Topology¶

connectedComponents(model, type, figures, files)

Assuming two reactions are connected if they share metabolites, calculates the connected components in the stoichiometric matrix, that is, the sets of reactions that share a set of metabolites

USAGE:

[groups, orphans, R, C] = connectedComponents(model, type, figures)

INPUT:

model:

OPTIONAL INPUTS:

type: {(‘allComponents’), ‘largestComponent’} figures: Will generate plots of the grouping algorithm as it creates block diagonal

groups in from top left to bottom right in W.

files: Indicator, whether several files containing indicator

matrices are generated.

OUTPUTS:

groups: a structure array (the number of distinct groups is length(groups)) with fields:

• groups(i).num_els - number of reactions in group i.

• groups(i).block - sub-block identity of group i.

• groups(i).elements - reactions of W that are in group i.

• groups(i).degrees - degrees of connection for each reaction in group i.

orphans: elements of W that were not in any group, becasue they did not meet the constraints. R: reaction adjacency C: compound adjacency

All components require: Connected Component Analysis on an Undirected Graph by Tristan Ursell http://www.mathworks.com/matlabcentral/fileexchange/35442-connected-component-analysis-on-an-undirected-graph.

Largest component requires: gaimc : Graph Algorithms In Matlab Code by David Gleich http://www.mathworks.com/matlabcentral/fileexchange/24134-gaimc-graph-algorithms-in-matlab-code.

findCyclicRxns(model, printLevel)

Computes the reactions that are part of one or more stoichiometrically balanced cycles in the network

USAGE:

[cyclicRxnBool, rankS] = findCyclicRxns(model, printLevel)

INPUT:

model: model structure printLevel: verbose level

OUTPUTS:

cyclicRxnBool: boolean value rankS: scalar giving rank of S

getCorrespondingCols(S, rowBool, colBool, mode)

Returns a boolean vector that is true for a subset of the true cols in colBool according to whether the cols ‘exclusive’, ‘inclusive’, or ‘partial’ -ly correspond to true entries in rowBool

USAGE:

restrictedColBool = getCorrespondingCols(S, rowBool, colBool, mode)

INPUTS:

S: m x n stoichiometric matrix rowBool: m x 1 boolean vector colBool: n x 1 boolean vector mode: ‘exclusive’ or ‘inclusive’ or ‘partial’

OUTPUT:

restrictedColBool: n x 1 boolean vector

Example

S =
-1

0 0 0 0 2 -3 0 0 0 0 4 -5 0 0 0 0 6 -7 0 0 0 0 0 0

rowBool = [1; 1; 1; 0; 0]; colBool = [1; 1; 1; 1; 1];

%Therefore, the subset of rows and columns considered for inclusion are % -1 0 0 0 0 % 2 -3 0 0 0 % 0 4 -5 0 0

%If mode = ‘exclusive’ then restrictedColBool corresponds to this subset % -1 0 % 2 -3 % 0 4 %i.e. subset of colBool reactions exclusively involving rowBool metabolites

%If mode = ‘inclusive’ then restrictedColBool corresponds to this subset % -1 0 0 % 2 -3 0 % 0 4 -5 %i.e. subset of colBool reactions involving at least one rowBool metabolite

%If mode =’partial’ then restrictedColBool corresponds to the extra cols %with inclusive that are not present with exclusive.

getCorrespondingRows(S, rowBool, colBool, mode)

Returns a boolean vector that is true for a subset of the true rows in rowBool according to whether the rows ‘exclusive’, ‘inclusive’, or ‘partial’ -ly correspond to true entries in colBool

USAGE:

restricedRowBool = getCorrespondingRows(S, rowBool, colBool, mode)

INPUTS:

S: m x n stoichiometric matrix rowBool: m x 1 boolean vector colBool: n x 1 boolean vector mode: ‘exclusive’ , ‘inclusive’ or ‘partial’

OUTPUT:

restrictedRowBool: m x 1 boolean vector

Example

S =
-1

0 0 0 0 2 -3 0 0 0 0 4 -5 0 0 0 0 6 -7 0 0 0 0 0 0

rowBool = [1; 1; 1; 1; 1]; colBool = [1; 1; 1; 0; 0];

% Therefore, the subset of rows and columns considered for inclusion are % -1 0 0 % 2 -3 0 % 0 4 -5 % 0 0 6 % 0 0 0

% If mode = ‘exclusive’ then restrictedRowBool corresponds to this subset % -1 0 0 % 2 -3 0 % 0 4 -5 % i.e subset of rowBool metabolites exclusively involved in the colBool % reactions

% If mode = ‘inclusive’ then restrictedRowBool corresponds to this subset % -1 0 0 % 2 -3 0 % 0 4 -5 % 0 0 6 % i.e subset of rowBool metabolites involved in colBool reactions

% If mode =’partial’ then restrictedRowBool corresponds to the extra rows % with inclusive that are not present with exclusive.

integerizeS(S, SIntRxnBool)

convert an S matrix with some non integer coefficients into an S matrix with all integer coefficients assumes that there are a maximum of six significant digits in the biomass reaction

INPUT

S stoichiometric matrix

OPTIONAL INPUT
SIntRxnBool Boolean of internal (mass balanced) reactions.

If provided, only these reactions are integerised

OUTPUT

SInteger stoichiometric matrix of integers G scaling matrix, SInteger=S*G;

matrixCoherence(A)

Computes the coherence of a matrix A, that is the maximum absolute value of the cross correlations between the columns of A

USAGE:

[mu, Q] = matrixCoherence(A)

INPUT:

A: Matrix

OUTPUTS:

mu: coherence Q: matrix used by mu

testForTypeIIIPathways(model, ListExch, filename)

Sets up the model to run extreme pathway analysis (expa) for identifying loops in the model (Type III pathways) and runs expa.

USAGE:

testForTypeIIIPathways(model, ListExch, filename)

INPUTS:

model: COBRA model structure ListExch: List of position of exchange reactions in S matrix filename: name of the file