Dynamics of Mitochondrial Redox and Energy Networks: Insights from an Experimental–Computational Synergy - Systems Biology of Metabolic and Signaling Networks - page 121

5.4 Second Iterative Loop: Mitochondrial Criticality
and Network Redox Energetics During Oscillations

5.4.1 Mitochondrial Criticality

Under oxidative stress mitochondrial behavior reaches a critical point that we called
mitochondrial criticality (Aon et al. 2004a ), an emergent macroscopic response
manifested as a generalized ΔΨ m collapse followed by synchronized oscillation in

the mitochondrial network under stress (Fig. 5.4 ). As the mitochondria approach
criticality, two main questions arise (Aon et al. 2006a ): (1) how does the signal
propagate throughout the network? and (2) how does

ΔΨ m depolarization occur

almost simultaneously in distant regions of the cell?
Applying percolation theory to the problem (see Box 5.1 ) we found that, prior to
the first global ΔΨ m depolarization, approximately 60 % of the mitochondria had

accumulated ROS to a level roughly 20 % above baseline (Aon et al. 2004a ), which
was the threshold for activation of the oscillator at the whole cell level. This critical
density of mitochondria (60 %) was consistent with that predicted by percolation
theory (Box 5.1 ). Moreover, the spatial distribution of mitochondria at the threshold
exhibits a fractal dimension in agreement with theory (Aon et al. 2003 , 2004b ).
Beyond criticality, self-sustained oscillations in ΔΨ m continue as a consequence
of a bifurcation in the dynamics of the system (Cortassa et al. 2004 ). However, the
spatial pattern of subsequent depolarization of the network will typically follow that
of the original percolation cluster, with some mitochondria always remaining
outside the cluster. Another important feature of the percolation model is that the
global transition can be prevented if the O 2 . concentration reaching the neighbor-
ing mitochondrion is decreased below threshold, either by decreasing O 2 . produc-
tion (e.g., by inhibiting respiration), decreasing O 2 . release (e.g., by inhibiting
IMAC), or increasing the local ROS scavenging capacity (e.g., by increasing the
GSH pool) (Aon et al. 2004a , 2007b ; Cortassa et al. 2004 ).

Box 5.1: Standard 2D Percolation Theory as Applied to Explain
Mitochondrial Criticality
Percolation describes how local neighbor-neighbor interactions among
elements in a lattice can scale to produce a macroscopic response spanning
from one end of the array to the other (Stauffer and Aharony 1994 ). Such a
“spanning cluster” forms when there is a critical density of elements close to
the threshold for a transition (the percolation threshold). Experimentally, the
“spanning cluster” involved ~60 % of the mitochondrial lattice with increased
levels of ROS (Aon et al. 2004a ). This value was consistent with a critical
density of mitochondria at the percolation threshold ( pc ), which, for a square
lattice in percolation theory, is equal to 0.593 or ~59 % (Feder 1988 ; Stauffer
and Aharony 1994 ).

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