What Is Life? - Molecular Theory of the Living Cell - page 568

living processes, since the time constants and amplitudes of Brownian (or thermal)
motions are mutually dependent and all biopolymer functions are postulated to
depend on Brownian motions that are required by the generalized Franck-Condon
principle as the prelude to all enzymic catalysis (see Sects. 2.2.3 , 15.12 and
Ji 1991).
The well-established phenomenon of the p53 mutation-induced tumor genesis
(Vogelstein et al. 2000) may be viewed as an example of the long-range
interactions (characteristic of all critical phenomena ) that occurs over a distance
range varying by a factor of at least 10 5 , namely, from 0.1 to 10 4 nm, in the sense
that the mutation in p53 at the microscopic level causes (or triggers) the macro-
scopic tumor formation in the human body in about 50% of all cancer patients
(Vogelstein et al. 2000). Another example of long-range interactions in living
systems is provided by the familiar phenomenon of weight lifting. Champion
weight lifters can raise heavy objects within a matter of seconds, presumably
triggered by some subcellular biochemical events such as membrane depolarization
(known as mental processes) initially occurring in one or a few neurons located in
the motor cortex of their brain, and subsequently propagating throughout their
bodies to support the objects often weighing more than their own body weight
(Sect. 15.12 ) .
Physicists have been studying long-range interactions in abiotic systems for at
least one and a half centuries (Domb 1996; Fisher 1998), including the phase
transitions occurring between liquid, gas, and solids, which are collectively referred
to as critical phenomena. The mutation of p53 leading to tumor formation in the
human body may be viewed as belonging to the same class of natural processes as
the snow crystal formation in which the sixfold symmetry of water molecules
dictates (or determines) the sixfold symmetry of all snowflakes visible on the
macroscopic scale (see Fig. 5.3 and http://www.its.caltech.edu/~atomic/
snowcrystals ) . To include living phenomena within the physics of critical phenom-
ena, it may be necessary to expand the meaning of phase transitions beyond the
traditional range, by defining two classes of phase transitions in analogy to the two
classes of transport processes, namely, active and passive . These two kinds of phase
transitions can be characterized in a broad framework of statistical mechanics as
shown in Table 16.2 .
Statistical mechanics deals with random motions of a large number of molecules
(in the order of Avogadro number, N 10 23 /mol) belonging to a few classes

that underlie macroscopically observable thermodynamic properties of physical
systems. In contrast, molecular cell biology deals with both random and nonrandom
motions of a small number (much smaller than N) of molecules belonging to a large
number (10 3 -10 50 [?]) of classes, leading Elsasser (1998) to refer to biological
systems as finite and heterogeneous in contrast to infinite and homogeneous physi-
cal systems (see the first three rows in Table 16.2 ). Some examples of phase
transitions (which are synonymous with “order-disorder” or “disorder-order”
transitions) in physics and biology are given in Row 4.
Enzymic catalysis may be viewed as phase transition in the sense that catalysis
involves the transition of the random thermal fluctuations of an enzyme molecule to

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