Rescale

liftCouplingConstraints(model, BIG, printLevel, equalities)[source]

Reformulates badly-scaled coupling constraints C*v <=> d by lifting them to a better scaled problem in a higher dimension by introducing dummy variables.

Assumes C does not contain very small entries and transforms constraints containing very large entries (entries larger than BIG).

Reformulation techniques are described in detail in: Sun, Y., Fleming, R. M., Thiele, I., & Saunders, M. A. (2013). Robust flux balance analysis of multiscale biochemical reaction networks. BMC Bioinformatics, 14(1). https://doi.org/10.1186/1471-2105-14-240 See also tutorial here: https://opencobra.github.io/cobratoolbox/stable/tutorials/tutorial_numCharactWBM.html

USAGE:

[LPproblem] = reformulate (model, BIG, printLevel)

INPUTS:

model –

  • C - k x n Left hand side of C*v <= d

  • d - k x 1 Right hand side of C*v <= d

  • ctrs k x 1 Cell Array of Strings giving IDs of the coupling constraints

  • dsense - k x 1 character array with entries in {L,E,G}

OPTIONAL INPUTS

‘BIG’ Value consided a large coefficient. BIG should be set between 1000 and 10000 on double precision machines. printLevel 1 or 0 enables/diables printing respectively.

equalities true means also deals with original constraints containing equalities (default false - only deals with original constraints that are inequalities)

OUTPUTS:

  • model –

    • E m x evars Sparse or Full Matrix of Double Matrix of additional, non metabolic variables (e.g. Enzyme capacity variables)

    • evarlb evars x 1 Column Vector of Doubles Lower bounds of the additional variables

    • evarub evars x 1 Column Vector of Doubles Upper bounds of the additional variables

    • evarc evars x 1 Column Vector of Doubles Objective coefficient of the additional variables

    • evars evars x 1 Column Cell Array of Strings IDs of the additional variables

    • evarNames evars x 1 Column Cell Array of Strings Names of the additional variables

    • C ctrs x n Sparse or Full Matrix of Double Matrix of additional Constraints (e.g. Coupling Constraints)

    • ctrs ctrs x 1 Column Cell Array of Strings IDs of the additional Constraints

    • ctrNames ctrs x 1 Column Cell Array of Strings Names of the of the additional Constraints

    • d ctrs x 1 Column Vector of Doubles Right hand side values of the additional Constraints

    • dsense ctrs x 1 Column Vector of Chars Senses of the additional Constraints

    • D ctrs x evars Sparse or Full Matrix of Double Matrix to store elements that contain interactions between additional Constraints and additional Variables.

  • The linear optimisation problem derived from this model is then of the form – [S, E; C, D]*x {L,E,G} [b;d]

liftModel(model, BIG, printLevel, fileName, directory)[source]

Lifts a COBRA model with badly-scaled stoichiometric and coupling constraints of the form: \(max c*v\) subject to: \(Sv = 0, x, Cv <= 0\) Converts it into a COBRA LPproblem structure, which can be used with solveCobraLP. Fluxes for the reactions should stay the same i.e. sol.full(1:nRxns) should yield an optimal flux vector.

USAGE:

LPproblem = liftModel (model, BIG, printLevel,fileName,directory)

INPUTS:

model – COBRA LPproblem Structure containing the original LP to be solved. The format of this struct is described in the documentation for solveCobraLP.m

OPTIONAL INPUTS:

  • BIG – A parameter the controls the largest entries that appear in the reformulated problem (default = 1000).

  • printLevel – printLevel = 1 enables printing of problem statistics (default); printLevel = 0 silent

  • fileName – name of th file to load

  • directory – file directory (if model is empty, you can load it using fileName and directory)

OUTPUTS:

LPproblem – COBRA Structure contain the reformulated LP to be solved.

liftRows(C, cupcon, BIG, logbig, printLevel, ctrs_cuprow, rxns)[source]

Helper for liftCouplingConstraints. Implements the lifting

INPUTS:

  • C k x n double – Subset of coupling constraints (2-variable rows to be lifted)

  • cupcon k x 1 char – Senses for rows in C (L/G/E)

  • BIG double – Threshold for “large” coefficients. TRiggers lifting

  • logbig double – log(BIG)

  • printLevel double – 0 or 1. If 1 prints extra information

  • ctrs_cuprow k x 1 cell array of chr – IDs of the selected constraints. Correspnds to rows in C

  • rxns nRxns x 1 cell array of chr – model rxn IDs

OUTPUTS:

  • Clifted k’ x n’ double – Lifted constraint matrix

  • newcon ndum x 1 char – Senses of added dummy constraints

  • ctrs_cuprow k’ x 1 cell array of char – Updated IDs for original coupling constraints.

  • ctrs_new ndum x 1 cell array of char – IDs for dummy constraints

  • evars nEvars x 1 cell array of char – IDs of new dummy variables

  • ndum double – Total number of dummy constraints rows added

  • cupcon k’ x 1 char – Senses for rows in Clifted (L/G/E)

  • nEvars double – Total number of dummy variables

reformulate(LPproblem, BIG, printLevel)[source]

Reformulates badly-scaled FBA program Transforms LPproblems with badly-scaled stoichiometric and coupling constraints of the form: \(max c*x\) subject to: math:Ax <= b

Eliminates the need for scaling and hence prevents infeasibilities after unscaling. After using PREFBA to transform a badly-scaled FBA program, please turn off scaling and reduce the aggressiveness of presolve.

Rransforms a badly-scaled LPproblem contained in the struct FBA and returns the transformed program in the structure FBA. reformulate assumes S and C do not contain very small entries and transforms constraints containing very large entries (entries larger than BIG). BIG should be set between 1000 and 10000 on double precision machines. printLevel = 1 or 0 enables/diables printing respectively.

Reformulation techniques are described in detail in: Y. Sun, R. M.T. Fleming, M. A. Saunders, I. Thiele, An Algorithm for Flux Balance Analysis of Multi-scale Biochemical Networks, submitted.

USAGE:

[LPproblem] = reformulate (LPproblem, BIG, printLevel)

INPUTS:

  • LPproblem – Structure contain the original LP to be solved. The format of this struct is described in the documentation for solveCobraLP.m

  • BIG – A parameter the controls the largest entries that appear in the reformulated problem.

  • printLevel – 1 enables printing of problem statistics; 0 = silent

OUTPUTS:

LPproblem – Structure contain the reformulated LP to be solved.

splitRow(A, ri, evars, evarlb, evarub, evarc, b, dsense, ctrs)[source]

Takes row ri of the constraint matrix A (e.g. -1e6*v1 -v2 + v3 < 0), identifies the coefficient with largest absolute value, and replaces the row by:

  1. a constraint containing only that largest coefficient and a new variable z (e.g. -1e6*v1 + z < 0)

  2. an equality constraint defining z as a combination of the remaining variables (e.g. z +v2 - v3 = 0)

Inputs:

  • A k x n constraint matrix.

  • ri Index of the row of A to split

  • evars Cell array of existing extra variable IDs

  • evarlb Lower bounds of extra variables

  • evarub Upper bounds of extra variables

  • evarc Objective coefficients of extra variables

  • b Right-hand side vector of constraints

  • dsense Constraint senses (L,E,G)

  • ctrs Cell array of constraint IDs

Outputs:

  • A Updated constraint matrix with one extra column and one extra row.

  • evars Updated extra variable IDs including the new z variable

  • evarlb Updated lower bounds (new z has -Inf)

  • evarub Updated upper bounds (new z has Inf)

  • evarc Updated objective coefficients (new z has 0)

  • b Updated RHS including 0 for the z-definition equality

  • dsense Updated senses including ‘E’ for the z-definition equality

  • ctrs Updated constraint IDs with a _splitN suffix for the new row