Biology Reference
In-Depth Information
Fig. 7.10 The dynamics of enzymic catalysis represented on a two-dimensional hypercube of
Kosko (1993) (reproduced from Ji 2004a). The
x
-axis represents the non-covalent changes of the
enzyme conformation and the
y
-axis indicates the covalent changes of the chemical subsystem
consisting of the substrate and the product bound to the enzymic active site. Also the
x
-axis
encodes the conformational states of the enzyme that can assume any numerical values between
0 and 1 inclusive, and the
y
-axis encodes the quantummechanical states of the chemical subsystem
which can assume only the numerical values of 0, ½, or 1
equilibrium) (Table
7.3
). One of the fundamental differences between these two
classes of phase transitions is that physical phase transitions are driven by free
energy, whereas biological phase transitions are driven by both
free energy
and
genetic information
that control phase transitions, thus justifying the neologism,
“info-statistical mechanics” proposed (Ji 2006a) and Sect.
4.9
.
7.2.5 Enzymes as Fuzzy Molecular Machines
Computer scientists distinguish between two kinds of computers - the traditional
Turing machines obeying the
crisp
(also called binary, Boolean, or Aristotelian)
logic
and the fuzzy Turing machines based on the
fuzzy
(or multivalued or multiva-
lent)
logic
(Bedregal and Figueira 2006; Peeva and Zahariev 2008). According to
Wiedermann (2004), fuzzy computers have more computing power than classical
Turing machines.
Although it has been widely recognized that enzymes can be treated as
molecular machines (Lumry 1974, 2009; Lumry and Gregory 1986; McClare
1971, 1974; Ji 1974a, b, 1991, 2000; 2004a; Alberts 1998; Astumian 2000, 2001),
little attention appears to have been given as to which of the two possible logics,
crisp or fuzzy, is being obeyed by enzymes. Two observations support the notion
that enzymes are fuzzy molecular machines:
1. Enzymes can be described in terms of a two-dimensional fuzzy cube of Kosko
(1993) (Ji 2004a) as show in Fig.
7.10
