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Box 5.2 (continued)
Reaction-diffusion theory (pioneered by Turing (
1952
)), as a basis for
pattern formation in biological or chemical systems, emphasizes the impor-
tance of two components; an autocatalytic reaction producing a local product
(mediator or 'morphogen' as originally defined by Turing), and the transport
of this product by diffusion away from the source. This process can give rise
to spontaneous symmetry-breaking and the appearance of self-organized
spatial patterns including waves and oscillations (Aon et al.
1989
; Cortassa
et al.
1990
; Meinhardt
1982
; Nicolis and Prigogine
1977
). With respect to the
present model, the reaction consists of the reduction of O
2
to produce ROS
(specifically O
2
.
) driven by mitochondrial electron donors (e.g., NADH).
The local concentration of O
2
.
around the mitochondrion is shaped by
several others factors, including buffering by the antioxidant reactions and
transport of O
2
.
across the mitochondrial membrane. Diffusion of the O
2
.
to
neighboring mitochondria is shaped by the O
2
.
diffusion coefficient,
D
O2
.
,
and the amount of the O
2
.
scavenger enzyme superoxide dismutase present,
which consequently determines the rate of propagation of
ΔΨ
m
depolariza-
tion through the network. As expected, increasing SOD concentration slowed
down the depolarization wave.
The rate of propagation of
the depolarization wave in the model
ms
1
with low
D
O2
.-
(of the order of 10
14
cm
2
s
1
),
which compares well with the experimentally determined 22
μ
corresponded to 26
ms
1
at 37
C
(Aon et al.
2004a
). A restricted diffusion range of O
2
.
in cells is consistent
with experimental data; however, the actual diffusion coefficient of O
2
.
in
cells (with antioxidant systems disabled) has not been determined and is
likely to be influenced by local reactions with other molecules and molecular
crowding around mitochondria, which would decrease the effective volume,
increase the viscosity of the medium, and increase collision probability. This
assumption of restricted diffusion is represented by the low
D
O2
.-
in the
model.
μ
5.4.3 Experimental-Theoretical Test of a Main Mechanistic
Assumption of Mitochondrial Oscillations: Superoxide
as a Trigger of
ΔΨ
m
Depolarization
The original ROS-dependent mitochondrial oscillator model (Cortassa et al.
2004
)
considered cytoplasmic O
2
.
as the primary ROS that would increase IMAC open
probability in an autocatalytic process. H
2
O
2
was ruled out because it had been
shown experimentally that superoxide dismutase mimetics, which should enhance
H
2
O
2
accumulation, in fact suppressed the oscillations in
ΔΨ
m
(Aon et al.
2003
). To
test the assumption that O
2
.
could directly trigger IMAC opening, we applied
increasing concentrations of potassium superoxide (KO
2
,anO
2
.
donor) to par-
tially permeabilized myocytes.
Increasing the exogenous cytoplasmic KO
2
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