Trimgdel

GRPRchecker(model, targetMet, gvalue)

GRPRchecker calculates the maximum GR and the minimu PR under the GR maximization when a constraint-based model, a target metabolite, and a gene deletion stratety are given.

USAGE:

function [GR, PR] – = GRPRchecker(model, targetMet, givenGvalue)

INPUTS:

• model – COBRA model structure containing the following required fields to perform gDel_minRN.

  *.rxns: Rxns in the model *.mets: Metabolites in the model *.genes: Genes in the model *.grRules: Gene-protein-reaction relations in the model *.S: Stoichiometric matrix (sparse) *.b: RHS of Sv = b (usually zeros) *.c: Objective coefficients *.lb: Lower bounds for fluxes *.ub: Upper bounds for fluxes *.rev: Reversibility of fluxes

• targetMet – target metabolites (e.g., ‘btn_c’)

• gvalue – The first column is the list of genes in the original model. The second column contains a 0/1 vector indicating which genes should be deleted.

  0: indicates genes to be deleted. 1: indecates genes to be remained.

OUTPUTS:

• GR – the growth rate obained when the gene deletion strategy is applied and the growth rate is maximized.

• PR – the minimum target metabolite production rate obained when the gene deletion strategy is applied and the growth rate is maximized.

TrimGdel(model, targetMet, maxLoop, PRLB, GRLB)

TrimGdel appropriately considers GPR rules and determines a minimal gene deletion strategies to achieve growth-coupled production for a given target metabolite and a genome-scale model. even in the worst-case analysis (ensures the weak-growth-coupled production).

Gurobi is required for this version. The CPLEX version is available on https://github.com/MetNetComp/TrimGdel

USAGE:

function [gvalue, GR, PR, size1, size2, size3, success] – = TrimGdel(model, targetMet, maxLoop, PRLB, GRLB)

INPUTS:

• model – COBRA model structure containing the following required fields to perform gDel_minRN.

  *.rxns: Rxns in the model *.mets: Metabolites in the model *.genes: Genes in the model *.grRules: Gene-protein-reaction relations in the model *.S: Stoichiometric matrix (sparse) *.b: RHS of Sv = b (usually zeros) *.c: Objective coefficients *.lb: Lower bounds for fluxes *.ub: Upper bounds for fluxes *.rev: Reversibility of fluxes

• targetMet – target metabolites (e.g., ‘btn_c’)

• maxLoop – the maximum number of iterations in gDel_minRN

• PRLB – the minimum required production rates of the target metabolites when gDel-minRN searches the gene deletion strategy candidates. (But it is not ensured to achieve this minimum required value when GR is maximized withoug PRLB.)

• GRLB – the minimum required growth rate when gDel-minRN searches the gene deletion strategy candidates.

OUTPUTS:

• gvalue – a small gene deletion strategy (obtained by TrimGdel). The first column is the list of genes. The second column is a 0/1 vector indicating which genes should be deleted.

  0: indicates genes to be deleted. 1: indecates genes to be remained.

• GR – the maximum growth rate when the obtained gene deletion strategy represented by gvalue is applied.

• PR – the minimum production rate of the target metabolite under the maximization of the growth rate when the obtained gene deletion strategy represented by gvalue is applied.

• size1 – the number of gene deletions after Step1.

• size2 – the number of gene deletions after Step2.

• size3 – the number of gene deletions after Step3.

• success – indicates whether TrimGdel obained an appropriate gene deletion strategy. (1:success, 0:failure)

Note

T. Tamura, “Trimming Gene Deletion Strategies for Growth-Coupled Production in Constraint-Based Metabolic Networks: TrimGdel,” in IEEE/ACM Transactions on Computational Biology and Bioinformatics, vol. 20, no. 2, pp. 1540-1549, 2023.

Comprehensive computational results are accumulated in MetNetComp database. https://metnetcomp.github.io/database1/indexFiles/index.html

T. Tamura, “MetNetComp: Database for Minimal and Maximal Gene-Deletion Strategies for Growth-Coupled Production of Genome-Scale Metabolic Networks,” in IEEE/ACM Transactions on Computational Biology and Bioinformatics, vol. 20, no. 6, pp. 3748-3758, 2023,

calculateGR(model, gvalue)

calculateGR is a function of gDel_minRN that reads a COBRA model and a 0-1 assignment for genes and outputs whether each reaction is repressed or not.

USAGE:

function [grRules] = calculateGR (model, gvalue)

INPUTS:

• model – COBRA model structure containing the following required fields to perform gDel_minRN.

  *.rxns: Rxns in the model *.mets: Metabolites in the model *.genes: Genes in the model *.grRules: Gene-protein-reaction relations in the model *.S: Stoichiometric matrix (sparse) *.b: RHS of Sv = b (usually zeros) *.c: Objective coefficients *.lb: Lower bounds for fluxes *.ub: Upper bounds for fluxes *.rev: Reversibility of fluxes

• gvalue – The first column is the list of genes in the original model. The second column contains a 0/1 vector indicating which genes should be deleted.

  0: indicates genes to be deleted. 1: indecates genes to be remained.

OUTPUT:

grRules – The first column is the list of GPR-rules. If a reaction does not have a GPR-rule, it is represented as 1. In the second columun, each gene is converted to 0 or 1 based on the given 0-1 assignment, with AND converted to * and OR converted to +. The third comumn contains the calculation results from the second column. The fourth column is 0 if the third column is 0 and 1 if it is greater. If it is 0, the reaction is repressed; if it is 1, it is not repressed.

example1()

example1 calculates the gene deletion strategy for growth coupling for succinate in e_coli_core.

USAGE:

function [] = example1()

example2()

example2 calculates the gene deletion strategy for growth coupling for biotin in iML1515.

USAGE:

function [] = example2()

example3()

example3 calculates the gene deletion strategy for growth coupling for riboflavin in iML1515.

USAGE:

function [] = example3()

example4()

example4 calculates the gene deletion strategy for growth coupling for pantothenate in iML1515.

USAGE:

function [] = example4()

example5()

example5 calculates the gene deletion strategy for growth coupling for succinate in iMM904.

USAGE:

function [] = example5()

gDel_minRN(model, targetMet, maxLoop, PRLB, GRLB)

gDel-minRN (Step 1 of TrimGdel) determines gene deletion strategies by mixed integer linear programming to achieve growth coupling for the target metabolite by repressing the maximum number of reactions via gene-protein-reaction relations.

USAGE:

function [vg gr pr it success] – = gDel_minRN(model, targetMet, maxLoop, PRLB, GRLB)

INPUTS:

• model – COBRA model structure containing the following required fields to perform gDel_minRN.

  *.rxns: Rxns in the model *.mets: Metabolites in the model *.genes: Genes in the model *.grRules: Gene-protein-reaction relations in the model *.S: Stoichiometric matrix (sparse) *.b: RHS of Sv = b (usually zeros) *.c: Objective coefficients *.lb: Lower bounds for fluxes *.ub: Upper bounds for fluxes *.rev: Reversibility of fluxes

• targetMet – target metabolites (e.g., ‘btn_c’)

• maxLoop – the maximum number of iterations in gDel_minRN

• PRLB – the minimum required production rates of the target metabolites when gDel-minRN searches the gene deletion strategy candidates. (But it is not ensured to achieve this minimum required value when GR is maximized withoug PRLB.)

• GRLB – the minimum required growth rate when gDel-minRN searches the gene deletion strategy candidates.

OUTPUTS:

• gvalue – The first column is the list of genes in the original model. The second column contains a 0/1 vector indicating which genes should be deleted.

  0: indicates genes to be deleted. 1: indecates genes to be remained.

• gr – the growth rate obained when the gene deletion strategy is applied and the growth rate is maximized.

• pr – the target metabolite production rate obained when the gene deletion strategy is applied and the growth rate is maximized.

• it – indicates how many iterations were necessary to obtain the solution.

• success – indicates whether gDel_minRN obained an appropriate gene deletion strategy. (1:success, 0:failure)

geneReactionMILP(model, term, ng, nt, nr, nko)

geneReactionMILP is a submodule to convert GPR relations to MILP.

USAGE:

function [f, A, b, Aeq, beq, lb, ub, xname] – = geneReactionMILP(model, term, ng, nt, nr, nko)

INPUTS:

• model – COBRA model structure containing the following required fields to perform gDel_minRN.

  *.rxns: Rxns in the model *.mets: Metabolites in the model *.genes: Genes in the model *.grRules: Gene-protein-reaction relations in the model *.S: Stoichiometric matrix (sparse) *.b: RHS of Sv = b (usually zeros) *.c: Objective coefficients *.lb: Lower bounds for fluxes *.ub: Upper bounds for fluxes *.rev: Reversibility of fluxes

• term – the list of Boolean functions extracted from the gene-protein-reaction relations

• ng – the number of genes

• nt – the number of internal terms

• nr – the number of reactions

• nko – the number of repressible reactions

OUTPUTS:

• f – the weighted vector for the objective function of the resulting MILP.

• A, b, Aeq, beq, lb, ub – correspond to each matrix included in the following part of the MILP constraints.

  A*x <= b Aeq*x=beq lb <= x <= ub

• xname – variable names in the resulting MILP.

modelSetting(model, targetMet)

modelSetting is a function of gDel_minRN that adds an auxiliary exchange reaction for the target metabolite when there is no original corresponding exchange reaction.

USAGE:

function [model2,targetRID,extype] = modelSetting (model,targetMet)

INPUTS:

• model – COBRA model structure containing the following required fields to perform gDel_minRN.

  *.rxns: Rxns in the model *.mets: Metabolites in the model *.genes: Genes in the model *.grRules: Gene-protein-reaction relations in the model *.S: Stoichiometric matrix (sparse) *.b: RHS of Sv = b (usually zeros) *.c: Objective coefficients *.lb: Lower bounds for fluxes *.ub: Upper bounds for fluxes *.rev: Reversibility of fluxes

• targetMet – target metabolites (e.g., ‘btn_c’)

OUTPUTS:

• model2 – the model that has the exchange reaction of the target metabolite

• targetRID – ID of the exchange reaction of the target metabolite

• extype – indicates that an auxiliary exchange reaction was added. 1,2: there was the corresponding exchange reaction. 3: An auxiliary exchange reaction was added.

readGeneRules(model)

readGeneRules is a function of gDel_minRN that reads gene-protein-reaction relations and outputs the necessary information for the MILP formalization

USAGE:

function [term, ng, nt, nr, nko, reactionKO, reactionKO2term] = readGeneRules (model)

INPUTS:

model – COBRA model structure containing the following required fields to perform gDel_minRN.

*.rxns: Rxns in the model *.mets: Metabolites in the model *.genes: Genes in the model *.grRules: Gene-protein-reaction relations in the model *.S: Stoichiometric matrix (sparse) *.b: RHS of Sv = b (usually zeros) *.c: Objective coefficients *.lb: Lower bounds for fluxes *.ub: Upper bounds for fluxes *.rev: Reversibility of fluxes

OUTPUTS:

• term – the list of Boolean functions extracted from the gene-protein-reaction relations

• ng – the number of genes

• nt – the number of internal terms

• nr – the number of reactions

• nko – the number of repressible reactions

step2and3(model, targetMet, givenGvalue)

The function step2and3 implements Step 2 and Step 3 of TrimGdel. Step 2 minimizes the number of deleted genes while maintaining which reactions are repressed. Step 3 trims unnecessary deleted genes while maintaining GR and PR at the maximization of GR.

USAGE:

function [gvalue, finalGRPR, size1, size2, size3] = step2and3 (model, targetMet, givenGvalue)

INPUTS:

• model – COBRA model structure containing the following required fields to perform gDel_minRN. *.rxns: Rxns in the model *.mets: Metabolites in the model *.genes: Genes in the model *.grRules: Gene-protein-reaction relations in the model *.S: Stoichiometric matrix (sparse) *.b: RHS of Sv = b (usually zeros) *.c: Objective coefficients *.lb: Lower bounds for fluxes *.ub: Upper bounds for fluxes *.rev: Reversibility of fluxes

• targetMet – target metabolites (e.g., ‘btn_c’)

• givenGvalue – a large gene deletion strategy (obtained by step1). The first column is the list of genes. The second column is a 0/1 vector indicating which genes should be deleted.

  0: indicates genes to be deleted. 1: indecates genes to be remained.

OUTPUTS:

• gvalue – a small gene deletion strategy (obtained by TrimGdel). The first column is the list of genes. The second column is a 0/1 vector indicating which genes should be deleted.

  0: indicates genes to be deleted. 1: indecates genes to be remained.

• GR – the maximum growth rate when the obtained gene deletion strategy represented by gvalue is applied.

• PR – the minimum production rate of the target metabolite under the maximization of the growth rate when the obtained gene deletion strategy represented by gvalue is applied.

• size1 – the number of gene deletions after Step1.

• size2 – the number of gene deletions after Step2.

• size3 – the number of gene deletions after Step3.