SCI:BIO:Kauffman in a nutshell (II)

Eugene Leitl (
Sun, 19 Jan 1997 22:08:39 +0100 (MET)

Stuart A. Kauffman, "The Origins of Order", Oxford University Press
(1993), pp. 30-31.

[ continued from the last post ]

Analysis of the structure of fitness landscapes and its implications
occupies Chapters 2 and 3. Chapter 4 considers adaptive evolution in the
space of possible proteins. Here we find that it is possible to to
construct statistical models of molecular fitness landscapes which apply
to the rapid protein evolution seen in maturation in of the immune
response. But protein evolution to carry out progressively different
catalytic functions drives us to conceive of an abstract catalytic _task
space_. Among the surprising implications of this view is the possibility
that a finite number of enzymes can carry out all enzymatic tasks: An
universal enzyme toolbox is possible. Remarkably, about 100 000 000
protoenzymes may well constitute such a universal toolbox, and the immune
repertoire of about 100 000 000 variant antibody molecules is probably
also a universal toolbox. These possibilities lead me, in Chapter 4, to
discuss what might become a vastly important new arena of biotechnology:
applied molecular evolution. I believe we are now crossing the threshold
into an era where it shall become possible to evolve biopolymers that act
as vaccines, drugs, enzymes, biosensors, and so forth, serving a wide
range of practical medical and other functions.

Chapter 5 and 6 present evidence for adaptation to the edge of chaos both
_within_ single complex systems and _between_ the linked members of a
coevolving system. Chapter 5 investigates the emergence of spontaneously
ordered behaviour in parallel-processing systems and elucidates the three
broad regimes which occur in such systems: ordered, complex, and chaotic.
Here we encounter our first powerful example of spontaneous order.
Contrary to intuition, even randomly constructed networks of elements
which turn one another on and off according to complex rules can exhibit
extremely ordered behaviour. This _ordered_ regime is characterized by
the formation of a large connected set of elements of the system that
freeze into fixed activity states. This frozen component percolates
(spans) across the system and leaves behind isolated unfrozen islands
free to vary activities in complex ways. The _chaotic_ regime corresponds
to the case where the frozen component does not percolate across the
system. Rather, the unfrozen component spans the system, leaving behind
isolated frozen islands embedded in the fluctuating sea. Transition bakc
and forth between these two regimes corresponds to a phase transition at
which the frozen component begins to melt and the fluctuating sea
[quiddity? -- 'gene] begins to coalesce; this phase-transition region is
the _complex_ regime. The most complex but controllable behaviour arises
in parallel-processing systems poised in this complex regime on the
boundary between order and chaos [now this sounds like elric m. -- 'gene].

I hold that the exorbitant order of the ordered regime underlies the
evolutionary emergence of order in ontogeny -- that spontaneous order
lies to hand, free, as it were, for selection's further molding. In
particular, asking what form such molding may take and what laws might
govern it leads us to to the hypothesis that the target which selection
achieves is complex systems poised in the complex regime on the boundary
between order and chaos. Such systems, it begins to appear, harbor
behaviour which is the most flexible, complex, and adaptable. If so, we
may have uncovered an universal in biology relating the mutual
implications and interpretations, the true marriage, of self-organisation
and selection: Selection, in attaining complex systems, may build toward
and sustain a characteristic poised order, an entire ensemble coursing
back and forth along a high-dimensional boundary between order and
disorder. Then further selection would be unable to avoid the typical
features of this poised ensemble, which generic features would emerge as
additional potential biologic universals.

Chapter 6 examines coevolution. Here we find evidence of a selective
metadynamics which may lead coevolving systems to the edge of chaos. I
ask in this chapter what the implications for coevolution may be of the
ruggedness of the fitness landscapes of each of the partners, and of how
much an adaptive move by one partner deforms the landscapes of others. We
are led to provocative results. If landscapes are too smooth compared
with the landscape deformation caused by partners, then each partner can
hardly respond by increasing fitness as other partners move. The entire
system is chaotic. Sustained fitness is low because the landscape of each
partner is drastically altered, typically casting the partner to low
fitness, by the moves of its coevolving partners. If landscapes are too
rugged compared with the deformation caused by others, then all partners
rapidly freeze into fixed but poor compromise phenotypes. Again,
sustained fitness is low. Just at the boundary between frozen order and
chaotic wandering, just at the edge of chaos when some, but not all,
partners cease changing and form a percolating frozen component, leaving
isolated islands of partners that continue to coevolve and change, the
coevolving system attains a structure where all partners attain the
highest expected sustained fitness. Adaptation, through a selective
metadynamics altering landscape structure and landscape deformation,
again attains the edge of chaos.

In summary, Part I investigates the mutual implications of
self-organization and selection for adaptive evolution. We ask what the
conditions are within and between evolving entities which permit adaptive
evolution, and whether the attainment of those conditions is itself a
lawful consequence of selection's operation. The tentative answer, to be
held as working hypothesis at this stage, is that at levels within
organisms which must coordinate complex tasks, within evolving
populations, and within coevolving systems, selection attains a
near-universal poised state hovering between unexpected, profound
spontaneous order and the incoherence of chaos. Borrowing a culminating
phrase from my colleagues N. Packard and C. Langton, life exists at the
edge of chaos.

[ in case you didn't notice: this ain't about biology. It's all about
complex systems engineering, being a roadmap for basic future gadgetry
-- 'gene ]