Metabolic Modeling Tutorial
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Metabolic Modeling Tutorial
discounted EARLY registration ends Dec 31, 2014
Metabolic Modeling Tutorial
discounted EARLY registration ends Dec 31, 2014
Metabolic Modeling Tutorial
discounted EARLY registration ends Dec 31, 2014
Metabolic Modeling Tutorial
discounted EARLY registration ends Dec 31, 2014

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Pathway/Genome Database Concepts Guide

Contents

    1  Overview

    2  What Mechanisms Exist for Accessing PGDB Data?

    3  PGDB Reactions
        3.1  Reaction Types
        3.2  Reaction Direction
        3.3  Reaction Locations and Compartments of Metabolites
        3.4  Reaction Balancing and Protonation State in PGDBs
            3.4.1  Background and Motivations
            3.4.2  Protonation State Normalization
            3.4.3  Computational Reaction Balancing for Hydrogen
            3.4.4  Statistics on Reaction Balance and Protonation circa 2009
        3.5  Reaction Atom Mappings
            3.5.1  Downloading Atom Mappings
            3.5.2  Atom Mapping Encoding
            3.5.3  Atom Mapping Data using SMILES
            3.5.4  Canonicalization of Atom Mapping Encoding

    4  Computing Gibbs Free Energy of Compounds and Reactions in MetaCyc

    5  PGDB Pathways
        5.1  How are Pathway Boundaries Defined?
        5.2  Super Pathways and Base Pathways
        5.3  Pathway Variants
        5.4  Conspecific and Chimeric Pathways
        5.5  Do We Force a Pathway View of the Metabolic Network?

    6  Evidence Codes

    7  Use of Gene Ontology Terms

    8  How to Learn More

1  Overview

This document describes concepts involved in Pathway/Genome Databases (PGDBs) managed by the Pathway Tools software, such as those in the BioCyc PGDB collection.

2  What Mechanisms Exist for Accessing PGDB Data?

PGDB data is accessible in several ways, which are described in more detail on the downloads page.

  • Query and visualization access is available through the BioCyc Web site and other Pathway Tools based Web sites.

  • Data files for PGDBs are available for download in multiple file formats.

  • PGDBs can be loaded into SRI’s BioWarehouse relational database system (Oracle or MySQL based) for querying.

  • SRI provides a downloadable "software/database bundle" that couples Pathway Tools with selected BioCyc PGDBs. It supports querying, visualization, and analysis of PGDBs in both a desktop mode of operation, and it will operate as a Web server. It also allows users to create their own Pathway/Genome Databases. The software/database bundle includes functionality not available through the BioCyc Web site.

  • Web services support many PGDB data queries and visualization operations.

  • The software/database bundle also allows users to query PGDB data via APIs for the Java, Perl, and Common Lisp languages.

  • The BioCyc iPhone application supports querying of PGDB gene data, and is available through the Apple iTunes store.

3  PGDB Reactions

This section introduces concepts relevant to PGDB reactions.

3.1  Reaction Types

PGDBs can encompass multiple types of reactions, which are classified using the PGDB reaction ontology. Most “standard” metabolic reactions are instances of the class Chemical-Reactions, which is a child of class Simple-Reactions. The main classes in the reaction ontology are as follows.

  • Simple-Reactions: Reactions that are considered indivisible at the current level of abstraction.

    • Binding-Reactions: Binding reactions involve binding or dissociation of non-covalent bonds; they do not involve formation or dissociation of covalent bonds. Example: association of two protein monomers to form a complex.

    • Chemical-Reactions: Chemical-Reactions are those for which at least one substrate molecule is chemically modified, meaning that either a chemical bond (covalent, ionic or coodination) is formed and/or broken, or that a redox modification has occurred.

    • Redox-Half-Reactions: Redox half reactions are elementary reactions, in which explicitly stated electrons are reducing an oxidized molecular species. These reactions do not stand alone, because electrons do not occur freely. Instead, a half reaction must be paired with another half reaction to form a complete, overall transformation.

    • Transport-Reactions: Transport reactions are reactions in which at least one species is transported (passively or actively) across a membrane. The species may or may not be chemically modified in the course of the reaction.

  • Complex-Processes: Instances of this type of reaction are known to be multi-step processes, but where the multiple steps are not currently represented. Example: Transcription.

  • Unknown-Conversions: Reactions for which it is not known whether they are simple reactions or complex processes.

3.2  Reaction Direction

How do PGDBs handle reaction direction?

In a PGDB, each reaction is stored as an object that is an instance of the Reactions class. That object includes two slots, Left and Right, each of which contains a list of chemicals that are the reactants and products (not necessarily respectively) of the reaction. That is, in some cases the Left slot stores the reaction reactants, in other cases the Left slot stores the products.

Following the conventions used by the IUBMB Enzyme Commission [1], the direction in which a reaction is stored in a PGDB has no implication for the physiological directionality of that reaction. In the IUBMB EC system, all reactions within a given class are written in a single consistent direction (e.g., all hydrolases are written in the hydrolysis direction). Reactions categorized by the IUBMB EC system are stored within a PGDB such that the EC left side of the reaction is stored in the Left slot.

The PGDB framework for defining reaction direction is designed both for flexibility in encoding a diverse range of biological situations, and to minimize the work curators must do to define reaction directions. The diverse biological situations to be encoded include the notions that the directionality of some reactions are invariant, whereas the directionalities of other reactions depend on the enzyme that is catalyzing the reaction, and on the organism in which the reaction occurs.

The directionality of some reactions is explicitly stored within the PGDB. The directionality of other reactions is not stored, but is computed on demand by Pathway Tools. The best way to query the directionality of a reaction is via the slot Reaction-Direction in reaction objects. Even when no value is explicitly stored in this slot, a method attached to this slot will attempt to compute a value for the slot. Possible values of this slot are as follows. The values PHYSIOL-LEFT-TO-RIGHT, IRREVERSIBLE-LEFT-TO-RIGHT, and LEFT-TO-RIGHT mean that the Left slot should be treated as containing the reactants; the values PHYSIOL-RIGHT-TO-LEFT, IRREVERSIBLE-RIGHT-TO-LEFT, and RIGHT-TO-LEFT mean that the Right slot contains the reactants.

  • REVERSIBLE: Reaction occurs in both directions in physiological settings.

  • PHYSIOL-LEFT-TO-RIGHT or PHYSIOL-RIGHT-TO-LEFT: The reaction occurs in the specified direction in physiological settings, because of several possible factors including the energetics of the reaction, local concentrations of reactants and products, and the regulation of the enzyme or its expression.

  • IRREVERSIBLE-LEFT-TO-RIGHT or IRREVERSIBLE-RIGHT-TO-LEFT: For all practical purposes, the reaction occurs only in the specified direction in physiological settings, because of chemical properties of the reaction.

    LEFT-TO-RIGHT or RIGHT-TO-LEFT: The reaction occurs in the specified direction in physiological settings, but it is unknown whether the reaction is considered irreversible.

The software computes values of the Reaction-Direction slot by integrating information within the enzymes and pathways associated with the reaction. Consider these examples where no information is stored in the Reaction-Direction slot of reaction R:

  • A single enzyme E is associated with R, and the Reaction-Direction slot of the Enzymatic-Reaction that connects E with R has a Reaction-Direction slot value of LEFT-TO-RIGHT; the software infers that the directionality of R is LEFT-TO-RIGHT.

  • Two enzymes E1 and E2 are associated with R. E1 has a Reaction-Direction of LEFT-TO-RIGHT; E2 has a Reaction-Direction of RIGHT-TO-LEFT. The software infers that R is reversible.

  • R is associated with a single pathway P, and within that pathway, R proceeds in the right-to-left direction. The software infers that the directionality of R is LEFT-TO-RIGHT.

In general, if the software finds information indicating that R proceeds in both the left-to-right and the right-to-left directions, then it infers that R is reversible.

The equilibrium constant and the change in Gibbs free energy stored for the reaction (if any) refer to the direction of the reaction as stored, that is, assuming that the Left slot contains the reactants.

3.3  Reaction Locations and Compartments of Metabolites

An accurate representation of metabolic processes must take into account the existence of multiple cellular compartments and structures, and that the processes and metabolites are partitioned among these compartments. Even a simple cell consisting of a single compartment has a membrane boundary to the extracellular space, which is crossed by transport reactions. This section describes how Pathway Tools records the compartments where reactions and metabolites occur.

In Pathway Tools, compartments are specified using the controlled vocabulary in the CCO (Cell Component Ontology). Every CCO term is represented by a PGDB frame that is a child of the class CCO-SPACE or of the class CCO-MEMBRANE. The default compartment for metabolites and reactions is assumed to be CCO-CYTOSOL in the S case, if no other information is specified in the reaction’s RXN-LOCATIONS slot that would override this default. In the T case, nothing can be assumed about the default locations, if no membrane and other mappings for CCO-IN and CCO-OUT were specified (see below). Such T reactions could not usefully become part of a reaction network model.

To avoid unnecessarily duplicating information, we store frames for metabolites and reactions once within each PGDB, even if they may simultaneously be present in more than one compartment in a PGDB. Instead, the compartments are specified by auxiliary information attached to reactions.

There are two types of reactions:

  • S Reactions: Reactions for which all of their substrates (meaning their reactants plus products) in the same compartment (e.g., a metabolic reaction that occurs in the cytosol). In a given PGDB, such a reaction could potentially occur in more than one compartment.

  • T Reactions: Reactions whose substrates occur in multiple compartments (e.g., a transport reaction with a reactant in the periplasm and a product in the cytosol). This condition can only happen at membranes, involving transport reactions or electron transfer reactions (ETRs). T reactions annotate their substrates to specify their locations. Those annotations may use the abstract directional compartments CCO-IN and CCO-OUT. These abstract compartments are mapped to the actual compartments in a given PGDB.

By default (meaning if no substrate locations are specified), S reactions are assumed to occur in the cytosol (CCO-CYTOSOL). To store non-default compartment information, reactions have a slot called RXN-LOCATIONS, the values of which differ between the S and T type reactions, as follows:

  • S Reactions: If the reaction occurs in a non-default compartment, or in several compartments, then the RXN-LOCATIONS slot stores for every compartment in which the reaction occurs, the corresponding identifier of the CCO term for that compartment. The metabolites in the reaction’s LEFT and RIGHT slots do not have any COMPARTMENT annotations, as those would be redundant and could cause conflicts.

    The following example depicts an S-type reaction in the periplasm. Because its RXN-LOCATIONS slot specifies CCO-PERI-BAC (the periplasm), every substrate of the reaction is interpreted as occurring in the periplasm.

          LEFT: GLC
    
          RIGHT: |D-Glucose|
    
          RXN-LOCATIONS: CCO-PERI-BAC
    
          SPONTANEOUS?: T
    

  • T: The slot RXN-LOCATIONS contains one or more frames that are children of class CCO-MEMBRANE (or potentially symbols that have to be unique in this slot, for situations where the metabolites are in spaces that are not directly adjacent to one membrane, or when 3 spaces are involved). If the reaction has not been assigned to any particular membrane, then no value needs to be stored at all.

    Additionally, each slot value in RXN-LOCATIONS will have annotations with the labels CCO-IN and CCO-OUT, and in the rare case of 3 compartments involved, also another label called CCO-MIDDLE. These annotations should be single-valued; each value should be a child of CCO-SPACE. These annotations define the mappings between the COMPARTMENT annotation values of the metabolites that are listed in the reaction’s LEFT and RIGHT slots, and the final compartments in this PGDB.

    Every metabolite in the reaction’s LEFT and RIGHT slots needs to have a COMPARTMENT annotation, the value of which needs to be one of CCO-IN, CCO-OUT, or possibly CCO-MIDDLE in complex situations. The purpose of CCO-IN, CCO-OUT, and CCO-MIDDLE, is to allow one transport reaction to be mapped to multiple membranes.

    Example of slot values for a transport reaction in the periplasmic membrane:

          LEFT:
            AMMONIUM
            ---COMPARTMENT: CCO-OUT
    
          RIGHT:
            AMMONIUM
            ---COMPARTMENT: CCO-IN
    
          RXN-LOCATIONS:
            CCO-PM-BAC-NEG
            ---CCO-IN: CCO-CYTOSOL    ---CCO-OUT: CCO-PERI-BAC
    

Whenever a reaction is transferred between PGDBs (by import or schema upgrade operations), all values in the RXN-LOCATIONS are filtered away (i.e. not copied). This prevents inapplicable compartments from being introduced into other PGDBs. In the future, PathoLogic and TIP will infer compartment information. The values of the RXN-LOCATIONS are listed in the flatfiles of the PGDB.

If the reaction is catalyzed by more than one enzyme (i.e. it has more than one enzymatic-reaction attached), then each value in the RXN-LOCATIONS slot must have an annotation called ENZRXNS, which has as its values the frame IDs of the corresponding enzymatic-reactions. This approach allows determining the precise compartment(s) in which the catalyzed reaction is occurring.

3.4  Reaction Balancing and Protonation State in PGDBs

3.4.1  Background and Motivations

This section addresses the state of reaction mass balance and protonation state of chemical compounds in PGDBs. Because these issues are still evolving and are influenced to a large degree by history, we include a historical discussion of these issues.

Our long-term goal is for all PGDB reactions to be fully mass balanced and charge balanced, and for all chemical compounds to be properly protonated at cellular pH. Although in some cases such a treatment may yield reactions or chemical structures that look non-traditional to biochemists, we believe this approach provides the most consistent and correct treatment. In addition, it provides a treatment that will facilitate automatic generation of flux-balance models from PGDBs.

Historically, the chemical structure data within BioCyc databases has been obtained from many different sources, including textbooks, articles from the primary research literature, and downloading from certain open databases. In the early years of the project we developed programs to check the mass balance and element balance of reactions within PGDBs. We found that these programs were extremely valuable because identification of unbalanced reactions allowed us to identify errors in both the reaction equations, and in the chemical structures. However, we also found that, because of the diverse sources from which we obtained chemical structure data, the structures were protonated inconsistently. Therefore, for many years we ignored element imbalances due to hydrogen only, while correcting imbalances due to other elements.

In 2008, we began to address the problem of inconsistent protonation to facilitate automatic generation of flux-balance models. Work was completed on ensuring that reactions in the MetaCyc and EcoCyc PGDBs are completely mass-balanced. The first releases of those fully mass-balanced MetaCyc and EcoCyc DBs were version 13.0 in early 2009. In time, other BioCyc PGDBs will become mass balanced as well. For example, because we periodically regenerate the Tier 3 BioCyc PGDBs, the next time these PGDBs are generated from version 13.0 or higher of MetaCyc, they will be based on the consistently protonated compounds, and the fully mass-balanced reactions.

The following sections describe the methodology by which the protonation-state normalization and reaction mass balancing were achieved.

3.4.2  Protonation State Normalization

For a given chemical compound, there can be atoms that will bind a variable number of hydrogen atoms, depending on their chemical structure and the pH of their environment. A term for the isomers of a compound that differ in the number of hydrogens bound to these atoms is proto-isomer. A term for the atoms with variable numbers of bonded hydrogens is the proto-isomerization centers of a compound. Oxygen, sulfur, phosphorus, and nitrogen are examples of typical proto-isomerization centers.

In order to bring a greater degree of consistency to our PGDBs, we protonated (i.e., assigned the correct number of bound hydrogens to the proto-isomerization centers of a compound) the compounds of EcoCyc with a reference pH value of 7.3, using the Marvin (version 5.1.02) computational chemistry software available from ChemAxon, Ltd [2]. The pH value of 7.3 was selected based on a paper on the measurement of cytoplasmic pH of E. coli [3]. In order to easily exchange compound data between MetaCyc and EcoCyc, MetaCyc was also protonated with a reference pH value of 7.3. This step is an approximation since MetaCyc contains reactions and compounds from many organisms and many cellular compartments.

The Marvin software calculates the protonation state of a compound’s proto-isomerization centers by first determining their pKA. The pKA of the proto-isomerization centers of a compound were obtained by computing the partial charge distribution. This, in turn, is calculated using a numerical partial differential equation solver, which computes the distribution by means of the structure of the compound, and the known electronegativities of the constituent atoms. Although we have worked with ChemAxon to improve the accuracy of their calculations to match that of experimentally-verified pKA’s of many biochemically-relevant compounds, this calculation is still based on an approximation technique, and will not necessarily yield fully correct pKA’s for every substance.

Some caveats about our protonation of compounds:

  • Some compounds are present in multiple reactions that take place in various different compartments in a cell, or across membranes, where the pH might vary from our stated value of 7.3.

  • For any given compound, only one proto-isomer is present in our PGDBs. We do not represent the other proto-isomers, nor do we represent the proto-isomerization reactions that inter-convert the various proto-isomers of a compound.

  • Sometimes a pKA value for a proto-isomerization center is very close to the pH of the solution, and therefore there is approximately a 50 / 50 split between the relative abundance of the two proto-isomers of that compound in solution. The Marvin software will select the most likely proto-isomer based on a comparison of the floating point value of the relative abundance in such situations.

  • Our compounds might have a slightly different structure than what you will find for the same compound in an alternate chemical compound database. Please ensure that you are comparing the two compounds for the correct protonation state at a reference pH value of 7.3.

3.4.3  Computational Reaction Balancing for Hydrogen

Once the compounds of EcoCyc and MetaCyc were protonated, all reactions that had a mass-imbalance due only to hydrogen atoms were computationally balanced. This balancing procedure added or removed instances of the proton from the appropriate side of a reaction to achieve mass-balance.

Some caveats about our computational reaction balancing:

  • One might notice some reactions that have more or less protons participating than what you would typically see depicted. This might be most evident in our EC reactions. One reason for this, beyond our computational reaction balancing, is that traditionally protons and other small, ubiquitous chemical moieties were considered auxiliary to the main function of a reaction and thus not depicted. In general, our EC reactions may vary from the IUBMB reactions by including more or fewer protons than the original reaction.

  • For use in FBA models, one must be aware that we are only representing one of the possibly many proto-isomers of a compound. We also do not represent the fast protonation reactions that inter-convert the proto-isomers. Thus, a FBA model that is attempting to simulate the flux of hydrogen in a PGDB may be inaccurate.

  • As of 2009, reactions that were computationally balanced for mass are not necessarily balanced for charge.

3.4.4  Statistics on Reaction Balance and Protonation circa 2009

This table provides information on the small-molecule reaction balance state for both EcoCyc and MetaCyc as of early 2009. The categories below represent reactions that are balanced, unbalanced, and those for which it is not possible to determine the balance state.

Reactions that remain unbalanced are due to non-trivial imbalances (i.e., imbalances not due solely to hydrogens or protons). These imbalances are usually due to omissions or errors in the structures and/or reaction composition obtained from the literature. Our curation staff are actively researching such compounds and reactions and correct the data whenever possible.

For the category of reactions where it is not possible to determine the balance state, these are mainly due to:

  • Reactions that have compound classes as substrates

  • Polymerization reactions. As of the beginning of 2009, BioCyc.org is working to extend our representation of polymerization reactions to allow for mass and charge balance.

  • Reactions with substrates that lack a chemical structure

  • Reactions with substrates that include R-groups

Number of Reactions
EcoCyc: Balanced Reactions 801
EcoCyc: Unbalanced Reactions 3
EcoCyc: Reactions that cannot be balanced 160
MetaCyc: Balanced Reactions 5,098
MetaCyc: Unbalanced Reactions 317
MetaCyc: Reactions that cannot be balanced 1,143

3.5  Reaction Atom Mappings

The atom mapping of a reaction describes for each reactant nonhydrogen atom its corresponding atom in a product compound. The bonds broken and made by a reaction can be inferred from an atom mapping of that reaction. On the reaction page this correspondence is shown using matching colors for atoms and bonds, between reactants and products, or/and numbers labelling the atoms. If a bond is broken or made by the reaction, the bond is black.

Some reactions have more than one atom mapping. In some cases not all mappings are not biologically relevant (e.g., the enzyme never produces them). It might also be the case that some of these multiple atom mappings are essentially the same due to symmetries within compound structures, or the inability to distinguish among some atoms.

For some reactions no atom mapping are shown since none were computed for them. This lack of an atom mapping might result from several possible factors including to the complexity of the reaction (e.g., large substrates), that the reaction operates on substrates that have no structures, or the reaction is not mass balanced.

When Pathway Tools displays a reaction, it first tries to obtain an atom mapping from that reaction in its PGDB. However, typically reactions in PGDBs other than MetaCyc do not contain atom mappings (except for reactions not found in MetaCyc). Thus, the software next tries to find the same reaction in MetaCyc and use its atom mapping, if any, for that reaction.

The atom mappings were computationally derived for MetaCyc without manual curation, but we expect a very low rate (< 3%) of errors. The approach used to compute these atom mappings was published in [4]. Essentially, this approach computes atom mappings that minimize the overall cost of bonds broken and made in the reaction, given assigned propensities for bond creation and breakage.

3.5.1  Downloading Atom Mappings

Atom mapping data are available in three ways. Note: some reactions have more than one atom mapping.

  • All atom mappings data for MetaCyc, as described in Section 3.5.2, may be downloaded as part of the MetaCyc downloadable data file package. See file atom-mappings.dat in the MetaCyc bundle. This file may contain more than one atom mapping per reaction.

  • All atom mappings data for MetaCyc, using the SMILES syntax as described in Section 3.5.3, may be downloaded as part of the MetaCyc downloadable data file package. See file atom-mappings-smiles.dat in the MetaCyc bundle. This file may contain more than one atom mapping per reaction.

  • On a reaction Web page, a textual representation of its atom mappings can be downloaded by using the menu bar command Reaction→Download atom mappings for this reaction.

3.5.2  Atom Mapping Encoding

For example, the encoding of the atom mapping of reaction EC 4.2.1.104 is

REACTION - R524-RXN
NTH-ATOM-MAPPING - 1
MAPPING-TYPE - NO-HYDROGEN-ENCODING
FROM-SIDE - (HCO3 0 3) (CPD-69 4 6) 
TO-SIDE - (CARBAMATE 0 3) (CARBON-DIOXIDE 4 6) 
INDICES - 4 5 6 3 0 2 1 
//

One atom mapping of a reaction is encoded using six fields:

REACTION — the unique id of the reaction the mapping applies to
NTH-ATOM-MAPPING — the index of that atom mapping in the set of atom mappings for that reaction
MAPPING-TYPE — only one type is currently used, namely NO-HYDROGEN-ENCODING
FROM-SIDE — list of compounds on the from-side with their starting and ending indices
TO-SIDE — list of compounds on the to-side with their starting and ending indices
INDICES — list of atom indices describing the permutation of atoms from the from-side to the to-side.

Before discussing this specific example, notice that the direction of the reaction in the PGDB (as given by the PGDB slots Left and Right) is not used in atom mapping. In particular, the From-Side in the mapping could be the left or the right side of the PGDB reaction. Also, the order of the compounds given by the from-side and to-side, and as discussed below, might not be the same as the order given by the Left side or Right side of the reaction. In fact, reconstructing the atom mapping relative to the reaction must be performed relative to the chemical structures of the compounds, not the encoding of the reaction.

For this example, the REACTION is R524-RXN which is the unique id (i.e. frame id) of the reaction in MetaCyc. That reaction has only one atom mapping so that this one is identified as NTH-ATOM-MAPPING 1. The mapping type is NO-HYDROGEN-ENCODING. This mapping type tells us that the hydrogen atoms are not mapped. The FROM-SIDE compounds are bicarbonate (HCO3) and cyanate (CPD-69), and the to-side compounds are carbamate and carbon dioxide.

The compounds are described with starting and ending atom indices for each side. In this atom mapping only the nonhydrogen atoms are indexed. For the from-side, the bicarbonate compound has 4 atoms indexed 0 to 3, and the compound cyanate has 3 atoms indexed 4 to 6. For the to-side, the compound carbamate has 4 atoms indexed 0 to 3 and carbon-dioxide has three atoms indexed 4 to 6. The most important point to note: the indices of the compounds are made continous on each side, which means that the indices of the atoms within these compounds are shifted accordingly. The example below shows this aspect more precisely.

The permutation indices (INDICES) describe the permutation of the atoms from the from-side to the to-side. An index j at position i gives the mapping of atom j of the from-side to the corresponding atom i of the to-side. For the example above, that is reaction R524-RXN, we have the following atom mapping (we index the atoms in the MOL files starting at 0):

   Indices j/Positions i From-side atoms To-side atoms
   4 → 0 4 is atom 0 (C) of cyanate → 0 is atom 0 (C) of carbamate
   5 → 1 5 is atom 1 (N) of cyanate → 1 is atom 1 (N) of carbamate
   6 → 2 6 is atom 2 (O) of cyanate → 2 is atom 2 (O) of carbamate
   3 → 3 3 is atom 3 (O) of bicarbonate → 3 is atom 3 (O) of carbamate
   0 → 4 0 is atom 0 (C) of bicarbonate → 4 is atom 0 (C) of carbon dioxide
   2 → 5 2 is atom 1 (O) of bicarbonate → 5 is atom 2 (O) of carbon dioxide
   1 → 6 1 is atom 2 (O) of bicarbonate → 6 is atom 1 (O) of carbon dioxide

The chemical structures of the compounds (and the numbering of atoms for each compound) are not encoded by the atom mapping. Chemical structures are stored in the PGDB objects that describe each compound, and are available in several forms:

The atom indices used in atom mappings refer to the index of each atom in the chemical structure as stored, such as in the atom section of a MOL file.

3.5.3  Atom Mapping Data using SMILES

The SMILES syntax not only allows the representation of reactions but also their atom mappings. The full description of the SMILES syntax is given at the following external link: SMILES Tutorial. We will only give a summary of that syntax and one example.

A reaction such as THIOSULFATE-SULFURTRANSFERASE-RXN described by the equation

   thiosulfate + hydrogen cyanide => sulfite + thiocyanate + 2 H+

has one atome mapping in MetaCyc. Using SMILES, this atom mapping is represented in the following way:

[C:2](#[N:3])[S-:4].[O-:1][S:5]([O-:1])=[O:1]>>[C:2]#[N:3].[O:1]=[S:5](=[O:1])([O-:1])[S:4]

The symbol >> separates the reactants and the products. The reactants are actually on the right and the products on the left of >>. This is correct as we do not encode the direction of the reaction using SMILES because, in general, it cannot be done.

The first part on the left before the dot, namely [C:2](#[N:3])[S‑:4], is the compound thiocyanate, next comes [O‑:1][S:5]([O‑:1]), which represents the compound sulfite. As can be seen the dot separates the compounds. Hydrogen cyanide and thiosulfate are encoded, in that order, on the right of >>.

The atom mapping is encoded by using integer labels between square brackets. For example, [C:2] labels the carbon atom of thiocyanate and hydrogen cyanide with the integer 2, which means that these carbon atoms are mapped to each other. Each atom is uniquely labelled on each side of the reaction, which creates a one-to-one mapping between the atoms of reactants and products. Note that the hydrogen atoms are not given in this representation.

As mentioned in Section 3.5.1, atom mapping data based on SMILES can be obtained by downloading the file atom-mappings-smiles.dat from the MetaCyc bundle.

That file contains one reaction per line, the first element on each line is the frame id of the reaction, followed by a tab, then one or more SMILES separated by a space, one for each atom mapping of that reaction.

3.5.4  Canonicalization of Atom Mapping Encoding

The atom mapping encoding presented in the previous subsection is the result of a canonicalization (i.e., a normalization) process. You do not need to know how this process is working to use and decode the atom mappings but it might be usefull if you want to create your own atom mapping encoding implementation that will result with the same atom mapping as the ones in your PGDB.

Canonicalization has one major goal: The atom mapping encoding does not depend on the manner in which the compounds and reactions are stored in a PGDB.

The encoding was also designed such that the atom mapping can be reconstructed from the compound structures without refering to the reaction.

The encoding depends on the compound InChi strings and the ordering of their atoms given by the program computing the InChi string. The process of canonicalization is as follows:

  • Determine the From-side as the side of the reaction that has the compound with the (lexicographically) smallest InChi string. If the same compound occurs on both sides, it is the second smallest InChi string, and so on. The To-side is the other side of the reaction.

  • For each side of the reaction, order the compounds based on their InChi string. This determines the order of all atoms for each side.

  • The indices giving the permutation of the atoms from the From-side to the To-side are then completely determined by the computed atom mapping. This permutation can be represented by a series of indices of atoms of the To-side.

4  Computing Gibbs Free Energy of Compounds and Reactions in MetaCyc

The computation (i.e., estimation) of the standard Δ Gibbs free energy for reactions and compounds in MetaCyc, that is Δr G⁄○ and Δf G⁄○, respectively, was done at pH 7.3 and ionic strength 0.25. We used pH 7.3 because the computation of the protonation state of all compounds in MetaCyc used that value.

The computation of the standard Gibbs free energy of change formation of compounds is first done by an estimation at pH 0 and ionic strength 0 (Δf G) based on the technique presented in [5]. This technique is based on the decomposition of the compounds into known “contribution groups”. Then, the standard Gibbs free energy at pH 7.3 and ionic strength 0.25 (Δf G⁄○) is computed based on a technique developed by Robert A. Alberty [6]. In his technique, Alberty proposes to use several protonation states for some compounds, but we had to simplify it by always using only one protonation state by compound, that is, the unique one stored in MetaCyc.

For the standard Gibbs free energy of reactions, Δr G⁄○, the computation is based on the Δf G⁄○ values of the compounds involved in the reaction.

The Δf G⁄○ could not be computed for some of the compounds in MetaCyc due to the impossibility to decompose them into the contribution groups provided by the technique of [5]. Consequently, the Δr G⁄○ is not computed for any reaction which has a substrate for which its Δf G⁄○ is not stored in MetaCyc.

5  PGDB Pathways

This section introduces concepts relevant to PGDB metabolic and signalling pathways. Many of the issues discussed here are also explored in [7].

5.1  How are Pathway Boundaries Defined?

Pathway boundaries [7] are defined heuristically, using the judgement of expert curators. Curators consider the following aspects of a pathway when defining its boundaries.

The preceding philosophy toward pathway boundary definition contrasts sharply with KEGG maps. KEGG maps are on average 4.2 times larger than MetaCyc pathways because KEGG tends to group into a single map multiple biological pathways that converge on a single metabolite [Pathway05] .

5.2  Super Pathways and Base Pathways

We define a super-pathway as a cluster of related pathways. Typically, a super-pathway consists of a linked set of smaller pathways that share a common metabolite. For example, the super pathway superpathway of phenylalanine, tyrosine, and tryptophan biosynthesis consists of several pathways that converge at the metabolite chorismate.

The components of super-pathways include base pathways (pathways that are not themselves super-pathways), other super-pathways, and individual reactions that have not necessarily been assigned to base pathways. Those reactions typically serve to connect together the component pathways within a super-pathway.

Super-pathways are stored within each PGDB – they are not computed dynamically.

5.3  Pathway Variants

Experimentalists have elucidated variants of a given metabolic pathway in different organisms. These pathway variants [7] are defined as distinct pathway objects in MetaCyc when they differ in their constituent reactions. For example, MetaCyc contains several variations of the TCA cycle that have been observed in different organisms. Variant pathways are assigned names such as “TCA cycle variation II” and “arginine degradation III” (meaning the third form of arginine degradation in MetaCyc).

Two pathways are not considered variants of one another in MetaCyc if their constituent reactions are identical. For example, if the glycolysis pathway occurs with identical constituent reactions in two different organisms, but with different enzymes (different protein sequences), these occurrences of glycolysis are not considered to be pathway variants.

When copied to other Pathway/Genome databases [def] by the PathoLogic pathway prediction program, the names of variant pathways are not changed. This approach provides for consistent naming across DBs, but does have the side effect that names may seem inconsistent if considered only in the context of one DB, such as a DB that contains only “arginine degradation III” and “arginine degradation VIII”.

5.4  Conspecific and Chimeric Pathways

We define [7] a conspecific pathway as a pathway that belongs to a specific species, whereas a chimeric pathway is a pathway that combines elements from many species but does not occur in any one species in its entirety. MetaCyc contains both types of pathways, which are labeled as such.

5.5  Do We Force a Pathway View of the Metabolic Network?

No. Pathways comprise a layer defined on top of the reaction-based metabolic network. Users can choose to compute with the metabolic (reaction) network directly, ignoring the pathway layer, if they so choose. Note that every PGDB contains some metabolic reactions that are not assigned to any metabolic pathway.

6  Evidence Codes

PGDB objects contain evidence codes that describe the types of evidence that support and justify the inclusion of that entry in the PGDB. For example, evidence codes on an enzyme entry indicate the type of evidence supporting the inference that the enzyme catalyzes its associated biochemical reaction. See [8] for a general description of the evidence-code system. The evidence-code ontology is available here.

Because the data in MetaCyc are derived from the experimental literature, the vast majority of evidence codes within MetaCyc will be experimental evidence codes that identify different classes of experimental methods that support data within MetaCyc. However, the evidence-system supports a larger set of evidence types, including evidence based on computational inferences, which are used more extensively in PGDBs other than MetaCyc.

Evidence codes appear as icons in the upper-right corner of displays pages such as pathway and enzyme pages (example). For example, a flask icon on a metabolic pathway page indicates that experimental evidence supports the existence of that pathway. Often a detailed evidence code has been assigned that indicates a specific type of experimental method – click on the flask icon to see a description of the type(s) of experimental method(s) used to elucidate the pathway (when available), and for associated citations (when available).

7  Use of Gene Ontology Terms

Gene Ontology (GO) terms from all three GO taxonomies (biological process, molecular function, cellular component) can be associated with either polypeptides or protein complexes. Ideally, GO terms that refer to the activity of a complex should be assigned to the complex directly rather than to its component gene products. However, since GO terms imported from external sources are often associated only with gene products, either is acceptable. Each GO term is represented by a class object that includes its description, links to its parent and child terms via both the is-a and part-of relationships, and links to all the objects in the PGDB that are directly annotated with that term. Each PGDB contains objects only for those GO terms actually used in the PGDB, i.e. those to which proteins are annotated plus all ancestors of those terms. The complete GO taxonomy is maintained in a separate database and updated periodically – terms from this database are imported into a PGDB if necessary in the course of annotating a protein. Pre-release consistency checks ensure that the GO terms in a PGDB match those in the master database, and any proteins annotated to obsolete terms are flagged for attention from a curator.

The assignment of a GO term to a protein should be annotated with an evidence code and citation. The evidence code is one from the Pathway Tools evidence code ontology described above, but a straightforward mapping between Pathway Tools evidence codes and Gene Ontology evidence codes allows easy conversion from one to the other. The evidence code assignment may include the GO with/from field (although it is not required and there are no restrictions on its use or format). No other GO qualifiers (e.g. not, contributes-to) are supported.

The GO terms for a protein are listed with their evidence codes and citations in a table on the protein page. Clicking on a GO term shows the page for that term, including links to all proteins annotated with that term. GO terms can be supplied as search criteria on the Gene/Protein/RNA Search page. In addition, the cellular component GO terms serve as the respository of protein cellular location information in Pathway Tools. A mapping between cellular component GO terms and Pathway Tools CCO terms (described in Section 3.3) allows the protein LOCATIONS slot (which describes the protein location using CCO terms) to be computed directly from the GO terms.

8  How to Learn More

References

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[6]   Robert A. Alberty. Thermodynamics of Biochemical Reactions. Wiley InterScience, 2003.

[7]   R. Caspi, K. Dreher, and P. D. Karp. The challenge of constructing, classifying, and representing metabolic pathways. FEMS Microbiol Lett, 345(2):85–93, 2013.

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[9]   P.D. Karp and M. Riley. Representations of metabolic knowledge. In L. Hunter, D. Searls, and J. Shavlik, editors, Proc First International Conference on Intelligent Systems for Molecular Biology, pages 207–215, Menlo Park, CA, 1993. AAAI Press.

[10]   P.D. Karp and S.M. Paley. Representations of metabolic knowledge: Pathways. In R. Altman, D. Brutlag, P. Karp, R. Lathrop, and D. Searls, editors, Proc Second International Conference on Intelligent Systems for Molecular Biology, pages 203–211, Menlo Park, CA, 1994. AAAI Press.

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