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 4

objects on earth and in heavens as well, gave rise to the notion of a “clockwork
universe.” This led Laplace to assert that given Newton's laws and the current
position and velocity of every particle in the universe, it would be possible to
predict everything for all time.
Poincar ´ , one of the most influential figures in the development of the modern field
of dynamical systems theory, described a sensitive dependence to initial conditions in
dealing with the “three body problem”—the motion of a third planet orbiting in the
gravitational field of two massive planets (Poincare 1892 ). This finding rendered
prediction impossible from knowledge of the situation at an initial moment to deter-
mine the situation at a succeeding moment. Otherwise stated: “ ... even if we knew the
laws of motion perfectly, two different sets of initial conditions even if they differ in

a minuscule way, can sometimes produce greatly different results in the subsequent
motion of the system” (Mitchell 2009 ). The discovery of chaos in two metaphorical
models applied to meteorology (Lorenz 1963 ) and population dynamics (May 1974 ),
and two different mathematical approaches—differential continuous and difference
discrete equations, respectively—[see (Gleick 1988 ) and (May 2001 ) for historical
accounts] introduced the notion that irregular dynamic behavior can be produced from
purely deterministic equations. Thus, the intrinsic dynamics of a system can produce
chaotic behavior independently of external noise. The existence of chaotic behavior
with its extreme sensitivity to initial conditions limits long-term predictability in the
real world.
The power of using mathematical modeling based on differential calculus was
shown in two papers published in 1952 by Turing and Hodgkin & Huxley (Hodgkin
and Huxley 1952 ; Turing 1952 ). Turing employed a theoretical system of nonlinear
differential equations representing reaction-diffusion of chemical species
(“morphogens” because he was trying to simulate morphogenesis). With this
system Turing attempted to simulate symmetry breaking, or the appearance of
spatial structures, from an initially homogeneous situation. This class of “concep-
tual modeling” contrasts with the approach adopted by Hodgkin and Huxley ( 1952 )
in which they modeled electrical propagation from their own experimental data
obtained in a giant nerve fiber to account for conduction and excitation in quantita-
tive terms. The “mechanistic modeling” approach of Hodgkin and Huxley is an
earlier predecessor of the experimental-computational synergy described in the
present topic. These two works had a long-lasting influence in the field of mathe-
matical modeling applied to biological systems.

...

1.3 From Multiple Interacting Elements to
Self-Organization

Systems Biology aims at “system-level understanding of biological systems”
(Kitano 2002b ). It represents an approach to unravel interrelations between
components in “multi-scale dynamic complex systems formed by interacting
macromolecules and metabolites, cells, organs, and organisms” (Vidal 2009 ).