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model includes periodic "pacemakers" and provides "regulation" without additional
assumptions.
The discussion in ch.6 is likewise based on the notion of wave propagation.
The chapter has sections on periodic patterns, on the insect epidermis, on
the chick wing bud (with a wave model for epimorphosis) , on imaginal discs
and the insect limb (with an interesting elaboration of the "clock-face"
model of French et at.), and on retino-tectal projection in amphibians. The
author concludes by saying that the notion of static diffusion gradients
providing positional information will probably have to be replaced by a combination
of wave propagation from defined organising centres, and (local or
global) "clocks" of some kind which generate spatial and temporal periodicities.
There is much more in the book (particularly in the last chapter) than can
be done justice to here. The author aspires after a "balance between knowledge
and vision", and to grasp the significance of this the perusal of the
entire book is necessary (even though for the average biologist the going is
difficult in places)
9.
G.NICOLIS and I.PRIGOGINE. 1977. SELF-ORGANIZATION IN NONEQUILIBRIUM SYSTEMS;
from dissipative structures to order through fluctuations
Wiley, New York, etc. XIV, 491 pp., 124 figs., subject index. £ 20.75
Contents (abridged): I. The thermodynamic background (4 chs.); II. Mathematical
aspects of self-organization: deterministic methods (4 chs.); III.
Stochastic methods (4 chs.); IV. Control mechanisms in chemical and biological
systems (4 chs.); V. Evolution and population dynamics (2 chs.)
On reading the word self-organisation every embryologist pricks up his
ears. Unfortunately this reviewer lacks all competence in mathematics, and
all I can do here is to try and highlight the main features of this book and
of its authors' thinking in order to bring them to the attention of developmental
biologists. (In this notice I will often use or paraphrase the words
of the authors without showing this by quotation marks.)
Most of the striking results of classical thermodynamics refer to equilibrium
situations. Later, linear nonequilibrium thermodynamics showed that
nonequilibrium may be a source of macroscopic (global) order (the example
adduced by the authors is thermal diffusion.) The results of the investigations
by Prigogine's group on situations further away from equilibrium, and
involving nonlinear equations, can be sketched as follows. When a system
(e.g. a chemically reacting mixture described by nonlinear functions of the
variables involved) is forced further and further away from equilibrium, the
equilibrium solution may become unstable and the system may evolve toward a
new type of organisation (a new long-range molecular order) involving coherent
space-time behaviour (cf . the Benard instability in liquids) . This type
of organisation depends on appropriate feedback conditions; the new structures
that appear can be maintained only through a sufficient flow of energy
and matter and are called "dissipative structures". (Turing's early work
concerned one of the first dissipative structures ever studied.)
The special interest of the biological applications of this approach discussed
in the book is brought out by the following quotation,: "While each
of the important biomolecules discovered in the recent years is obviously
formed according to the laws of physics and chemistry, we have to identify
the mechanisms that make the "mass production" of these molecules possible
and coordinate their production according to the needs of the organism. It
has often been stated that biological organisation requires a series of
structures and functions of growing complexity and hierarchial character.
One of our main concerns is to understand the way in which transitions between
levels occur and to relate the molecular level to the supermolecular
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