Molecular Mechanisms: From Enzymes to Evolution - Molecular Theory of the Living Cell - page 220

where a is the number of the subunits acting as the necessary component coinci-
dence detectors. Without losing generality, we can assume, for simplicity, that all P i
values are the same and equal to p. Then Eq. 7.23 reduces to

p a

¼

P (7.24)

P can be increased while holding a constant in two ways:
1. Divide the subunits of the high-order coincidence detector into two groups “a”
subunits whose activities are all necessary and “b” subunits, any one of which,
working with the “a” necessary components, is sufficient to activate the high-
order coincidence detector. We may refer to the former kind of subunits as
multiplicative (a) and the latter additive (b) components. Again, assuming that
these two kinds of subunits all have the same probability of activation, p ,
Eq. 7.24 can be transformed into a product of two terms:

p a

P ¼ (bp) ð Þ

bp a þ 1 ¼ (7.25)

2. Make all p 's positively dependent on the total number, N , of the subunits in the
high-order coincidence detector (i.e., the enzyme complex under consideration).
In other words, let all the subunits, no matter where they are located within the
complex, interact (i.e., constrain one another) mechanically/conformationally/
allosterically in such a way that the probability of activating (through thermal
fluctuations, I presume) individual subunits is directly proportional to N , which
appears eminently feasible. We can incorporate this idea into Eq. 7.25 to obtain:

Þ ð a þ 1 Þ P ¼ b p ð N (7.26)

where p ( N ) indicates that the probability p is the function of N. Equation 7.26 is rather
crude at this stage but can be readily elaborated on to make it more realistic, but it is
good enough for drawing qualitative conclusions about the possible biological role of
subunit architecture of many enzyme complexes in the cell: To improve the
probability of activating coincidence detection through thermal fluctuations, which
is equivalent to increasing the probability, P, of realizing highly rare events, namely,
the activation of the enzyme complex, through orderly (hence free energy-
dissipating) interactions among N subunits of higher-order coincidence detectors.

Thus, if these theoretical arguments based on viewing enzymes as coincidence
detectors are correct, we can conclude that it would be possible to produce any rare
physicochemical processes inside the cell (e.g., activation of the expression of select
genes at right loci at right times, RNA synthesis, protein synthesis, cell division, etc.)
usingmulti-subunit enzyme complexes (i.e., SOWAWNmachines or hyperstructures
discussed in Sect. 2.4 ) consisting of N subunits (of which a are multiplicative and b
are additive) by increasing b more rapidly than increasing a in Eq. 7.25 .