Biomedical Engineering Reference
In-Depth Information
5.5.6.1
Calcium-Release Couplon
A typical cardiomyocyte possesses 10,000 to 20,000 Ca
2
+
-release couplons; each
couplon consists of 5 to 20 Ca
V
1.2 channels and 50 to 300 ryanodine receptors.
5.5.6.2
Modeling
The model of a Ca
2
+
-release unit characterized by a given spatial distribution on
the cell cortex contains 6 to 7 compartments through which Ca
2
+
moves with
given fluxes at interfaces: the bulk and junctional sarcoplasmic reticulum; cytosol,
possibly a cortical subdomain (with sodium-calcium exchanger), and dyadic space;
plasma membrane; and extracellular space.
The differential equations describing the Ca
2
+
concentrations in different com-
partments are [
396
]:
2
c
C
1
j
+
B
C
1
j
(
c
C
1
j
)
∂
t
c
C
1
j
=
D
C
1
j
∇
J
C
1
j
,
B
C
2
(
c
C
2
)
d
t
c
C
2
=
J
C
2
,
(5.1)
where type-1 compartment
C
1
j
2) represents the cytosol (
C
C
)and
sarcoplasmic reticulum (
C
SR
) and type-2 compartment
C
2
(
(
j
=
1
,
=
1
,
2) dyadic space
compartmental Ca
2
+
concentrations [mol/L
3
],
B
C
i
compartmental Ca
2
+
buffering functions (of the Ca
2
+
concentration [L]),
J
C
i
resulting Ca
2
+
flux for each compartment [mol/L
2
/T], and
D
C
i
compartmental Ca
2
+
diffusivity [L
2
/T].
Numerical simulations of a ventriculomyocyte couplon network are aimed at
studying: (1) influence on Ca
2
+
signals of various parameters, such as sensitivity of
ryanodine receptors of Ca
2
+
-release units (couplons), sarco(endo)plasmic reticulum
Ca
2
+
load and uptake rate, Na
+
-Ca
2
+
exchange magnitude, and Ca
2
+
buffer levels;
and (2) stochastic and deterministic aspects of intracellular calcium dynamics.
(
C
DS
) and junctional sarcoplasmic reticulum (
C
jSR
),
c
C
i
(
x
,
t
)
5.5.6.3
Calcium Wave and Alternans
Transitions from Ca
2
+
spark to Ca
2
+
wave can occur when spark-induced sparks
becomes significant, i.e., when sarcoplasmic reticulum Ca
2
+
load progressively
increases. Because both Ca
V
channels and ryanodine receptors open randomly,
Ca
2
+
sparks can happen stochastically and sparsely at low Ca
V
open probability
and/or under strong Ca
2
+
buffering, but more regularly at higher Ca
V
open
probability and weak Ca
2
+
buffering [
397
].
Random Ca
2
+
sparks from Ca
2
+
-release couplons that interact collectively
provoke entire-cell
Ca
2
+
alternans
. Cellular calcium transient alternans are beat-to-
beat variations in the peak cytosolic Ca
2
+
concentration in cardiomyocytes during
rapid electrical stimulation or under pathological conditions.
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