Fastcore

LP10(K, P, v, LPproblem, epsilon, adaptiveScalingFlag, nonPen)

Finds a flux vector that maintains the activity of any active irreversible core reaction (K) yet minimises the activity of any non-core reaction (P). Implementation of LP-10 for input sets K, P (see FASTCORE paper)

USAGE:

V = LP10 (K, P, v, LPproblem, epsilon, adaptiveScalingFlag, nonPen)

INPUTS:

• K – indices of active irreversible core reactions to keep active

• P – indices of non-core reactions whose activity is minimised

• v – flux vector from the preceding LP7 solve, used to set core bounds

• LPproblem – LP problem structure derived from the model with fields:

  • .A - constraint (stoichiometric) matrix

  • .b - right hand side vector for A*v = b

  • .lb - lower bounds on the variables

  • .ub - upper bounds on the variables

  • .csense - constraint sense character array ({L, E, G})

• epsilon – smallest flux value that is considered nonzero

• adaptiveScalingFlag – 0 = fixed scaling factor of 1e4, 1 = adaptive scaling

• nonPen – indices of reactions that are not penalized in the objective

OUTPUT:

V – flux vector minimising the activity of the non-core reactions

LP10cvx(K, P, model, epsilon)

CPLEX implementation of LP-9 for input sets K, P (see FASTCORE paper)

USAGE:

V = LP10cvx (K, P, model, epsilon)

INPUTS:

• K – indices of active core reactions to keep active

• P – indices of non-core reactions whose activity is minimised

• model – COBRA model structure with fields:

  • .S - m x n stoichiometric matrix

  • .lb - n x 1 lower flux bounds

  • .ub - n x 1 upper flux bounds

• epsilon – smallest flux value that is considered nonzero

OUTPUT:

V – flux vector minimising the activity of the non-core reactions

LP10weighted(W, K, P, model, LPproblem, epsilon)

Weighted implementation of LP-9 for input sets K, P (see FASTCORE paper). Finds a flux vector that keeps the core reactions (K) active while minimising a weighted sum over the non-core reactions (P).

USAGE:

V = LP9weighted (W, K, P, model, LPproblem, epsilon)

INPUTS:

• W – n x 1 nonnegative weight for each reaction (penalises high weights)

• K – indices of active core reactions to keep active

• P – indices of non-core reactions whose weighted activity is minimised

• model – COBRA model structure with field:

  • .S - m x n stoichiometric matrix

• LPproblem – LP problem structure derived from the model with fields:

  • .A - constraint (stoichiometric) matrix

  • .b - right hand side vector for A*v = b

  • .lb - lower bounds on the variables

  • .ub - upper bounds on the variables

  • .csense - constraint sense character array ({L, E, G})

• epsilon – smallest flux value that is considered nonzero

OUTPUT:

V – flux vector minimising the weighted activity of the non-core reactions

LP3(J, model, LPproblem, basis)

Implementation of LP-3 for input set J (see FASTCORE paper)

USAGE:

[v, basis] = LP3 (J, model, LPproblem, basis)

INPUTS:

• J – indices of reactions whose flux is maximised in the objective

• model – COBRA model structure with fields:

  • .S - m x n stoichiometric matrix

  • .ub - n x 1 upper flux bounds

• LPproblem – LP problem structure derived from the model with fields:

  • .A - constraint (stoichiometric) matrix

  • .b - right hand side vector for A*v = b

  • .lb - lower bounds on the variables

  • .ub - upper bounds on the variables

  • .csense - constraint sense character array ({L, E, G})

OPTIONAL INPUT:

basis – basis to warm-start the LP solve

OUTPUTS:

• v – optimal steady state flux vector

• basis – basis returned by the LP solver

LP3cvx(J, model)

CVX implementation of LP-3 for input set J (see FASTCORE paper). Maximises the total flux through the reactions indexed by J.

USAGE:

V = LP3cvx (J, model)

INPUTS:

• J – indices of reactions whose summed flux is maximised

• model – COBRA model structure with fields:

  • .S - m x n stoichiometric matrix

  • .lb - n x 1 lower flux bounds

  • .ub - n x 1 upper flux bounds

OUTPUT:

V – steady state flux vector returned by the CVX solve

LP7(J, model, LPproblem, epsilon, basis)

Implementation of LP-7 for input set J (see FASTCORE paper). Maximises the number of feasible fluxes in J whose value is at least epsilon

USAGE:

[v, basis] = LP7 (J, model, LPproblem, epsilon, basis)

INPUTS:

• J – indicies of irreversible reactions

• model – COBRA model structure

• LPproblem – LP problem structure derived from the model with fields:

  • .A - constraint (stoichiometric) matrix

  • .b - right hand side vector for A*v = b

  • .lb - lower bounds on the variables

  • .ub - upper bounds on the variables

  • .csense - constraint sense character array ({L, E, G})

• epsilon – tolerance (smallest flux considered nonzero)

OPTIONAL INPUT:

basis – basis to warm-start the LP solve

OUTPUTS:

• v – optimal steady state flux vector

• basis – basis returned by the LP solver

LP7cvx(J, model, epsilon)

CVX implementation of LP-7 for input set J (see FASTCORE paper). Maximises the number of reactions in J that carry a flux of at least epsilon.

USAGE:

V = LP7cvx (J, model, epsilon)

INPUTS:

• J – indices of reactions to drive above the epsilon threshold

• model – COBRA model structure with fields:

  • .S - m x n stoichiometric matrix

  • .lb - n x 1 lower flux bounds

  • .ub - n x 1 upper flux bounds

• epsilon – smallest flux value that is considered nonzero

OUTPUT:

V – steady state flux vector returned by the CVX solve

LP7cvx2(J, model, epsilon)

CVX implementation of LP-7 for input set J (see FASTCORE paper), scaling the indicator variables by epsilon. Maximises the number of reactions in J that carry a flux of at least epsilon.

USAGE:

V = LP7cvx2 (J, model, epsilon)

INPUTS:

• J – indices of reactions to drive above the epsilon threshold

• model – COBRA model structure with fields:

  • .S - m x n stoichiometric matrix

  • .lb - n x 1 lower flux bounds

  • .ub - n x 1 upper flux bounds

• epsilon – smallest flux value that is considered nonzero

OUTPUT:

V – steady state flux vector returned by the CVX solve

fastCoreWeighted(C, model, weights, epsilon)

Based on: The FASTCORE algorithm for context-specific metabolic network reconstruction, Vlassis et al., 2013, PLoS Comp Biol.

USAGE:

A = fastCoreWeighted (C, model, weights, epsilon)

INPUTS:

• C – List of reaction numbers corresponding to the core set

• model – Model structure with the fields:

  • .rxns - n x 1 cell array of reaction abbreviations

  • .lb - n x 1 lower flux bounds

• weights – Weight vector for each reaction in the model

• epsilon – Parameter (default: getCobraSolverParams(‘LP’, ‘feasTol’)*100; see Vlassis et al for more details)

OUTPUT:

A – A most compact model consistent with the applied constraints and containing the desired core set reactions (as given in C)

fastcc(model, epsilon, printLevel, modeFlag, method)

The FASTCC algorithm for testing the consistency of a stoichiometric model. Output A is the consistent part of the model.

USAGE:

[A, orientation, V] = fastcc (model, epsilon, printLevel, modeFlag, method)

INPUTS:

model – cobra model structure containing the fields:

• .S - m x n stoichiometric matrix

• .lb - n x 1 flux lower bound

• .ub - n x 1 flux upper bound

• .rxns - n x 1 cell array of reaction abbreviations

• .csense - m x 1 character array of constraint senses in {L,E,G} (optional; defaults to E)

• .C - k x n left hand side of C*v <= d (optional coupling constraints)

OPTIONAL INPUTS:

• epsilon – smallest flux that is considered nonzero

• printLevel – 0 = silent, 1 = summary, 2 = debug

• modeFlag – {(0), 1}; 1 = return matrix of modes V

• method – ‘original’ - default or ‘nonconvex’

OUTPUTS:

• A – indices of flux consistent reactions in model

• orientation – n x 1 vector indicating the orientation of flux consistency, where -1 means flux consistent in reverse direction only

• V – n x k matrix such that S(:,A) * V(:,A) = 0 and |V(:,A)|’ * 1 > 0

fastcc_cvx(model, epsilon)

The FASTCC algorithm for testing the consistency of a stoichiometric model, solving the underlying LPs with the CVX modelling framework.

USAGE:

A = fastcc_cvx (model, epsilon)

INPUTS:

• model – cobra model structure containing the fields:

  • .S - m x n stoichiometric matrix

  • .lb - n x 1 flux lower bounds

  • .ub - n x 1 flux upper bounds

  • .rxns - n x 1 cell array of reaction abbreviations

• epsilon – smallest flux value that is considered nonzero

OUTPUT:

A – indices of the flux consistent reactions in the model

fastcore(model, coreRxnInd, epsilon, printLevel, adaptiveScalingFlag, nonPen)

Use the FASTCORE algorithm (‘Vlassis et al, 2014’) to extract a context specific model. FASTCORE algorithm defines one set of core reactions that is guaranteed to be active in the extracted model and find the minimum of reactions possible to support the core.

USAGE:

[tissueModel, coreRxnBool, coreMetBool, coreCtrsBool] = fastcore (model, coreRxnInd, epsilon, printLevel, adaptiveScalingFlag, nonPen)

INPUTS:

• model – COBRA model structure with the required fields:

  • .S - m x n stoichiometric matrix

  • .lb - n x 1 lower bounds

  • .ub - n x 1 upper bounds

  • .rxns - n x 1 cell array of reaction abbreviations

  • .mets - m x 1 cell array of metabolite abbreviations

  • .ctrs - coupling-constraint identifiers (optional)

• coreRxnInd – indices of reactions in cobra model that are part of the core set of reactions (called ‘C’ in ‘Vlassis et al, 2014’)

OPTIONAL INPUTS:

• epsilon – smallest flux value that is considered nonzero (default getCobraSolverParams(‘LP’, ‘feasTol’)*100)

• printLevel – 0 = silent, 1 = summary, 2 = debug (default - 0)

• adaptiveScalingFlag – 0 = adaptive scaling is off (default), 1 = adaptive scaling is on (recommended for ill scaled models)

• nonPen – list of reactions whose addition to the model is not penalized

OUTPUTS:

• tissueModel – extracted context-specific model

• coreRxnBool – n x 1 boolean vector indicating core reactions

• coreMetBool – boolean vector indicating metabolites retained in tissueModel

• coreCtrsBool – boolean vector indicating coupling constraints retained in tissueModel

‘Vlassis, Pacheco, Sauter (2014). Fast reconstruction of compact context-specific metbolic network models. PLoS Comput. Biol. 10, e1003424.’

findSparseMode(J, P, singleton, model, LPproblem, epsilon, adaptiveScalingFlag, basis, nonPen)

Finds a mode that contains as many reactions from J and as few from P. Returns its support, or [] if no reaction from J can get flux above epsilon

USAGE:

Supp = findSparseMode (J, P, singleton, model, LPproblem, epsilon, adaptiveScaling, basis, nonPen)

INPUTS:

• J – Indicies of irreversible reactions

• P – Reactions

• singleton – Takes only first instance from J, else takes whole J

• model – Model structure (for reference)

• LPproblem – LPproblem structure

• epsilon – Parameter (default: getCobraSolverParams(‘LP’, ‘feasTol’)*100; see Vlassis et al for more details)

OPTIONAL INPUT:

• adaptiveScalingFlag – scaling choice for LP10

• basis – Basis

• nonPen – indexes of unpenalized reactions

OUTPUTS:

• Supp – Support or [] if no reaction from J can get flux above epsilon

• basis – Basis

findSparseModeWeighted(J, P, singleton, model, LPproblem, weights, epsilon)

Finds a mode that contains as many reactions from J and as few from P. Returns its support, or [] if no reaction from J can get flux above epsilon. Based on: The FASTCORE algorithm for context-specific metabolic network reconstruction. Input C is the core set, and output A is the reconstruction, Vlassis et al., 2013, PLoS Comp Biol.

USAGE:

Supp = findSparseModeWeighted (J, P, singleton, model, LPproblem, weights, epsilon)

INPUTS:

• J – Indicies of irreversible reactions

• P – Reactions

• singleton – Takes only first instance from J, else takes whole J

• model – Model structure

• LPproblem – The LP problem for the model structure

• weights – The weights associated with the reactions.

• epsilon – Parameter (default: getCobraSolverParams(‘LP’, ‘feasTol’)*100; see Vlassis et al for more details)

OUTPUT:

Supp – Support or [] if no reaction from J can get flux above epsilon

tmplp7cvx(J, model, epsilon)

CVX implementation of LP-7 for input set J (see FASTCORE paper). Maximises the number of reactions in J that carry a flux of at least epsilon.

USAGE:

V = tmplp7cvx (J, model, epsilon)

INPUTS:

• J – indices of reactions to drive above the epsilon threshold

• model – COBRA model structure with fields:

  • .S - m x n stoichiometric matrix

  • .lb - n x 1 lower flux bounds

  • .ub - n x 1 upper flux bounds

• epsilon – smallest flux value that is considered nonzero

OUTPUT:

V – steady state flux vector returned by the CVX solve

tmplp8cvx

CVX code fragment for a weighted LP-8 style solve: minimise the summed absolute flux over the penalised reaction set (Penal) subject to the steady state constraint and flux bounds, while forcing the core set (K) above the threshold z. Expects n, Penal, K, z, and model to be defined in the workspace.