Building blocks

Apart from metabolic predictions, as discussed in the last section, the concept of scopes can be used to analyze the structure of metabolic networks and to formulate hypotheses about principles which determined this structure

during evolution.

Metabolic networks are obviously shaped by the chemical structure of their metabolites. Two metabolites can only be interconvertible if they pos-sess the same chemical content. This content is defined by the set of chemical groups or chemical elements in the metabolites. Clearly, two such compounds must have the same chemical elements, as these can neither be created nor annihilated by chemical reactions. The two compounds may however also share common chemical groups. In fact, they must share a specific group if this group is conserved in the network, meaning that there is no reaction which assembles or disassembles the group.

The chemical content imposes a hierarchy on the scopes. In this hierar-chy, scopes containing more chemical content are superordinated to scopes possessing less content. Seeds and their scopes contain the same chemi-cal content (cf. equation 1.21 indicating that a scope is interconvertible with its seed) and hence also a hierarchy on the seed metabolites is inferred.

The resulting hierarchy graph can be interpreted as an alternative view on metabolism, specifically highlighting the chemical richness of the participat-ing compounds.

The coherence of the hierarchy and the chemical content has been con-firmed in artificial metabolic networks. Here, compounds hold building blocks, which may represent chemical elements or conserved chemical groups.

In particular, this analysis revealed the connection between the building blocks and specific prominent scopes, the so called characteristic scopes.

Clearly, if the network contains all in principle possible reactions, all com-pounds with the same building blocks must be interconvertible and will be represented by a single node in the hierarchy graph. If not all conversions are included, interconvertibilities are lost. However, over a wide range of reaction deletions, the majority of compounds with the same building blocks remain interconvertible. The scopes of these compounds become the charac-teristic scopes. Those compounds not anymore interconvertible with other compounds yield new and distinct scopes. The corresponding nodes in the hierarchy are often directly connected to one or more of the characteristic scopes which in turn explains the high degree of these.

The characteristic scopes can also be identified in the KEGG network.

High degree nodes in this hierarchy correspond to scopes containing a specific set of chemical elements. These also possess a large number of interconver-tible seed compounds. In particular, the characteristic scopes representing combinations of the elements C,N,P and S, except CS could be identified.

Even though there exist compounds with the element combination CS, these apparently do not form larger groups of interconvertible compounds. Also, scopes containing only N or P do not possess a large number of seed

com-pounds. These two peculiarities may be accounted to the fact that not all combinations of elements have the same probability to constitute biologically relevant metabolites. Absolute frequencies of compounds with specific chem-ical elements can be found in appendix A.5. It should again be noted that the conservation of the elements H and O cannot be seen in the hierarchy, as water has always been included in the seed.

In the KEGG hierarchy there exist also characteristic scopes which can be accounted to the existence of specific chemical groups. All interconvertible seed compounds producing such a scope contain the corresponding group.

Two examples have been analyzed, the scopes of Arachidonate and Retinal.

The synthesis of Arachidonate is not included in the data set and hence Arachidonate and its products, the leukotrienes and prostaglandins contain at least one own conserved building block.

The situation for Retinal is somewhat different. It contains the chemical element C (along with H and O) only (chem. formula: C₂₀H₂₈O). It is not interconvertible with most other compounds containing only C (and possibly H and O). However, there does not exist a specific conserved chemical group in Retinal. Retinal can actually be produced from ATP which does not contain any group similar to Retinal. There exists however a conserved group if only reactions are considered which exclusively use compounds containing the elements C,H and O. As described, for the synthesis phosphorylated intermediates (e.g. Isopentenyl-PP) are necessary which additionally contain the element P. This leads to the existence of a separate characteristic scope for Retinal.

Such a partial conservation of chemical groups generally implies that the production of the group, and if applicable also their degradation, proceeds via chemically more complex intermediates. Equally, the need for cofactors may define a partially conserved building block. Clearly, if a cofactor is not present, certain compounds may not be produceable from compounds with the same chemical content. However, other, chemically more potent compounds may able to produce the cofactor as well as the desired compound, indicating that no additional strictly conserved building block is involved.

This behavior effectively defines subnetworks in which certain chemical groups are conserved. Such a subnetwork is surrounded by reactions which utilize compounds with a larger chemical content or are dependent on cofac-tors.

As argued before, many cofactors are ubiquitous in the cell. Hence, the cofactor-dependent partially conserved building blocks may not play an im-portant biological role as the necessary reactions can generally operate. To address this, the analysis is also performed assuming that the functionalities of certain cofactors is present. In fact, the corresponding hierarchy unifies

many different nodes indicating the increased capacity of the network to do conversions.

On the other hand, the existence of partially conserved building blocks due to more complex intermediates may have a biological meaning. In partic-ular the ligation of phosphates to intermediates may indicate special energetic or regulatory needs in the synthesis of a specialized chemical group. In that way, the occurrence of a partially conserved building block in the hierarchy may indicate a special role of the metabolites containing it.

Generally, the conservation of building blocks depends on the reactions in the network. While the conservation of chemical elements in the hierarchy graph is due to the principal inability of chemical reactions to convert ele-ments into one another, the conservation of chemical groups depends on the ability of the network to synthesize or degrade such groups. If such reactions are missing for a specific group, this group becomes a conserved building block.

In a broad interpretation, each node in the hierarchy graph represents a unique combination of strictly or partially conserved building blocks. The special role of characteristic scopes would then be that they represent a popular building block combination which many compounds share. The other scopes contain building blocks which occur in only a few compounds. For such less frequent building blocks it cannot be assumed that they occur in various combinations with other building blocks. Consequently, they will not be part of a clear subhierarchy of characteristic scopes as seen specifically for the chemical elements C,N,P and S which occur in all combinations in the network. It can rather be expected that the manifold of implicitly defined building blocks together creates the background of non characteristic scopes observed in the hierarchy graph.

The chemical content is also visible in the results of the seed prediction.

This analysis has been done for the seeds of central parts of the metabolism and for the seeds of the complete network.

Only a few seed compounds were needed to produce the central metabo-lites. Still the scopes of these seed compounds cover more than 50% of the whole network which is comprehensible if considering that a single, but com-plex compound like APS alone covers a similar fraction of the network. From the chemical structure of the calculated seed compounds it can be seen that each compound actually provides one or more chemical elements, rather than specific chemical groups. It should be noted that the elements themselves are not among the seeds, as they are usually metabolically difficult to ac-cess. These findings indicate that at least the central region of the KEGG network is autotroph, meaning that all compounds can be synthesized from small inorganic compounds, like CO₂, NH₃, H₃PO₄ or H₂SO₄.

To produce all compounds of the KEGG network, in average 534 seed compounds were needed. As each seed compound must provide at least one additional conserved building block, 534 gives a lower limit for the number of conserved building blocks in the network. As eventually all compounds of the network are produced, including all building blocks and cofactors, no partially conserved building blocks exist and 534 is an lower limit for the number of strictly conserved building blocks.

On the other hand, the number of nodes in the hierarchy graph calculated with cofactor functionalities (2098) gives the number of strictly and partially conserved building blocks. Hence, 2098 is an upper limit of the number of strictly conserved building blocks in the network.

The building blocks as defined here, are also accessable through calcula-tion of the left side kernel of the stoichiometric matrix, as discussed in Schus-ter and Höfer [1991], SchusSchus-ter and Hilgetag [1995], Imielinski et al. [2006].

This method yields weighted sets of metabolites which are conserved by all reactions in the network. Some of these sets represent strictly conserved building blocks (moieties in their nomenclature) which are present in the corresponding metabolites. The weights define the occurrence of the moi-eties within each metabolite. However, the method tends to produce an excessive number of conservation relations which makes it difficult to ana-lyze for large metabolic networks. The scope hierarchy on the other hand indicates through its structure the most important conserved building blocks.

The exact equivalence of the conserved entities predicted by the two methods still has to be shown in a later work.