A21 Metabolic Control Analysis Functions

The following is an alphabetical listing of the 21 functions included in the add-on package MetabolicControlAnalysis. These functions can be used after applying the command, «MetabolicControlAnalysis . This listing of functions is followed by the program used to create the package MetabolicControlAnalysis.

ConcControlMatrix

ConcControlMatrix[S, N, v, p, SteadyState^steadystate] calculates a matrix for the metabolic system defined by S, N, v, and p, at the steady state given by the replacement rule steadystate, where the element my is the normalized concentration control coefficient of metabolite i with respect to reaction j.

■ Inclusion of the parameter table p is optional.

■ steadystate in the argument SteadyStateConc^steadystate must have the form of a replacement rule as generated by SteadyState or NSteadyState.

■ The default value for the Option, SteadyStateConc, is S.

■ The Option Normalized^False can be included to calculate non-normalized control coefficients.

■ See also: FluxControlMatrix. ConcResponseMatrix

■ ConcResponseMatrix[S, N, v, {parameter list}, p, SteadyState^ steadystate ] returns a matrix where the element mik is the concentration response coefficient of the concentration of metabolite i in S with respect to the kth parameter of {parameter list}.

■ Inclusion of the parameter table p is optional.

■ steadystate in the argument SteadyStateConc ^steadystate must have the form of a replacement rule as generated by SteadyState or NSteadyState.

■ The default value for the Option, SteadyStateConc, is S.

■ The Option Normalized^False can be included to calculate non-normalized response coefficients.

■ See also: FluxResponseMatrix. ConservationRelations

■ ConservationRelations[S, N] determines non-negative conservation relations between the metabolites Si in the metabolic network defined by N.

■ The Option, GMatrix^True, will return a matrix, G, such that G.S = Const where Const is a matrix of constants. The default value for GMatrix is False.

■ All entries in N must be exact numbers.

■ See also: NSteadyState.

EpsilonElasticityMatrix

■ EpsilonElasticityMatrix[S, N, v, p, SteadyState^steadystate] returns a matrix where the element m j is the e-elasticity of reaction i in v with respect to substrate j in S.

■ Inclusion of the parameter table p is optional.

■ steadystate in the argument SteadyStateConc^steadystate, must have the form of a replacement rule as generated by SteadyState or NSteadyState.

■ The default value for the Option, SteadyStateConc, is S.

■ The Option Normalized^False can be included to calculate non-normalized elasticity coefficients.

■ The Option Normalized^zerofluxposition, where zerofluxposition is a list {{/},{/}, }, can be included so that normalized coefficients are not calculated for fluxes through reactions i, j, ... . This is important when there are zero fluxes in the system as the normalized coefficients become undefined.

■ See also: PiElasticityMatrix.

FluxControlMatrix

■ FluxControlMatrix[S, N, v, p, SteadyState^ steadystate ] calculates a matrix for the metabolic system defined by S, N, v, and p, at the steady state given by the replacement rule steadystate, where the element mj is the normalized flux control coefficient of the flux through reaction i with respect to reaction j.

■ Inclusion of the parameter table p is optional.

■ steadystate in the argument SteadyStateConc ^steadystate, must have the form of a replacement rule as generated by SteadyState or NSteadyState.

■ The default value for the Option, SteadyStateConc, is S.

■ The Option Normalized^False can be included to calculate non-normalized control coefficients.

■ The Option Normalized^zerofluxposition, where zerofluxposition is a list {{/},{/}, }, can be included to so that normalized coefficients are not calculated for fluxes through reactions i, j, ... . This is important when there are zero fluxes in the system as the normalized coefficients become undefined.

■ See also: ConcControlMatrix.

FluxResponseMatrix

■ FluxResponseMatrix[S, N, v, {parameter list}, p, SteadyState0 steadystate ] returns a matrix where the element mjk is the flux response coefficient of the flux through reaction j in v with respect to the kth parameter of {parameter list}.

■ Inclusion of the parameter table p is optional.

■ steadystate in the argument SteadyStateConc0steadystate, must have the form of a replacement rule as generated by SteadyState or NSteadyState.

■ The default value for the Option, SteadyStateConc, is S.

■ The Option Normalized^False can be included to calculate non-normalized response coefficients.

■ The Option Normalized^zerofluxposition, where zerofluxposition is a list {{i},{j}, }, can be included so that normalized coefficients are not calculated for fluxes through reactions i, j, ... This is important when there are zero fluxes in the system as the normalized coefficients become undefined.

■ See also: ConcResponseMatrix.

LinkMatrix

■ LinkMatrix [S, N] rearranges the rows of N so that its upper rank(N) rows are linearly independent and form a submatrix No. Output of this function is a table. The first element of the table gives the new S. The second gives a 'Link Matrix', L, such that N = LNo = No. The third row gives the No matrix, the fourth the rearranged

N. The fifth element contains the matrix G which has the property GN = 0, and the last row gives the transformation rules for transforming the old matrices into the new matrices. Each transformation rule is in the form {old row number, new row number}.

■ See Section 4.9 for more information.

MMatrix

■ MMatrix[S, N, v, p, Normalized^False, SteadyStateConc0steadystate] calculates the Jacobian of the differential equation system defined by S, N, v, and p.

■ Note that the last three arguments are optional, however, the default value for Normalized is True.

NDSolveMatrix

■ NDSolveMatrix[S, N, v, initial conditions, {t,tmin,tmax}] uses the function NDSolve to find a numerical solution for the metabolite concentrations, S, with time in the range tmin to tmax, for a system of ordinary differential equations defined by the matrices S, N, and v, and subject to the initial conditions.

■ NDSolveMatrix[S, N, v, initial conditions, {t,tmin,tmax}, p] solves the system of ordinary differential equations defined by the matrices S, N, v, and the parameter matrix p. p has the form {{p1, value1},{p2, value2 }, ...}.

■ NDSolveMatrix has the same Options as NDSolve. NMatrix

■ NMatrix[eqn, extpars] generates a numerical-only stoichiometry matrix for the reaction system defined in the equation list, eqn; it takes into account the parameters in the list, extpars, are external parameters.

■ See also: StoichiometryMatrix. NSteadyState

■ NSteadyState[S, N, v, p, init] uses FindRoot to determine an approximate numerical solution to N v = 0 for a system of ordinary differential equations defined by the matrices S, N, v, and p. init contains initial estimates of the steady-state concentrations in the form of a replacement rule.

■ Inclusion of the parameter table p is optional.

■ NSteadyState gives solutions in terms of rules of the form x -> sol.

■ The constants returned by ConservationRelations must be assigned values before NSteadyState can be applied.

■ NDSteadyState has the same Options as FindRoot.

■ See also: NSteadyState, NDSolveMatrix, ConservationRelations. PartialConcResponse

■ PartialConcResponse[S, N, v, n, {parameter list}, p, SteadyState 0 steadystate] returns a matrix of partial concentration response coefficients for a metabolite at position n in S. Each entry mjk in the matrix gives the product of the concentration control coefficient with respect to reaction j and the p-elasticity coefficient with respect to reaction j and parameter k.

■ Inclusion of the parameter table p is optional.

■ steadystate in the argument SteadyStateConc^steadystate, must have the form of a replacement rule as generated by SteadyState or NSteadyState.

■ The default value for the Option, SteadyStateConc, is S.

■ The Option Normalized^False can be included to calculate non-normalized partial response coefficients.

■ See also: PartialFluxResponse.

PartialFluxResponse

■ PartialFluxResponse[S, N, v, n, {parameter list}, p, SteadyState 0 steadystate ] returns a matrix of partial flux response coefficients for a flux at position n in v. Each entry m jk in the matrix gives the product of the flux control coefficient with respect to reaction j and the p-elasticity coefficient with respect to reaction j and parameter k.

■ Inclusion of the parameter table p is optional.

■ steadystate in the argument SteadyStateConc0steadystate, must have the form of a replacement rule as generated by SteadyState or NSteadyState.

■ The default value for the Option, SteadyStateConc, is S.

■ The Option Normalized0False can be included to calculate non-normalized partial response coefficients.

■ The Option Normalized0zerofluxposition, where zerofluxposition is a list {{i},{}, }, can be included so that normalized coefficients are not calculated for fluxes through reactions i, j, ... . This is important when there are zero fluxes in the system as the normalized coefficients become undefined.

■ See also: PartialConcResponse.

PartialInternalConcResponse

■ PartialInternalConcResponse[S, N, v, n, m, p, SteadyState 0 steadystate]

returns a vector which contains the partial internal concentration response coefficients for a metabolite at position n in S with respect to a metabolite at position m in S. The jth position in the vector is the partial internal response coefficient for reaction j.

■ Inclusion of the parameter table p is optional.

■ steadystate in the argument SteadyStateConc0steadystate, must have the form of a replacement rule as generated by SteadyState or NSteadyState.

■ The default value for the Option, SteadyStateConc, is S.

■ The Option Normalized0False can be included to calculate non-normalized partial internal response coefficients.

■ See also: PartialInternalFluxResponse.

PartialInternalFluxResponse

■ PartialInternalFluxResponse[S, N, v, n, m, p, SteadyState 0 steadystate]

returns a vector which contains the partial internal flux response coefficients for a flux at position n in v with respect to a metabolite at position m in S. The jth position in the vector is the partial internal response coefficient for reaction j.

■ Inclusion of the parameter table p is optional.

■ steadystate in the argument SteadyStateConc0steadystate, must have the form of a replacement rule as generated by SteadyState or NSteadyState.

■ The default value for the Option, SteadyStateConc, is S.

■ The Option Normalized0False can be included to calculate non-normalized partial internal response coefficients.

■ The Option Normalized0zerofluxposition, where zerofluxposition is a list {{/},{/}, }, can be included so that normalized coefficients are not calculated for fluxes through reactions i, j, ... . This is important when there are zero fluxes in the system as the normalized coefficients become undefined.

■ See also: PartialInternalConcResponse.

PiElasticityMatrix

■ PiElasticityMatrix[S, N, v, {parameter list}, p, SteadyState 0 steadystate] returns a matrix where the element mik is the p-elasticity of reaction i in v with respect to the kth parameter of {parameter list}.

■ Inclusion of the parameter table p is optional.

■ steadystate in the argument SteadyStateConc0steadystate, must have the form of a replacement rule as generated by SteadyState or NSteadyState.

■ The default value for the Option, SteadyStateConc, is S.

■ The Option Normalized^False can be included to calculate non-normalized elasticity coefficients.

■ The Option Normalized^zerofluxposition, where zerofluxposition is a list {{/},{/}, }, can be included so that normalized coefficients are not calculated for fluxes through reactions i, j, ... . This is important when there are zero fluxes in the system as the normalized coefficients become undefined.

■ See also: EpsilonElasticityMatrix.

SMatrix

■ SMatrix[eqn, extpars] generates the corresponding substrate list, S, for the reaction system defined by eqn and extpars.

■ See also: NMatrix, VMatrix. Stability

■ Stability[S, N, v, p, SteadyStateConc 0 steadystate] assesses whether the differential equation system defined by, N, v, and p is asymptotically stable at the steady state given by the replacement rule steadystate. This function also returns the eigenvalues of the Jacobian of the differential equation system.

■ Inclusion of the parameter table p is optional.

■ steadystate in the argument SteadyStateConc ^steadystate, must have the form of a replacement rule as generated by SteadyState or NSteadyState.

SteadyState

■ SteadyState[S, N, v, p] uses Solve to determine the solution to N v = 0 for a system of ordinary differential equations defined by the matrices S, N, v, and p.

■ Inclusion of the parameter table p is optional.

■ SteadyState gives solutions in terms of rules of the form x -> sol.

■ See also: NSteadyState, NDSolveMatrix.

StoichiometryMatrix

■ StoichiometryMatrix[eqn, extpars] is similar to NMatrix except that it returns a stiochiometry matrix which has rows and columns labelled by metabolite names and reaction names, respectively.

■ See also: NMatrix. VMatrix

■ VMatrix [eqn, extpars] generates the corresponding reaction velocity list, v, for the reaction system defined by eqn.

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