# sparseFBA¶

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 – (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
• ‘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

Outputs

• 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

Authors: - Hoai Minh Le, Ronan Fleming