From Physiology, Genomes, Systems, and Self-Organization to Systems Biology: The Historical Roots of a Twenty-First Century Approach to Complexity - Systems Biology of Metabolic and Signaling Networks - page 6

oscillators in a network, later refined by Kuramoto ( 1984 ) [reviewed in (Strogatz
2003 )].Considering idealized systems of nearly identical weakly coupled sinusoidal
oscillators, Winfree found that below a certain threshold of coupling, each oscilla-
tor runs at its own frequency, thus behaving incoherently until a further increase in
coupling overcomes the threshold for synchronization (Winfree 1967 , 2002 ). This
synchronization event was characterized as the analog of a phase transition, reveal-
ing an insightful connection between nonlinear dynamics and statistical physics
(Strogatz 2003 ).
1.4 Dynamics in Developing Systems
Feedback is a prominent source of nonlinear behavior, and biological systems
exhibit both negative and positive types of feedback. The central importance of
negative feedback as a control device in biological systems was formulated by
Wiener ( 1948 ). The discovery of negative feedback devices in a variety of
biological systems revealed the universality and simplicity of this control mecha-
nism, whereby a process generates conditions which discourage the continuation of
that process. End-product inhibition [later renamed “allosteric” inhibition by
Monod and Jacob ( 1961 )] is a prominent example of the latter; Umbarger ( 1956 )
and Pardee and Yates ( 1956 ) showed that the end product in the biosynthesis of
isoleucine or pyrimidine inhibited the pathway. Feedback control was highlighted
as a mechanism of avoiding behavioral extremes, echoing the concept of constancy
of the milieu int ´rieur by Claude Bernard [1865; 1927 translation by Green
(Bernard 1927 )] and Walter Cannon's ( 1932 ) notion of homeostasis. Long before
the discovery of feedback inhibition, Max Delbruck had introduced a mathematical
model of mutually inhibiting chemical reactions (Delbruck 1949 ). By such a system
of cross-feedback, two independent metabolic pathways can switch between stable
steady states under unaltered environmental conditions or as a response to the
stimulus of transient perturbations.
Positive feedbacks like autocatalysis are also ubiquitous in biology; their
importance as a source of instability giving rise to bifurcation and nonlinear
behavior was put forward by Turing ( 1952 ) in the context of morphogenesis.
Turing's pioneer work demonstrated that an autocatalytic reaction occurring in
an initially uniform or isotropic field, when coupled to the transport of matter
through diffusion, can produce symmetry breaking visualized as spatial patterns.
This work was ground breaking because it explained that stable spatial
structures could arise—without assuming a preexistent pattern—through self-
organization arising from bifurcations in the dynamics. This work opened the
way to a reaction-diffusion theory of pattern formation (Meinhardt 1982 )rather
than its original goal “to account for the main phenomena of morphogenesis”
(Turing 1952 ). Later on, Wolpert (1969) proposed “positional information” to
account for the mechanisms by which cells seem to know where they are. In
order to differentiate, cells interpret their position according to the concentration