Engineering - Molecular Theory of the Living Cell - page 126

short-lived organisms during evolution) just as the shapes of snowflakes (see
Fig. 5.3 ) cannot be derived or predicted from the Second Law because these
embody the trajectories (or a series of boundary conditions of Polanyi 1968)
traversed by incipient snowflakes through the atmosphere, the information about
which being lost to the past, except whatever is recorded in snowflakes.
Although all snowflakes exhibit a sixfold symmetry due to the unique structure
of the water molecule (see the lower panels in Fig. 5.3 ), no two snowflakes
look alike, and this phenomenon has now been well understood as the result
of experimental works on artificial snowflakes produced in laboratories (see
Sect. 15.1 ) (Libbrecht 2008): No two snowflakes look alike because no two
snowflakes traverse the same trajectories from the atmosphere to the ground as
they evolve from the incipient clusters of a few water molecules formed high up in
the atmosphere to the final macroscopic snowflakes seen on the ground (see the
left-hand panel in Fig. 5.3 ). Similarly, no two RNA trajectories measured from
the yeast cell undergoing the glucose-galactose shift look exactly alike (see the
bottom of the right-hand panel in Fig. 5.3 ), most likely because (1) no two RNA
polymerases inside the nucleus and (2) no two RNA molecules in the cytosol
experience identical microenvironments (see the RNA localizations in Drosophila
embryios, Fig. 15.3 ). Consequently, no two RNA molecules are associated with
identical rates of production (through transcription) and degradation (catalyzed by
RNases or ribonucleases). In analogy to the sixfold symmetry exhibited by all
snowflakes reflecting the geometry of the water molecule, all RNA trajectories
share a common feature of being above the zero concentration levels reflecting
the fact that the yeast cell is a dissipative structure, continuously dissipating free
energy to maintain its dynamic internal structures, including RNA trajectories.
Most of the discussions on complexity in the past several decades in the field
of computer science and physics concern “passive complexity,” which was taken
over by biologists apparently without realizing that living systems may exhibit a
totally new kind of complexity here dubbed “active complexity.” The time- and
space-dependent heterogeneous distributions of RNA molecules observed in
developing Drosophila embryo (Fig. 15.1 ) provide a prototypical example of
“active complexity,” since depriving energy supply to the embryo would certainly
abolish most of the heterogeneous RNA distributions.

5.2.4 The Principle of Recursivity

A “recursive definition,” also called “inductive definition,” defines something
partly in terms of itself, that is, recursively . A clear example of this is the definition
of the Fibonacci sequence:

F(n) ¼ F(n 1 Þþ F(n 2 Þ¼ 1 ; 1 ; 2 ; 3 ; 5 ; ; ::::::::::::::::::::::::: (5.13)