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Example Problems: Chapters 6 & 7

Example Problems: Chapters 6 & 7. Systems Biology Study Group Sarah Munro 11-19-2007. Examples. Drawing networks Creating the S Matrix Verifying the S Matrix Topological Properties of the network S for E. coli core metabolism S for Glycolysis. Reaction Network Map. byp. v 1. v 2.

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Example Problems: Chapters 6 & 7

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  1. Example Problems:Chapters 6 & 7 Systems Biology Study Group Sarah Munro 11-19-2007

  2. Examples Drawing networks Creating the S Matrix Verifying the S Matrix Topological Properties of the network S for E. coli core metabolism S for Glycolysis

  3. Reaction Network Map byp v1 v2 C A B b1 2 Axt v6 2 b2 v5 cof cof v3 E Ext v4 byp D b3 bypxt

  4. Metabolite Connectivity Map byp Axt A B 2 C b1 v1 v2 2 Ext b2 v6 b3 v5 v4 v3 cof E cof byp D bypxt

  5. Carbamoyl Phosphate CH2NO5P Argininosuccinate C10H17N4O6 Ornithine C5H13N2O2 Fumarate C4H2O4 Citrulline C6H13N3O3 Arginine C6H15N4O2 Aspartate C4H6NO4 Urea CH4N2O Create E1, the elemental matrix for S1:

  6. Multiply the elemental and stoichiometric matrices in MATLAB: E1·S1 ≠ 0 Something is missing!

  7. Multiply the new elemental and stoichiometric matrices in MATLAB: E2·S2 = 0 The S matrix is now correct !

  8. H2O H+ HPO4

  9. Reaction Adjacency Matrix, Av: How many compounds participate in va? In v1? How many compounds do v2 and vc have in common?

  10. Compound Adjacency Matrix, Ax: How many reactions does compound A participate in? How many reactions do A and B participate in together? What about compounds A and C?

  11. Teusink_Glycolysis Teusink et al. Eur. J. Biochem. (267) 2000

  12. Teusink_Glycolysis_core Teusink et al. Eur. J. Biochem. (267) 2000

  13. function [Ax, Av, Sbin] = topo_properties(S) %Plots the number of metabolites y that participate in x reactions %Function file input is a mxn matrix that defines the stoichiometry of a %reaction network %Function file outputs include: Ax = compound adjacency matrix, %Av = reactions adjacency matrix, Sbin = binary form of Smatrix %Generate binary form of S matrix [m,n] = size(S); Sbin = zeros(m,n); for i= 1:m for j= 1:n if S(i,j)~=0; Sbin(i,j) = 1; if S(i,j) == 0; Sbin(i,j) = 0; end end end end %calculate transpose of Sbin SbinT = transpose(Sbin);

  14. %calculate Ax, the compound adjacency matrix Ax = Sbin*SbinT; %calculate Av, the reaction adjacency matrix Av = SbinT*Sbin; % bar plot of the number of metabolites y, that participate in x reactions [m,n] = size(Ax); y = []; for i = 1:m y = [y Ax(i,i)]; end maxreactions = max(y); minreaction = min(y); reactions = [minreactions:1:maxreactions]; compounds = zeros(1,length(reactions)); for j = 1:length(reactions); I = find(y == reactions(j)); compounds(j) = [length(I)]; end bar(reactions,compounds) xlabel('number of reactions') ylabel('number of compounds')

  15. What’s Next? Singular Value Decomposition? Calculating Extreme Pathways? Running Simulations using ODE solvers?

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