Biomedical Engineering Reference
In-Depth Information
that is approximated by a Fokker-Planck equation, using the differential vectorial
operator
∇
[
104
]:
∂
t
P
=
−
∇
·
(
P
φ
)+
∇
(
D·
∇
P
)+b(
V
,
Hb
,
t
)
−
d(
V
,
Hb
,
t
)
P
,
(3.2)
D
V
0
D
=
0
D
Hb
3.5.2
Shape
A red blood capsule experiences large reversible deformations during its 120-d
lifespan. It recovers its initial shape after large deformations undergone in narrow
capillaries owing to the composition of the membrane and membrane-cytoskeleton
interaction. Its plasma membrane and the cell cortex, with the spectrin net-
work tethered to the phospholipid bilayer, are the main load-bearing components.
Membrane-spectrin interaction results from the phosphorylation of the interconnec-
tion protein-4.1R, or erythrocyte membrane protein band EPB4.1.
In thermal equilibrium, red blood cells, like lipid vesicles, can have various shape
types according to the environmental conditions. The spectrin network enables
RBCs to remain intact while deforming in blood flow through narrow capillaries. In
normal conditions, RBCs adopt a biconcave disc shape with a given area (
A
)S and
volume (
V
; mean radius R
m
=(A/[4
])
1
/
2
R
0
/3)
π
∼
3.4
m; reduced volume V/(4
π
∼
0.6).
Membrane fluctuates over a short time scale (
100 ms). Membrane fluctuations
depend on its bending stiffness, ATP, and integrity of the spectrin cytoskeleton con-
nected to the membrane by actin, glycophorin-C, and protein 4.1R. Phosphorylation
of 4.1R protein by protein kinase-C disassembles the EPB4.1-spectrin-actin trimer,
hence spectrin-membrane connection. Inhibition and activation of this phosphory-
lation significantly affects tension and effective viscosity (
∼
10
−
3
Pa.s) [
105
].
In the microcirculation, RBC deformation reduces flow resistance. Deformation
also provokes ATP release from RBCs that requires cystic fibrosis transmembrane
conductance regulator activated via the cAMP-PKA axis [
106
]. Release of ATP
causes nitric oxide synthesis and augments the vascular caliber [
107
]. In addition,
erythrocytes stimulate nitric oxide production in platelets [
108
].
Spectrin tetramers in the unstressed state form dimers under shear. The cell
periphery undergoes fluidization beyond a shear threshold [
109
]. Spectrins remodel
into tetramers upon unloading and the RBC membrane stiffness rises. Stretching by
optical tweezers estimates the shear modulus (4-10
∼
100
×
N/m) [
110
].
The RBC shape represents an equilibrium configuration that minimizes the
curvature energy of a closed surface (a vesicle) for given surface area and volume
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