Sparsefba

findSparsePathway(model, rxnPenalty, param)[source]

Find a sparse pathway in a COBRA model by penalising or incentivising the activity of individual reactions and minimising the resulting cardinality

Reactions with rxnPenalty(j) > 0 are penalised when active, reactions with rxnPenalty(j) < 0 are incentivised when active, and reactions with rxnPenalty(j) == 0 are indifferent to activity.

USAGE:

[solution, sparseRxnBool] = findSparsePathway (model, rxnPenalty, param)

INPUTS:

model – COBRA model structure passed to buildOptProblemFromModel

OPTIONAL INPUTS:

  • rxnPenalty – n x 1 vector of per-reaction penalties (default ones(n, 1)); positive penalises activity, negative incentivises it, zero is neutral

  • param – parameter structure with fields:

    • .printLevel - verbosity level (default 1)

    • .theta - starting parameter of the Capped-L1 approximation

OUTPUTS:

  • solution – solution structure with fields:

    • .v - n x 1 sparse flux vector

    • .stat - solver status of the cardinality optimisation

  • sparseRxnBool – n x 1 logical, true for reactions active in the sparse solution

sparseFBA(model, osenseStr, checkMinimalSet, checkEssentialSet, zeroNormApprox, printLevel)[source]

Finds the minimal set of reactions subject to a LP objective

\[\begin{split}min ~&~ ||v||_0 \\ s.t ~&~ S v \leq, = or \geq b \\ ~&~ c^T v = f* \\ ~&~ l \leq v \leq u\end{split}\]

where \(f*\) is the optimal value of objective (default is \(max c^T v\)).

USAGE:

[vSparse, sparseRxnBool, essentialRxnBool] = sparseFBA (model, osenseStr, checkMinimalSet, checkEssentialSet, zeroNormApprox, printLevel)

INPUT:

model – COBRA model structure. Required fields:

  • .S - m x n stoichiometric matrix

  • .b - m x 1 right hand side (dx/dt) of the mass balance

  • .c - n x 1 linear objective coefficients

  • .lb - n x 1 lower flux bounds

  • .ub - n x 1 upper flux bounds

OPTIONAL INPUTS:

  • model – COBRA model structure. Optional fields:

    • .C - k x n matrix of additional coupling constraints (C v <= d)

    • .d - k x 1 right hand side of the coupling constraints

    • .dsense - k x 1 sense of the coupling constraints (‘L’, ‘G’, ‘E’)

    • .csense - m x 1 sense of the mass-balance constraints (‘L’, ‘G’, ‘E’)

    • .dxdt - m x 1 right hand side of the mass balance (defaults to .b)

    • .osenseStr - objective sense string used when the osenseStr argument is omitted

  • osenseStr – (default = ‘max’)

    • max: \(f* = argmax \{max\ c^T v: Sv \leq, = or \geq b, l \leq v \leq u\}\)

    • min: \(f* = argmin \{min\ c^T v: Sv \leq, = or \geq b, l \leq v \leq u\}\)

    • none: ignore the constraint \(c^T v = f*\)

  • checkMinimalSet – {0,(1)} Heuristically check if the selected set of reactions is minimal by removing one by one the predicted active reaction

    • true = check (default value)

    • false = do not check

  • checkEssentialSet – {0,(1)} Heuristically check if the selected set of reactions is essential

  • zeroNormApprox – appoximation type of zero-norm (only available when minNorm = ‘zero’) (default = ‘cappedL1’)

    • ‘cappedL1’ : Capped-L1 norm

    • ‘exp’ : Exponential function

    • ‘log’ : Logarithmic function

    • ‘SCAD’ : SCAD function

    • ‘lp-’ : \(L_p\) norm with \(p < 0\)

    • ‘lp+’ : \(L_p\) norm with \(0 < p < 1\)

    • ‘l1’ : L1 norm

    • ‘all’ : try all approximations and return the best result

  • printLevel – Printing level

    • 0 - Silent (Default)

    • 1 - Summary information

OUTPUT:

  • vSparse – Depends on the set of reactions

  • sparseRxnBool – Returns a vector with 1 and 0’s, where 1 means sparse

  • essentialRxnBool – Returns a vector with 1 and 0’s, where 1 means essential