23.5 The Physical Chemistry of Interactions

319

Combining tensor analysis with statistical principal component analysis yields the

“tensor robust principal component analysis” (TRPCA) method. ²¹

23.5 The Physical Chemistry of Interactions

Although knowledge of the state structure of a network (system) does not require

knowledge of the physical structure, there can be no information transfer, and hence

no regulatory control, in the absence of physical interaction. “Interaction” as implied

by elementary chemical reactions of the type

upper A plus upper B underset k Subscript normal d Baseline of right harpoon over left harpoon Overscript k Subscript normal a Baseline Endscripts upper C commaA + B

ka⇌

kd ^{C ,}

(23.6)

where C is a complex of A and B and for which an affinity (or equilibrium) constant

upper KK is defined according to the mass action law (MAL) by

upper K equals StartFraction a b Over c EndFraction commaK = ^ab

c ^,

(23.7)

where the lowercase letters denote mole fractions, ²² is nearly always quite inade-

quate to characterize the association between two proteins. In practical terms, if an

experiment is carried out with scant regard to the underlying physical chemistry,

even slight differences in the way of carrying out the reaction or in the way the data

are interpreted could result in considerable differences in the corresponding numer-

ical values attributed to the interaction. At present, the interactome has mostly been

assembled on the basis of dichotomous inquiry (i.e., does the protein interact or does

it not?), but as technical capabilities improve, this is obviously going to change, and

it will become important to assign gradations of affinity to the interactions.

The cytoplasm is crowded and compartmentalized. Hence, many pairs of pro-

teins potentially able to interact have a negligible chance of encountering each other

in practice. Moreover, local concentrations of inorganic ions and small molecules,

which may greatly influence the strength of an interaction, often differ greatly from

place to place within the cell. This gives an advantage to methods probing interac-

tions in vivo over those requiring the proteins to be extracted. On the other hand,

in vivo measurements cannot usually yield data sophisticated enough to go beyond

the elementary model of interaction encapsulated by Eq. (23.6) and mostly cannot

go beyond a simple yes/no appraisal of interaction. Additionally, unless the in vivo

technique involves some three-dimensional spatial resolution, the result will be an

average over different local microenvironments, physiological states, and so forth.

21 Hu et al. (2019).

22 In the literature,upper KK is often loosely defined using Eq. (23.7) with concentrations rather than mole

fractions, whereupon it loses its dimensionless quality.