334

23

Regulatory Networks

metabonomic data consisting of a snapshot of the concentrations of 100 metabolites

is a point in a space of 100 dimensions. One rotates the original axes to find a new

axis along which there is the highest variation in the data. This axis becomes the first

principal component. The second one is orthogonal to the first and has the highest

residual variation (i.e., that remaining after the variation along the first axis has

been taken out), the third axis is again orthogonal and has the next highest residual

variation, and so on. Very often, the first two or three axes are sufficient to account

for an overwhelming proportion of the variation in the original data. Since they are

orthogonal, the principle components are uncorrelated (have zero covariance).

In supervised methods, the initial information is given as learning descriptions

(i.e., sequences of parameter values (features) characterizing the object whose class is

known beforehand). ⁴¹ The classes are nonoverlapping. During the first stage, decision

functions are elaborated, enabling new objects from a dataset to be recognized, and

during the second stage, those objects are recognized. Neural networks (Sect. 24.3)

are often used as supervised methods.

23.14 Metabolic Regulation

Once all of the data have been gathered and analysed, one attempts to interpret the

regularities (patterns). Simple regulation describes the direct chemical relationship

between regulatory effector molecules, together with their immediate effects, such

as feedback inhibition of enzyme activity or the repression of enzyme biosynthesis.

Complex regulation deals with specific metabolic symbols and their domains. These

“symbols” are intracellular effector molecules that accumulate whenever the cell is

exposed to a particular environment (cf. Table 23.1). Their domains are the metabolic

processes controlled by them; for example, hormones encode a certain metabolic

state; they are synthesized and secreted, circulate in the blood and, finally, are decoded

into primary intracellular symbols (Sect. 23.14.2).

23.14.1

Metabolic Control Analysis

Metabolic control analysis (MCA) is the application of systems theory (Sect. 12.1)

or synergetics (Sect. 12.3) to metabolism. ⁴² Let bold upper X equals StartSet x 1 comma x 2 comma ellipsis comma x Subscript m Baseline EndSetX = {x1, x2, . . . , xm}, where x Subscript ixi

is the concentration of the iith metabolite in the cell; that is, the set bold upper XX consti-

tutes the metabolome. These concentrations vary in both time and space. Let

bold v equals StartSet v 1 comma v 2 comma ellipsis comma v Subscript r Baseline EndSetv = {v1, v2, . . . , vr}, wherev Subscript jv j is the rate of thej jth process. To a first approximation,

each process corresponds to an enzyme. Then

41 See, e.g., Tkemaladze (2002).

42 See also Schuster et al. (2000).