyzer download and have on your computers for in-class exercises Flux Balance Analysis Applications Predict effects of gene knockouts Central metabolism TB mycolic acid biosynthesis

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Metabolic Flux Analysis Use universal reaction stoichiometries to predict network metabolic capabilities at steady state
Stoichiometric Matrices Look at substances that are conserved in system, mass and flow Coefficients are proportion of substrate and product 1 2 2 S S P + 1 1 2 1 1 2 - - → ← - 1 2 , , 2 , dS dS dP v v v dt dt dt = - = - =

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Stoichiometric Network Matrix with m substrates and r reactions N = {n ij } is the matrix of size mxr 1 1, r i ij j j S n v i m = = = & S = Nv &
Stoichiometry As Vectors We can denote the stoichiometry of a reaction by a vector of coefficients One coefficient per metabolite Positive if metabolite is produced Negative if metabolite is consumed Example: Metabolites: [ A B C D ] T Reactions: 2A + B -> C C -> D Stoichiometry Vectors: [ -2 -1 1 0 ] T [ 0 0 -1 1 ] T

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b i are External fluxes or Exchange Reactions Conventions are left to right and top down.
A B C D E [ ] 1 2 3 4 5 6 1 2 3 4 v v v v v v b b b b 1 2 3 2 dB v v v b dt = - + - dA dt dB dt dC S v dt dD dt dE dt =

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dA dt dB dt dC S v dt dD dt dE dt = = A B C D E 1 2 3 4 5 6 1 2 3 4 v v v v v v b b b b S 1 2 3 4 5 6 1 2 3 4 v v v v v v b b b b
Steady-State A B C D E

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Calculating changes in concentration A B C D v1 v2 v3 v4 v5 b 1 b 2 -1 0 0 1 0 0 -1 0 1 0 0 0 -1 1 0 0 0 -1 1 0 0 0 1 -1 0 0 -1 1 A B D C b 1 v1 v3 v2 v5 b 2 v4 What happens if 1 0 0 0 0 0 0 0 v1 0 v2 0 v3 0 v4 0 v5 1 b1 0 b 2 = 1 0 0 0 dA/dt dB/dt dC/dt dD/dt A grows by 1 “unit” per “second” We can calculate this with S Given these fluxes These are the changes in metabolite concentration
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Stoichiometric - Stoichiometric Analysis Reading and...

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