Moiety vectors for DAS.

<p>Moiety vectors for DAS.</p

Characteristics of conserved moieties identified in the three metabolic networks treated here.

<p>The total number of instances of a moiety is plotted against the number of atoms per instance. Classification of moieties as transitive, internal, or integrative is described in, Methods, Section Classification of moieties.</p

Instantaneous iCore moieties.

<p>Carbon and phosphate containing moieties in an extreme pathway of the <i>E. coli</i> core network that corresponds to glycolysis. Four conserved moieties are distinguished by shape in the figure. The pathway also conserves one oxygen atom moiety and two hydrogen atom moieties that were omitted to simplify the figure. Metabolite abbreviations are, Glc: D-glucose (VMH [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004999#pcbi.1004999.ref023" target="_blank">23</a>] ID: glc_D), PEP: phosphoenolpyruvate (VMH ID: pep), Pyr: pyruvate (VMH ID: pyr), F6P: D-fructose 6-phosphate (VMH ID: f6p), ATP: adenosine triphosphate (VMH ID: atp), ADP: adenosine diphosphate (VMH ID: adp), FDP: D-fructose 1,6-bisphosphate (VMH ID: fdp), DHAP: dihydroxyacetone phosphate (VMH ID: dhap), G3P: glyceraldehyde 3-phosphate (VHM ID: g3p), NAD: nicotinamide adenine dinucleotide (VMH ID: nad), P_<i>bluei</i>: orthophosphate (VMH ID: pi), NADH: reduced nicotinamide adenine dinucleotide (VMH ID: nadh), DPG: 1,3-bisphospho-D-glycerate (VMH ID: 13dpg), Lac: D-lactate (VMH ID: lac_D). The glucose moiety (circles) is transitive whereas the other three moieties are internal, including the phosphate moiety (squares) which was classified as integrative in the full iCore network.</p

A graphical representation of an atom transition network for the DOPA decarboxylase reaction.

<p>Nodes (open circles) represent atoms. Atoms can be matched to metabolite structures in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004999#pcbi.1004999.g002" target="_blank">Fig 2</a> on their metabolite identifiers, colours and numbers. Directed edges (arrows) represent atom transitions. All except one hydrogen atom are omitted to simplify the figure.</p

The total stoichiometric matrix <i>S</i> = [<i>N</i>, <i>B</i>] for DAS.

<p>The total stoichiometric matrix <i>S</i> = [<i>N</i>, <i>B</i>] for DAS.</p

Coupling between internal moiety pools in iCore.

<p>The five pools from <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004999#pcbi.1004999.t006" target="_blank">Table 6</a> are coupled into a gearwheel-like mechanism. An increase in the NAD/NADH concentration ratio would affect driving forces in the direction shown. (a) Any reactions that interconvert NAD and NADH would be driven in the direction of increased NAD consumption. These include reactions of glycolysis and the TCA cycle, reactions converting malate and lactate to pyruvate, and reactions converting pyruvate, ethanol, and acetaldehyde to acetyl CoA. In short, NAD/NADH coupled reactions would be driven in the direction of increased acetyl CoA production from available carbon sources. (b) The increased NAD/NADH concentration ratio would also affect driving forces through reactions that couple the NAD pool to other cofactor pools. Altered flux through these reactions would in turn affect concentration ratios within those pools which are coupled to their own sets of reactions. (c) An increased NADP/NADPH ratio would drive flux through the pentose phosphate pathway and conversion of glutamate to alpha-ketoglutarate. An increased Q8/Q8H2 ratio would inhibit flux through the electron transport chain. Increased acetyl-CoA/CoA and succinyl-CoA/CoA ratios would drive acetate production and TCA cycle reactions, respectively, which are coupled to ATP production from ADP. (d) An increase in the ATP/ADP ratio resulting from increased flux through these reactions would drive ATP consuming reactions. In iCore, ATP consuming reactions are mainly found in gluconeogenesis so the increased ATP/ADP ratio would counteract the effects of an increased NAD/NADH ratio to some extent.</p

Moiety subnetworks of DAS.

<p>(a) Moiety vectors <i>l</i>₁, <i>l</i>₂, <i>l</i>₃, <i>l</i>₆, and <i>l</i>₇ (<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004999#pcbi.1004999.t004" target="_blank">Table 4</a>) were used to decompose the stoichiometric matrix for DAS (<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004999#pcbi.1004999.t003" target="_blank">Table 3</a>) into five subnetworks. Colours match the corresponding moieties in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004999#pcbi.1004999.g004" target="_blank">Fig 4</a>. Linestyles match the corresponding reactions in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004999#pcbi.1004999.g004" target="_blank">Fig 4</a>. The two hydrogen atom moiety subnetworks (<i>l</i>₄ and <i>l</i>₅) were omitted to simplify the figure. (b) A subnetwork derived from an extreme ray that did not represent moiety conservation. This subnetwork is not mass balanced as there is no mass transfer between Phe and BH₂, Tyr and BH₂, or BH₂ and CO₂ in the full metabolic network (<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004999#pcbi.1004999.g004" target="_blank">Fig 4</a>).</p

Different types of conservation vectors for the DOPA decarboxylase reaction.

<p>Different types of conservation vectors for the DOPA decarboxylase reaction.</p

Sets of conservation vectors for metabolic networks.

<p>The set of real-valued conservation vectors consists of all vectors in the left null space of a stoichiometric matrix. Real-valued basis vectors can be computed using efficient linear algebra algorithms but are difficult to interpret as they generally contain negative and noninteger elements. Nonnegative integer vectors are easier to interpret but more difficult to compute. Existing algorithms have exponential worst case time complexity. Algorithms exist to compute extreme rays, the set of all nondecomposable nonnegative integer vectors, and a maximal set of linearly independent nonnegative integer vectors. These vector sets intersect with the set of moiety vectors but are not equivalent to it. Moiety vectors represent conservation of an identifiable group of atoms in network metabolites. They are a property of the specific set of metabolites and reactions that constitute a metabolic network whereas other conservation vectors are a property of the network’s stoichiometric matrix. The method presented here computes moiety vectors in polynomial time.</p

A metabolic map for an example metabolic network.

<p>The network consists of one internal reaction and four exchange reactions. The internal reaction is the DOPA decarboxylase reaction (VMH [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004999#pcbi.1004999.ref023" target="_blank">23</a>] ID: 3HLYTCL) that produces dopamine (DA, VMH ID: dopa) and CO₂ (VMH ID: co2) from levodopa (L-DOPA, VMH ID: 34dhphe) and H⁺ (VMH ID: h). The open network includes source reactions for the two substrates and sink reactions for the two products. Arrowheads indicate reaction directionality. Metabolite structures were rendered from molfiles (Accelrys, San Diego, CA) with MarvinView (ChemAxon, Budapest, Hungary). Atoms are numbered according to their order in each metabolite’s molfile. Atoms of different elements are numbered separately, in colours matching their elemental symbol. The internal reaction conserves three metabolic moieties. Atoms belonging to the same moiety have identically coloured backgrounds. Levodopa and dopamine each contain one instance of a dopamine moiety (blue background). Implicit hydrogen atoms on both metabolites are also part of this moiety. Levodopa and CO₂ each contain one instance of a CO₂ moiety (red background). Finally, the hydrogen ion and dopamine each contain one instance of a hydrogen moiety (orange background).</p