Complex Systems Biology of Networks: The Riddle and the Challenge - Systems Biology of Metabolic and Signaling Networks - page 28

• Scaling—Fractal dynamics
Scaling tackles the question of functional coordination in a living cell that
exhibits spatially distributed and compartmentalized subsystems with time
constants in sequentially consecutive and overlapping temporal scales. Scaling
involves both spatial and temporal levels of organization and reveals the inter-
dependence between processes happening at different spatio-temporal
coordinates (Aon and Cortassa 2009 ; Aon et al. 2012b ; Lloyd et al. 2012 ).
Genome-wide expression (transcriptome, ~5300 transcripts) during the time
frame period provided by the ~40 min ultradian clock revealed the existence
of two blocks of redox superclusters manifested in two phases of ~600 and
~4,700 maximally expressed genes during active respiration (oxidative) and low
respiration (reductive), respectively (Klevecz et al. 2004 ; Lloyd and Murray
2005 ) (see also Chap. 12 ). Within the 40 min time frame of the clock, there is a
10-15 min period conducive to DNA synthesis and replication, a time window
that opens during the reductive phase of the clock cycle: this suggests an
evolutionary strategy to avoid oxidative damage.
A bottom up modeling strategy provides an insight into how scaling arises,
and what it reveals. For the sake of example, during a heartbeat, macroscopic
and measurable properties of the cardiac cell such as action potentials, cell
shortening-relaxation, and concomitant Ca 2+ transients emerge from the
integrated dynamic behavior of excitation-contraction and mitochondrial ener-
getics (Aon and Cortassa 2012 ; Aon et al. 2012b ). Underlying key electro-
mechanical macroscopic functional properties, fast ionic currents operating in
the few milliseconds range are revealed. These, in turn, are fueled by relatively
slower (few seconds) mitochondrial energetic processes involving rapid trans-
port processes in different subcellular compartments: sarcolemma, mitochondria,
sarcoplasmic reticulum (see Chaps 5 and 10 ) . The processes involved in the
phenomenon of a heartbeat are simultaneous, and their apparent sequential
nature results from the differential relaxation properties exhibited by the
processes involved. Thus, the scale-free dynamic behavior exhibited by mito-
chondrial network energetic-redox function is based on the simultaneous
operation of processes of different nature (electrical, mechanical, metabolic)
in distinct compartments. Faster to slower temporal relaxation reflects the time
it takes a process to return to the state previous to the stimulation that elicited
the response, e.g., the initial potential depolarization triggered by the opening
of Na channels in the sarcolemma.
The inverse power law behavior of the power spectrum and the invariant
relative dispersion across temporal scales obtained from the analysis of experi-
mentally obtained time series in yeast and cardiac mitochondria support the
existence of scale-free dynamics. The multi-oscillatory behavior of yeast and
heart cells corresponds to statistical fractal dynamics, a behavior consistent with
scale-free dynamics spanning a wide range of frequencies of at least three orders
of magnitude (Aon et al. 2007 , 2008 ; Lloyd et al. 2012 ). Scale-free temporal
organization for organelle, cell, and organism implies timekeeping occurring
across temporal scales in living systems (Aon et al. 2008 ; Sasidharan et al. 2012 )
(see also Chap. 12 ).