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 11

networks are intimately related concepts. Networks exhibit scale-free topologies and
dynamics. Topologically, networks are scale free because most of the nodes in a
network will have only a few links and these will be held together by a small number
of nodes exhibiting high connectivity (Barabasi 2003 ). Dynamically, the scale-free
character of networks manifests as diverse frequencies across multiple and highly
dependent temporal scales (Aon et al. 2012 ; Lloyd et al. 2012 ).
The present topological view of networks evolved from multiply and randomly
interacting elements in a system (Erdos and Renyi 1960 ) to “small worlds” (Watts
and Strogatz 1998 ) to “scale-free” networks (Barabasi 2003 ). From the classical
work of Erdos and Renyi based on random graphs, in which every node is linked to
other node irrespective of their nature and connectivity, the “small world” concept
introduced the notion that real networks as disparate as the neural network of the
worm Caenorhabditis elegans, or those of power grids exhibit high clustering (i.e.,
densely connected subgraphs) and short path lengths. Barabasi and collaborators
presented the view that nodes in a network are held together by a small number of
nodes exhibiting high connectivity, rather than most of the nodes having the same
number of links as in “random” networks (Barabasi and Albert 1999 ; Barabasi and
Oltvai 2004 ). The “scale-free” organization of networks expresses the fact that the
ratio of highly connected nodes or “hubs” to weakly connected ones remains the
same irrespective of the total number of links in the network (Albert and Barabasi
2002 ; Helms 2008 ). Mechanistically, it has been proposed that the scale-free
topology of networks is based on growth and preferential attachment (Albert and
Barabasi 2002 ; Barabasi 2003 ).
The networks approach was introduced into biochemistry as metabolic control
analysis (MCA). Independently developed in the second half of the past century by
Kacser and Burns ( 1973 ) and Heinrich and Rapoport ( 1974 ), MCA represents an
experimental approach with mathematical bases founded on the kinetics of enzy-
matic and transport networks in cells and tissues. MCA deals with networks of
reactions of any topology and complexity to quantifying the control exerted by
each process on systemic and local levels (Fell 1997 ; Westerhoff et al. 2009 ).
Metabolic flux analysis (MFA), also called flux balance analysis, represents another
methodological approach to the study of reaction networks (Savinell and Palsson
1992a , b ). Developed in the 1990s MFA is based on stoichiometric modeling and
accounts for mass-energy relationships among metabolic network components.
1.9 Systems Biology: A Twenty First Century
Approach to Complexity
Our potential to address and solve increasingly complex problems in fundamental
and applied research has expanded enormously. The following developments
underscore our possibilities to address increasingly complex behavior in complex
systems (Aon et al. 2012 ; Cortassa et al. 2012 ):