336

23

Regulatory Networks

23.15 Metabolic Networks

Metabolism can be represented as a network in which the nodes are the enzymes

and the edges connecting them are the substrates and products of the enzymes. A

metabolic network is a kind of chemical reaction network. There are two main lines

of investigation in this area, which have hitherto been pursued fairly independently

from one another.

The first line is centred on metabolic pathways, defined as series of consecutive

enzyme-catalysed reactions producing specific products; “intermediates” in the series

are defined as substances with a sole reaction producing them and a sole reaction

consuming them. The complexity of the ensemble of metabolic pathways in a cell

is typified by Gerhard Michal’s famous chart found on the walls of biochemistry

laboratories throughout the world. Current work focuses on ways of rendering this

ensemble tractable; for example, a set of transformations can be decomposed into

elementary flux modes. An elementary flux mode is a minimal set of enzymes able

to operate at steady state for a selected group of transformations (“minimal” implies

that inhibition of any one enzyme in the set would block the flux). A related approach

is to construct linearly independent basis vectors in flux space, combinations of which

express observed flux distributions. The extent to which the requirement of a steady

state is realistic for living cells remains an open question. In analogy to electrical

circuits, use has also been made of Kirchhoff’s laws to analyse metabolic networks,

especially his first law stating that the sum of all (metabolite) currents at a node is

zero.

The second line is to disregard the dynamic aspects and focus on the distribution

of the density of connexions between the nodes. The number of nodes of degree kk

appears to follow a power law distribution (i.e., the probability that a node has kk

edges tilde k Superscript negative gamma∼k^−γ). ⁴⁴ Moreover, there is evidence that metabolic networks thus defined

have small world properties (cf. Sect. 12.2).

There is a perhaps obvious analogy to electric circuits, and attempts are being

made to apply concepts and develop them to metabolic networks. ⁴⁵

Just as in the abstract networks (automata) discussed previously (Chap. 12), a

major challenge in metabolomics is to understand the relationship between the phys-

ical structure (the nodes and their connecting edges) and the state structure. As the

elementary demonstrations showed (cf. the discussion around Fig. 12.1), physical

and state structures are only tenuously related. Much work is still needed to inte-

grate the two approaches to metabolic networks and to further integrate metabolic

networks into expression networks. ⁴⁶ Life is represented by essentially one network,

in which the nodes are characterized by both their amounts and their activities, and

the edges likewise.

44 See Wagner and Fell (2001) or Raine and Norris (2002).

45 Theorell and Stelling (2022).

46 Shlomi et al. (2008).