1 / 29

Analyzing E. Coli Core Metabolism via Stoichiometric Matrices and Network Connectivity

This study focuses on the application of stoichiometric matrices and network connectivity analysis to explore the core metabolism of *Escherichia coli*, particularly through glycolysis. By utilizing MATLAB for matrix multiplication and adjacency calculations, we uncover vital relationships within metabolic networks, represented as elemental and stoichiometric matrices. The results include generating the compound and reaction adjacency matrices, allowing deeper insights into compound participation in various reactions, with potential future steps including singular value decomposition and ODE simulations.

bruno-munoz
Download Presentation

Analyzing E. Coli Core Metabolism via Stoichiometric Matrices and Network Connectivity

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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?

More Related