Network Dynamics in Cardiac Electrophysiology - Systems Biology of Metabolic and Signaling Networks - page 242

role in pacemaking activity (Lakatta et al. 2003 ). Local Ca 2+ releases generating
Ca 2+ waves via criticality may provide a subcellular mechanism accounting for the
fractal (i.e., power law) properties of heart rate variability (Ivanov et al. 1999 ;
Ponard et al. 2007 ). (4) Why cardiac arrhythmias occur suddenly and unpredictably
is a key clinical question (Zipes and Rubart 2006 ). The fact that a small random
noise can result in a macroscopic fluctuation under criticality may provide some
mechanistic insight into sudden cardiac death. In other words, the random and
sudden occurrence of arrhythmias may originate for the random fluctuations at the
single channel through the dynamics of criticality. This hypothesis needs to be
validated in future studies.
10.2.3 The Mitochondrial Network and Spatiotemporal
Depolarization Dynamics
A ventricular myocyte contains about 7,000-10,000 mitochondria. Similar to the
CRU network, mitochondria form a network inside the cell coupled by Ca 2+ , ATP,
ROS, and many other metabolites. The mitochondrial network generates mitochon-
drial depolarization waves and oscillations (Brady et al. 2004 ; Aon et al. 2003 ,
2004 ; Kurz et al. 2010 ; Honda et al. 2005 ), which have also been modeled in
computer simulations (Zhou et al. 2010 ; Zhou and O'Rourke 2012 ; Yang
et al. 2010 ).
Similar to Ca 2+ cycling dynamics, the transient single mitochondrial
depolarizations, known as “flickers,” tend to occur randomly in space and time.
A question that needs to be answered is how the transition from random flicking to
whole-cell oscillations occurs. In a recent study (Nivala et al. 2011 ), we developed a
mathematical model to study how single mitochondrial flickering events self-
organize to cause mitochondrial depolarization waves and whole-cell oscillations.
We developed a Markov model of the inner membrane anion channel in which
ROS-induced inner membrane anion channel opening causes transient mitochon-
drial depolarizations in a single mitochondrion, which occur in a nonperiodic
manner, simulating flickering. We then coupled the individual mitochondria into
a network, in which flickers occur randomly and sparsely (first panel in Fig. 10.5a )
in the network when a small number of mitochondria are in the state of high
superoxide production (determined by the parameter p ). As the number of
mitochondria in high superoxide production state increases, short lived or abortive
waves due to ROS-induced ROS release coexist with flickers. When the number of
mitochondria in high superoxide production state reaches a critical number, recur-
ring propagating waves are observed. The origins of the waves occur randomly in
space and are self-organized as a consequence of random flickering and local
synchronization. At this critical state, the depolarization clusters exhibit a power-
law distribution (Fig. 10.5b ). In addition, the whole-cell mitochondrial membrane