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The origins of the inverse power law behavior exhibited by
mitochondrial network dynamics
Physiological
Oscillations
Pathophysiological
a
Period
Amplitude
d
500
150
*
DDY
m
400
120
0.125
300
90
0.124
200
60
0.123
0.122
100
30
0.121
0
0
1
0
0 ms
p
erio
d
1.0
1.2
1.4
0.120
SOD concentration (
m
M)
0.0
0.2
0.4
0.6
0.8
1.0
b
2.0
0.12
1.6
0.08
1.2
0.8
0.04
300 ms
0.4
0.00
0.0
0.2
0.4
0.6
0.8
1.0
-2.6
-2.4
-2.2
-2.0
-1.8
log Frequency
c
0.12
-6
= 1.77 (r= -0.8)
b
0.08
-8
-10
0.04
-12
1 s
0.00
-14
0
1
2
3
4
5
Time (s)
-16
-2
-1
0
1
log Frequency
Fig. 5.11 Modulation of the oscillation period by the rate of ROS scavenging through SOD, and
inverse power law behavior of the amplitude versus frequency relationship exhibited by the
mitochondrial oscillator. (a) Oscillations with different periods and amplitude in
m
were
simulated with our computational model of the mitochondrial oscillator by changing SOD
concentration (Cortassa et al.
2004
). (b) The double log graph of the amplitude versus frequency
(1/period) was plotted from
ΔΨ
m
oscillations with amplitudes in the range of 2-124 mV and
periods ranging from 70 to 430 ms, respectively (see Aon et al. 2006, and their Supplemental
Material for more details). (c, d) From the simulations, we selected five oscillatory periods in the
high-frequency domain (between 70 and 300 ms) and one from the low-frequency (1-min period)
domain and attributed each one of them proportionally to a network composed by
500 mitochondria as described in Aon et al. (2006). A matrix containing a total of 500 columns
(mitochondria) and 6,000 rows was constructed. The time steps represented by the rows corre-
spond to a fixed integration step of 20 ms for the numerical integration of the system of ordinary
differential equations. We applied RDA and PSA to the average value of each row of the matrix at,
e.g., time 1, T1, that represents the experimental average value of fluorescent intensity of the
ΔΨ
m
probe (corresponding to mV) obtained every 110 ms from 500 mitochondria (on average) from
ΔΨ
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