Biology Reference
In-Depth Information
Box 5.2: Accounting for ROS-Induced ROS Release Based on
Reaction-Diffusion: Computational Model of a Network Comprised by
500 Mitochondria Based on the ROS-Dependent Mitochondrial
Oscillator
The thin optical sectioning ability of two-photon laser scanning fluorescence
microscopy can be used to examine the behavior of the mitochondrial net-
work in a single plane of a cardiomyocyte (Fig.
5.4
) (Aon et al.
2003
,
2004a
).
To compare the experimental results obtained with optical imaging
experiments in cardiomyocytes subjected to oxidative stress, a mitochondrial
reaction-diffusion ROS-induced ROS release (RD-RIRR) computational
model was developed. Each non-boundary node (mitochondrion) in the
network was considered to have four nearest neighbors for O
2
.
interaction
(Fig.
5.8
). At each node (
j
,
k
) of the 2D network, O
2
.
dynamics is described
by the mass balance equation based on O
2
.
reaction and diffusion (Zhou
et al.
2010
):
2
C
O
2
i
ð
2
C
O
2
i
ð
@
C
O
2
i
ð
x
;
y
;
t
Þ
D
O
2
i
@
x
;
t
Þ
þ
@
y
;
t
Þ
¼
þ
f
ð
C
O
2
i
;
t
Þ
@
t
@
x
2
@
y
2
:
@
C
O
2
i
ð
0
;
t
Þ
;
@
C
O
2
i
ð
X
;
t
Þ
¼
¼
Boundaryconditions
0
0
@
x
@
x
(5.1)
@
C
O
2
i
ð
0
;
t
Þ
;
@
C
O
2
i
ð
Y
;
t
Þ
¼
0
¼
0
@
y
@
y
Initial conditions
C
O
2
i
ð
x
;
y
;
0
Þ¼
g
ð
x
;
y
Þ
:
where
D
O
2.
- is the cytoplasmic O
2
.
diffusion coefficient,
X
and
Y
indicate the
total lengths in the dimensions
x
and
y
, respectively, and
f(C
O2
.i
,t)
¼
Vt
O2
.i
(t) - VSOD
O
2.
-
i (t)
.
Vt
O2
.i
is the rate of O
2
.
transport (release) from
the mitochondrion (via IMAC), and
VSOD
O2.-i
, the O
2
.
scavenging rate by
Cu, Zn superoxide dismutase (SOD). The function
g
(
x
,
y
) describes the distri-
bution of O
2
.
at time 0 (the initial condition). The spatial coordinates,
x
and
y
, are subjected to discretization to numerically solve the system by the finite
difference method. Non-flux boundary conditions were used.
To solve this large nonlinear network consisting of 500 (50
10)
mitochondria (each node described by 15 state variables), a high-performance
parallel computer was used. To be suitable for parallel computation, Eq. (
5.1
)
was rewritten in the matrix form using forward Euler method to approximate
the time derivative of
C
O2
.-i
at each node (
j
,
k
):
C
O
2
i
ð
j
;
k
;
t
þ Δ
t
Þ¼
C
O
2
i
ð
j
;
k
;
t
Þþ½
Diff
O
2
i
ð
j
;
k
;
t
Þþ
f
ð
C
O
2
i
ð
j
;
k
;
t
ÞÞ Δ
t
(continued)
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