This model's stoichiometry consistent

Stoichiometric inconsistency violates universal constraints: 1. Molecular masses are always positive, and 2. On each side of a reaction the mass is conserved. A single incorrectly defined reaction can lead to stoichiometric inconsistency in the model, and consequently to unconserved metabolites. Similar to insufficient constraints, this may give rise to cycles which either produce mass from nothing or consume mass from the model. Implementation: This test uses an implementation of the algorithm presented in section 3.1 by Gevorgyan, A., M. G Poolman, and D. A Fell. "Detection of Stoichiometric Inconsistencies in Biomolecular Models." Bioinformatics 24, no. 19 (2008): 2245. doi: 10.1093/bioinformatics/btn425

A total of 19 (0.82%) reactions are mass unbalanced with at least one of the metabolites not having a formula or the overall mass not equal to 0: __iECx55__ENLIPIDAt2ex, __iECx55__CLBtex, __iECx55__ACGAL6PISO, __iECx55__ENLIPIDAt1ex, __iECx55__GALAMPTSpp, ...

This will exclude biomass, exchange and demand reactions as they are unbalanced by definition. It will also fail all reactions where at least one metabolite does not have a formula defined. In steady state, for each metabolite the sum of influx equals the sum of efflux. Hence the net masses of both sides of any model reaction have to be equal. Reactions where at least one metabolite does not have a formula are not considered to be balanced, even though the remaining metabolites participating in the reaction might be. Implementation: For each reaction that isn't a boundary or biomass reaction check if each metabolite has a non-zero elements attribute and if so calculate if the overall element balance of reactants and products is equal to zero.

A total of 0 (0.00%) reactions are charge unbalanced with at least one of the metabolites not having a charge or the overall charge not equal to 0:

This will exclude biomass, exchange and demand reactions as they are unbalanced by definition. It will also fail all reactions where at least one metabolite does not have a charge defined. In steady state, for each metabolite the sum of influx equals the sum of efflux. Hence the net charges of both sides of any model reaction have to be equal. Reactions where at least one metabolite does not have a charge are not considered to be balanced, even though the remaining metabolites participating in the reaction might be. Implementation: For each reaction that isn't a boundary or biomass reaction check if each metabolite has a non-zero charge attribute and if so calculate if the overall sum of charges of reactants and products is equal to zero.

A total of 0 (0.00%) metabolites are not associated with any reaction of the model:

Disconnected metabolites are not part of any reaction in the model. They are most likely left-over from the reconstruction process, but may also point to network and knowledge gaps. Implementation: Check for any metabolites of the cobra.Model object with emtpy reaction attribute.

A large fraction of model reactions able to carry unlimited flux under default conditions indicates problems with reaction directionality, missing cofactors, incorrectly defined transport reactions and more. Implementation: Without changing the default constraints run flux variability analysis. From the FVA results identify those reactions that carry flux equal to the model's maximal or minimal flux.

A total of 0 metabolites (0.00%) lack annotation with any type of SBO term:

The Systems Biology Ontology (SBO) allows researchers to annotate a model with terms which indicate the intended function of its individual components. The available terms are controlled and relational and can be viewed here http://www.ebi.ac.uk/sbo/main/tree. Implementation: Check if each cobra.Metabolite has a non-zero "annotation" attribute that contains the key "sbo".

A total of 91 transport reactions (4.73% of all metabolites) lack annotation with the SBO term "SBO:0000247" for 'simple chemical': 3hdecACP_c, tdec2eACP_c, 3hddecACP_c, tddec2eACP_c, 3hcddec5eACP_c, ...

SBO:0000247 represents the term 'simple chemical'. Every metabolite should be annotated with this. Implementation: Check if each cobra.Metabolite has a non-zero "annotation" attribute that contains the key "sbo" with the associated value being one of the SBO terms above.

A total of 0 reactions (0.00%) lack annotation with any type of SBO term:

The Systems Biology Ontology (SBO) allows researchers to annotate a model with terms which indicate the intended function of its individual components. The available terms are controlled and relational and can be viewed here http://www.ebi.ac.uk/sbo/main/tree. Implementation: Check if each cobra.Reaction has a non-zero "annotation" attribute that contains the key "sbo".

A total of 0 metabolic reactions (0.00% of all purely metabolic reactions) lack annotation with the SBO term "SBO:0000176" for 'biochemical reaction':

SBO:0000176 represents the term 'biochemical reaction'. Every metabolic reaction that is not a transport or boundary reaction should be annotated with this. The results shown are relative to the total amount of pure metabolic reactions. Implementation: Check if each pure metabolic reaction has a non-zero "annotation" attribute that contains the key "sbo" with the associated value being the SBO term above.

A total of 0 metabolic reactions (0.00% of all transport reactions) lack annotation with one of the SBO terms: ['SBO:0000185', 'SBO:0000588', 'SBO:0000587', 'SBO:0000655', 'SBO:0000654', 'SBO:0000660', 'SBO:0000659', 'SBO:0000657', 'SBO:0000658'] for 'biochemical reaction':

'SBO:0000185', 'SBO:0000588', 'SBO:0000587', 'SBO:0000655', 'SBO:0000654', 'SBO:0000660', 'SBO:0000659', 'SBO:0000657', and 'SBO:0000658' represent the terms 'transport reaction' and 'translocation reaction', in addition to their children (more specific transport reaction labels). Every transport reaction that is not a pure metabolic or boundary reaction should be annotated with one of these terms. The results shown are relative to the total of all transport reactions. Implementation: Check if each transport reaction has a non-zero "annotation" attribute that contains the key "sbo" with the associated value being one of the SBO terms above.

A total of 0 exchange reactions (0.00% of all exchange reactions) lack annotation with the SBO term "SBO:0000627" for 'exchange reaction':

SBO:0000627 represents the term 'exchange reaction'. The Systems Biology Ontology defines an exchange reaction as follows: 'A modeling process to provide matter influx or efflux to a model, for example to replenish a metabolic network with raw materials (eg carbon / energy sources). Such reactions are conceptual, created solely for modeling purposes, and do not have a physical correspondence. Exchange reactions, often represented as 'R_EX_', can operate in the negative (uptake) direction or positive (secretion) direction. By convention, a negative flux through an exchange reaction represents uptake of the corresponding metabolite, and a positive flux represent discharge.' Every exchange reaction should be annotated with this. Exchange reactions differ from demand reactions in that the metabolites are removed from or added to the extracellular environment only. Implementation: Check if each exchange reaction has a non-zero "annotation" attribute that contains the key "sbo" with the associated value being one of the SBO terms above.

The model has no demand reactions.

SBO:0000628 represents the term 'demand reaction'. The Systems Biology Ontology defines a demand reaction as follows: 'A modeling process analogous to exchange reaction, but which operates upon "internal" metabolites. Metabolites that are consumed by these reactions are assumed to be used in intra-cellular processes that are not part of the model. Demand reactions, often represented 'R_DM_', can also deliver metabolites (from intra-cellular processes that are not considered in the model).' Every demand reaction should be annotated with this. Demand reactions differ from exchange reactions in that the metabolites are not removed from the extracellular environment, but from any of the organism's compartments. Demand reactions differ from sink reactions in that they are designated as irreversible. Implementation: Check if each demand reaction has a non-zero "annotation" attribute that contains the key "sbo" with the associated value being one of the SBO terms above.

No sink reactions found.

SBO:0000632 represents the term 'sink reaction'. The Systems Biology Ontology defines a sink reaction as follows: 'A modeling process to provide matter influx or efflux to a model, for example to replenish a metabolic network with raw materials (eg carbon / energy sources). Such reactions are conceptual, created solely for modeling purposes, and do not have a physical correspondence. Unlike the analogous demand (SBO:....) reactions, which are usually designated as irreversible, sink reactions always represent a reversible uptake/secretion processes, and act as a metabolite source with no cost to the cell. Sink reactions, also referred to as R_SINK_, are generally used for compounds that are metabolized by the cell but are produced by non-metabolic, un-modeled cellular processes.' Every sink reaction should be annotated with this. Sink reactions differ from exchange reactions in that the metabolites are not removed from the extracellular environment, but from any of the organism's compartments. Implementation: Check if each sink reaction has a non-zero "annotation" attribute that contains the key "sbo" with the associated value being one of the SBO terms above.

A total of 0 biomass reactions (0.00% of all biomass reactions) lack annotation with the SBO term "SBO:0000629" for 'biomass production':

SBO:0000629 represents the term 'biomass production'. The Systems Biology Ontology defines an exchange reaction as follows: 'Biomass production, often represented 'R_BIOMASS_', is usually the optimization target reaction of constraint-based models, and can consume multiple reactants to produce multiple products. It is also assumed that parts of the reactants are also consumed in unrepresented processes and hence products do not have to reflect all the atom composition of the reactants. Formulation of a biomass production process entails definition of the macromolecular content (eg. cellular protein fraction), metabolic constitution of each fraction (eg. amino acids), and subsequently the atomic composition (eg. nitrogen atoms). More complex biomass functions can additionally incorporate details of essential vitamins and cofactors required for growth.' Every reaction representing the biomass production should be annotated with this. Implementation: Check if each biomass reaction has a non-zero "annotation" attribute that contains the key "sbo" with the associated value being one of the SBO terms above.

1924 metabolites are defined in the model.

To be useful a metabolic model should consist at least of a few metabolites that are converted by reactions. This test simply checks if there are more than zero metabolites. Implementation: Check if the cobra.Model object has non-empty "metabolites" attribute, this list is populated from the list of sbml:listOfSpecies which should contain at least one sbml:species.

2724 reactions are defined in the model.

To be useful a metabolic model should consist at least of a few reactions. This test simply checks if there are more than zero reactions. Implementation: Check if the cobra.Model object has non-empty "reactions" attribute, this list is populated from the list of sbml:listOfReactions which should contain at least one sbml:reaction.

This model contains 0 unconserved metabolites:

The list of unconserved metabolites is computed using the algorithm described in section 3.2 of "Detection of Stoichiometric Inconsistencies in Biomolecular Models." Bioinformatics 24, no. 19 (2008): 2245. doi: 10.1093/bioinformatics/btn425.

There are a total of 0 metabolites in the model which have duplicates in the same compartment:

The main reason for having this test is to help cleaning up merged models or models from automated reconstruction pipelines as these are prone to having identical metabolites from different namespaces (hence different IDs). This test therefore expects that every metabolite in any particular compartment has unique inchikey values. Implementation: Identifies duplicate metabolites in each compartment by determining if any two metabolites have identical InChI-key annotations. For instance, this function would find compounds with IDs ATP1 and ATP2 in the cytosolic compartment, with both having the same InChI annotations.

There are a total of 0 metabolites (0.00%) without a charge:

To be able to ensure that reactions are charge-balanced, all model metabolites ought to be provided with a charge. Since it may be difficult to obtain charges for certain metabolites this test serves as a mere report. Models can still be stoichiometrically consistent even when charge information is not defined for each metabolite. Implementation: Check if each cobra.Metabolite has a non-empty "charge" attribute. This attribute is set by the parser if there is an fbc:charge attribute for the corresponding species in the SBML.

There are a total of 23 metabolites (1.20%) without a formula: __iECx55__colipaOA_e, __iECx55__diact_e, __iECx55__indpyr_c, __iECx55__pprdn_c, __iECx55__5aptn_c, ...

To be able to ensure that reactions are mass-balanced, all model metabolites ought to be provided with a chemical formula. Since it may be difficult to obtain formulas for certain metabolites this test serves as a mere report. Models can still be stoichiometrically consistent even when chemical formulas are not defined for each metabolite. Implementation: Check if each cobra.Metabolite has a non-empty "formula" attribute. This attribute is set by the parser if there is an fbc:chemicalFormula attribute for the corresponding species in the SBML.

This test checks all boundary reactions in the model that permit flux towards creating a metabolite, and reports those metabolites. This test does not have any mandatory 'pass' criteria. Implementation: Identify the metabolite IDs of each reaction in the method cobra.Model.medium. Model.medium returns exchange reactions whose bounds permit the uptake of metabolites.

A total of 1500 (55.07%) purely metabolic reactions are defined in the model, this excludes transporters, exchanges, or pseudo-reactions: GPDDA1, 3OAR40, GPDDA1pp, ALATA_D2, MTHFC_1, ...

If a reaction is neither a transport reaction, a biomass reaction nor a boundary reaction, it is counted as a purely metabolic reaction. This test requires the presence of metabolite formula to be able to identify transport reactions. This test is passed when the model contains at least one purely metabolic reaction i.e. a conversion of one metabolite into another. Implementation: From the list of all reactions, those that are boundary, transport and biomass reactions are removed and the remainder assumed to be pure metabolic reactions. Boundary reactions are identified using the attribute cobra.Model.boundary. Please read the description of "Transport Reactions" and "Biomass Reaction Identified" to learn how they are identified.

A total of 830 (30.47%) transport reactions are defined in the model, this excludes purely metabolic reactions, exchanges, or pseudo-reactions: OCDCEAtexi, MELIBt2pp, URIt2pp, FRUpts2pp, CHTBStex, ...

Cellular metabolism in any organism usually involves the transport of metabolites across a lipid bi-layer. This test reports how many of these reactions, which transports metabolites from one compartment to another, are present in the model, as at least one transport reaction must be present for cells to take up nutrients and/or excrete waste. Implementation: A transport reaction is defined as follows: 1. It contains metabolites from at least 2 compartments and 2. at least 1 metabolite undergoes no chemical reaction, i.e., the formula and/or annotation stays the same on both sides of the equation. A notable exception is transport via PTS, which also contains the following restriction: 3. The transported metabolite(s) are transported into a compartment through the exchange of a phosphate. An example of transport via PTS would be pep(c) + glucose(e) -> glucose-6-phosphate(c) + pyr(c) Reactions similar to transport via PTS (referred to as "modified transport reactions") follow a similar pattern: A(x) + B-R(y) -> A-R(y) + B(y) Such modified transport reactions can be detected, but only when the formula is defined for all metabolites in a particular reaction. If this is not the case, transport reactions are identified through annotations, which cannot detect modified transport reactions.

A total of 5 (0.60%) transport reactions have fixed constraints in the model: 0.0 <= SUCTARTtpp <= 0.0, 0.0 <= SUCMALtpp <= 0.0, 0.0 <= SUCASPtpp <= 0.0, 0.0 <= __iECx55__CHITOBpts <= 0.0, 0.0 <= SUCFUMtpp <= 0.0

Cellular metabolism in any organism usually involves the transport of metabolites across a lipid bi-layer. Hence, this test reports how many of these reactions, which transports metabolites from one compartment to another, have fixed constraints. This test does not have any mandatory 'pass' criteria. Implementation: Please refer to "Transport Reactions" for details on how memote identifies transport reactions. From the pool of transport reactions identify reactions which are constrained to values other than the model's median lower and upper bounds.

Based on metabolites, directionality and compartment there are a total of 0 reactions in the model which have duplicates:

Identify reactions in a pairwise manner that use the same set of metabolites including potentially duplicate metabolites. Moreover, it will take a reaction's directionality and compartment into account. The main reason for having this test is to help cleaning up merged models or models from automated reconstruction pipelines as these are prone to having identical reactions with identifiers from different namespaces. Implementation: Compare reactions in a pairwise manner. For each reaction, the metabolite annotations are checked for a description of the structure (via InChI and InChIKey).If they exist, substrates and products as well as the stoichiometries of any reaction pair are compared. Only reactions where the substrates, products, stoichiometry and reversibility are identical are considered to be duplicates. This test will not be able to identify duplicate reactions if there are no structure annotations. Further, it will report reactions with differing bounds as equal if they otherwise match the above conditions.

There are a total of 154 reactions (5.65%) without GPR: PHEMEtiex, ACACt2pp, MOX, XYLUt2pp, CYSIabcpp, ...

Gene-Protein-Reaction rules express which gene has what function. The presence of this annotation is important to justify the existence of reactions in the model, and is required to conduct in silico gene deletion studies. However, reactions without GPR may also be valid: Spontaneous reactions, or known reactions with yet undiscovered genes likely lack GPR. Implementation: Check if each cobra.Reaction has a non-empty "gene_reaction_rule" attribute, which is set by the parser if there is an fbc:geneProductAssociation defined for the corresponding reaction in the SBML.

There are a total of 77 transport reactions (9.28% of all transport reactions) without GPR: 12DGR180tipp, __iECx55__FECRMUtex, BTNt2ipp, GUAtpp, PYDXtpp, ...

As it is hard to identify the exact transport processes within a cell, transport reactions are often added purely for modeling purposes. Highlighting where assumptions have been made versus where there is proof may help direct the efforts to improve transport and transport energetics of the tested metabolic model. However, transport reactions without GPR may also be valid: Diffusion, or known reactions with yet undiscovered genes likely lack GPR. Implementation: Check which cobra.Reactions classified as transport reactions have a non-empty "gene_reaction_rule" attribute.

A total of 297 reactions are catalyzed by complexes defined through GPR rules in the model.

Based on the gene-protein-reaction (GPR) rules, it is possible to infer whether a reaction is catalyzed by a single gene product, isozymes or by a heteromeric protein complex. This test checks that at least one such heteromeric protein complex is defined in any GPR of the model. For S. cerevisiae it could be shown that "essential proteins tend to [cluster] together in essential complexes" (https://doi.org/10.1074%2Fmcp.M800490-MCP200). This might also be a relevant metric for other organisms. Implementation: Identify GPRs which contain at least one logical AND that combines two different gene products.

In this model 2 the following biomass reactions were identified: __iECx55__BIOMASS_Ec_iJO1366_WT_53p95M, __iECx55__BIOMASS_Ec_iJO1366_core_53p95M

The biomass composition aka biomass formulation aka biomass reaction is a common pseudo-reaction accounting for biomass synthesis in constraints-based modelling. It describes the stoichiometry of intracellular compounds that are required for cell growth. While this reaction may not be relevant to modeling the metabolism of higher organisms, it is essential for single-cell modeling. Implementation: Identifies possible biomass reactions using two principal steps: 1. Return reactions that include the SBO annotation "SBO:0000629" for biomass. If no reactions can be identifies this way: 1. Look for the ``buzzwords`` "biomass", "growth" and "bof" in reaction IDs. 2. Look for metabolite IDs or names that contain the ``buzzword`` "biomass" and obtain the set of reactions they are involved in. 3. Remove boundary reactions from this set. 4. Return the union of reactions that match the buzzwords and of the reactions that metabolites are involved in that match the buzzword. This test checks if at least one biomass reaction is present.

A total of 2 NGAM reactions could be identified: ATPM, ATPM:2

The Non-Growth Associated Maintenance reaction (NGAM) is an ATP-hydrolysis reaction added to metabolic models to represent energy expenses that the cell invests in continuous processes independent of the growth rate. Memote tries to infer this reaction from a list of buzzwords, and the stoichiometry and components of a simple ATP-hydrolysis reaction. Implementation: From the list of all reactions that convert ATP to ADP select the reactions that match the irreversible reaction "ATP + H2O -> ADP + HO4P + H+", whose metabolites are situated within the main model compartment. The main model compartment is assumed to be the cytosol, yet, if that cannot be identified, it is assumed to be the compartment with the most metabolites. The resulting list of reactions is then filtered further by attempting to match the reaction name with any of the following buzzwords ('maintenance', 'atpm', 'requirement', 'ngam', 'non-growth', 'associated'). If this is possible only the filtered reactions are returned, if not the list is returned as is.

There are a total of 5 reversible oxygen-containing reactions (11.11% of all oxygen-containing reactions): MOX, EX_o2_e, O2tpp, O2Stex, O2tex

The directionality of oxygen-producing/-consuming reactions affects the model's ability to grow anaerobically i.e. create faux-anaerobic organisms. This test reports how many of these oxygen-containing reactions are reversible. This test does not have any mandatory 'pass' criteria. Implementation: First, find the metabolite representing atmospheric oxygen in the model on the basis of an internal mapping table or by specifically looking for the formula "O2". Then, find all reactions that produce or consume oxygen and report those that are reversible.

Universally blocked reactions are reactions that during Flux Variability Analysis cannot carry any flux while all model boundaries are open. Generally blocked reactions are caused by network gaps, which can be attributed to scope or knowledge gaps. Implementation: Use flux variability analysis (FVA) implemented in cobra.flux_analysis.find_blocked_reactions with open_exchanges=True. Please refer to the cobrapy documentation for more information: https://cobrapy.readthedocs.io/en/stable/autoapi/cobra/flux_analysis/ variability/index.html#cobra.flux_analysis.variability. find_blocked_reactions

A total of 63 (3.27%) metabolites are not produced by any reaction of the model: apoACP_c, ag_c, trnaala_c, __iECx55__alpp_p, ap5a_c, ...

Orphans are metabolites that are only consumed but not produced by reactions in the model. They may indicate the presence of network and knowledge gaps. Implementation: Find orphan metabolites structurally by considering only reaction equations and bounds. FBA is not carried out.

A total of 87 (4.52%) metabolites are not consumed by any reaction of the model: hqn_c, acanth_c, aconm_c, alatrna_c, __iECx55__lpp_p, ...

Dead-ends are metabolites that can only be produced but not consumed by reactions in the model. They may indicate the presence of network and knowledge gaps. Implementation: Find dead-end metabolites structurally by considering only reaction equations and bounds. FBA is not carried out.

Stoichiometrically Balanced Cycles are artifacts of insufficiently constrained networks resulting in reactions that can carry flux when all the boundaries have been closed. Implementation: Close all model boundary reactions and then use flux variability analysis (FVA) to identify reactions that carry flux.

In complete medium, a model should be able to divert flux to every metabolite. This test opens all the boundary reactions i.e. simulates a complete medium and checks if any metabolite cannot be produced individually using flux balance analysis. Metabolites that cannot be produced this way are likely orphan metabolites, downstream of reactions with fixed constraints, or blocked by a cofactor imbalance. To pass this test all metabolites should be producible. Implementation: Open all model boundary reactions, then for each metabolite in the model add a boundary reaction and maximize it with FBA.

In complete medium, a model should be able to divert flux from every metabolite. This test opens all the boundary reactions i.e. simulates a complete medium and checks if any metabolite cannot be consumed individually using flux balance analysis. Metabolites that cannot be consumed this way are likely dead-end metabolites or upstream of reactions with fixed constraints. To pass this test all metabolites should be consumable. Implementation: Open all model boundary reactions, then for each metabolite in the model add a boundary reaction and minimize it with FBA.

The ratio of the absolute values of the largest coefficient 54.124831 and the lowest, non-zero coefficient 2e-06 is: 2.71E+07.

This test will return the absolute largest and smallest, non-zero coefficients of the stoichiometric matrix. A large ratio of these values may point to potential numerical issues when trying to solve different mathematical optimization problems such as flux-balance analysis. To pass this test the ratio should not exceed 10^9. This threshold has been selected based on experience, and is likely to be adapted when more data on solver performance becomes available. Implementation: Compose the stoichiometric matrix, then calculate absolute coefficients and lastly use the maximal value and minimal non-zero value to calculate the ratio.

The number of independent conservation relations is 52.

This test will return the number of conservation relations, i.e., conservation pools through the left null space of the stoichiometric matrix. This test is not scored, as the dimension of the left null space is system-specific. Implementation: Calculate the left null space, i.e., the null space of the transposed stoichiometric matrix, using an algorithm based on the singular value decomposition adapted from https://scipy.github.io/old-wiki/pages/Cookbook/RankNullspace.html Then, return the estimated dimension of that null space.

The rank of the S-Matrix is 1872.

The rank of the stoichiometric matrix is system specific. It is calculated using singular value decomposition (SVD). Implementation: Compose the stoichiometric matrix, then estimate the rank, i.e. the dimension of the column space, of a matrix. The algorithm used by this function is based on the singular value decomposition of the matrix.

The degrees of freedom of the S-Matrix are 852.

The degrees of freedom of the stoichiometric matrix, i.e., the number of 'free variables' is system specific and corresponds to the dimension of the (right) null space of the matrix. Implementation: Compose the stoichiometric matrix, then calculate the dimensionality of the null space using the rank-nullity theorem outlined by Alama, J. The Rank+Nullity Theorem. Formalized Mathematics 15, (2007).