sparseFBA

findSparsePathway(model, rxnPenalty, param)

input a cobra model and find a sparse pathway given penalties on certain reactions being active rxnPenalty(j)>0 and incentives on certain reactions being active rxnPenalty(j)<0 and indifferent to the activity of other reactions rxnPenalty(j)==0

sparseFBA(model, osenseStr, checkMinimalSet, checkEssentialSet, zeroNormApprox, printLevel)

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: (the following fields are required - others can be supplied):

  • S - Stoichiometric matrix

  • b - Right hand side = dx/dt

  • c - Objective coefficients

  • lb - Lower bounds

  • ub - Upper bounds

OPTIONAL INPUTS:
model: (optional for C*v<=d):

  • C - Stoichiometric matrix

  • d - Right hand side = dx/dt

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