There is extensive ultrastructural evidence in endothelium for the presence of chained vesicles or clusters of attached vesicles, and they are considered to be involved in specific transport mechanisms, such as the formation of trans-endothelial channels. However, few details are known about their mechanical characteristics. In this study, the formation mechanism and mechanical aspects of vascular endothelial chained vesicles are investigated theoretically, based on membrane bending strain energy analysis. The shape of the axisymmetric vesicles was computed on the assumption that the cytoplasmic side of the vesicle has a molecular layer or cytoskeleton attached to the lipid bilayer, which induces a spontaneous curvature in the resting state. The bending strain energy is the only elasticity involved, while the shear elasticity is assumed to be negligible. The surface area of the membrane is assumed to be constant due to constant lipid bilayer thickness. Mechanically stable shapes of chained vesicles are revealed, in addition to a cylindrical tube shape. Unfolding of vesicles into a more flattened shape is associated with increase in bending energy without a significant increase in membrane tension. These results provide insights into the formation mechanism and mechanics of the chained vesicle.

1.
Alberts, B., Bray, D., Lewis, J., Raff, M., Roberts, K., and Watson, J. D., 1994, Molecular Biology of the Cell, 3rd ed., Garland Pub., pp. 599–651.
2.
Cross, P. C., and Mercer, K. L., 1993, Cell and Tissue Ultrastructure—A Functional Perspective, W. H. Freeman and Co., pp. 148–149.
3.
Deuling
H. J.
, and
Helfrich
W.
,
1976
, “
Red Blood Cell Shapes as Explaned on the Basis of Curvature Elasticity
,”
Biophysical J.
, Vol.
16
, pp.
861
868
.
4.
Evans, E. A., and Skalak, R., 1980, Mechanics and Thermodynamics of Biomembranes, CRC Press, Inc., pp. 141–180.
5.
Hochmuth, R. M., 1987, “Properties of Red Blood Cells,” in: Handbook of Bioengineering, R. Skalak and S. Chien, eds., McGraw-Hill, New York, pp. 12.1–12.17.
6.
Jian-Guo
H.
, and
Zhong-can
O.
,
1993
, “
Shape Equations of the Axisymmetric Vesicles
,”
Physical Review E
, Vol.
47
-
1
, pp.
461
467
.
7.
Kosawada, T., Skalak, R., Schmid-Scho¨nbein, G. W., Chien, S., and Yoshida, O., 1995, “Dynamic Aspects of Vascular Endothelial Vesicles,” Proc. 2nd International Conference on Cellular Engineering, San Diego, pp. 57–57.
8.
Lee
J.
, and
Schmid-Scho¨nbein
G. W.
,
1995
, “
Biomechanics of Skeletal Muscle, Capillaries: Hemodynamic Resistance, Endothlial Distensibility, and Pseudopod Formation
,”
Annals of Biomedical Engineering
, Vol.
23
, pp.
226
246
.
9.
Luke
J. C.
,
1982
, “
A Method for the Calculation of Vesicle Shapes
,”
SIAM J. Appl. Math.
, Vol.
42
-
2
, pp.
333
345
.
10.
Naito
H.
,
Okuda
M.
, and
Zhong-can
O.
,
1996
, “
Polygonal Shape Transformation of a Circular Biconcave Vesicle Induced by Osmotic Pressure
,”
Physical Review E
, Vol.
54
-
3
, pp.
2816
2826
.
11.
Palade
G. E.
, and
Bruns
R. R.
,
1968
, “
Structural Modulations of Plasmalemmal Vesicles
,”
The Journal of Cell Biology
, Vol.
37
, pp.
633
646
.
12.
Palade
G. E.
,
Simionescu
M.
, and
Simionescu
N.
,
1979
, “
Structural Aspects of the Permeability of the Microvascular Endothelium
,”
Acta Physiol. Scand., Suppl.
,
463
, pp.
11
32
.
13.
Pamplona
D. C.
, and
Calladine
C. R.
,
1993
, “
The Mechanics of Axially Symmetric Liposomes
,”
ASME JOURNAL OF BIOMECHANICAL ENGINEERING
, Vol.
115
, pp.
149
159
.
14.
Pamplona
D. C.
, and
Calladine
C. R.
,
1996
, “
Aspects of The Mechanics of Lobed Liposomes
,”
ASME JOURNAL OF BIOMECHANICAL ENGINEERING
, Vol.
118
, pp.
482
488
.
15.
Press, W. H., Teukolsky, S. A., Vetterling, W. T., and Flannery, B. P., 1992, Numerical Recipes in Fortran, 2nd ed., Cambridge Univ. Press, pp. 745–778.
16.
Schmid-Scho¨nbein
G. W.
,
Kosawada
T.
,
Skalak
R.
, and
Chien
S.
,
1995
, “
Membrane Model of Endothelial Cells and Leukocytes. A Proposal for the Origin of a Cortical Stress
,”
ASME JOURNAL OF BIOMECHANICAL ENGINEERING
, Vol.
117
, pp.
171
178
.
17.
Schnitzer
J. E.
,
Oh
P.
,
Pinney
E.
, and
Allard
J.
,
1994
, “
Filipin-Sensitive Caveolae-Mediated Transport in Endothelium: Reduced Transcytosis, Scavenger Endocytosis, and Capillary Permeability of Select Macromolecules
,”
The Journal of Cell Biology
, Vol.
127
-
5
, pp.
1217
1232
.
18.
Schnitzer
J. E.
,
Oh
P.
,
Jacobson
B. S.
, and
Dvorak
A. M.
,
1995
, “
Caveolae From Luminal Plasmalemma of Rat Lung Endothelium: Microdomains Enriched in Caveolin, Ca2+ -ATPase, and Inositol Trisphosphate Receptor
,”
Proc. Nat. Acad. Sci.
, Vol.
92
, pp.
1759
1763
.
19.
Simionescu
N.
,
1983
, “
Cellular Aspects of Transcapillary Exchange
,”
Physiological Reviews
,
63
-
4
, pp.
1536
1579
.
20.
Skalak
R.
,
Tozeren
A.
,
Zarda
R. P.
, and
Chien
S.
,
1973
, “
Strain Energy Function of Red Blood Cell Membranes
,”
Biophysical J.
, Vol.
13
, pp.
245
264
.
21.
Skalak, R., 1992, “Cellular Biomechanics,” Encyclopedia of Applied Physics, Vol. 3, VCH Publishers, Inc., pp. 141–167.
22.
Wagner
R. C.
, and
Casley-Smith
J. R.
,
1981
, “
Endothelial Vesicles
,”
Microvascular Research
, Vol.
21
, pp.
267
298
.
23.
Wolfram, S., 1991, Mathematica, 2nd ed., Addison-Wesley Pub., Company, Inc.
24.
Zarda
P. R.
,
Chien
S.
, and
Skalak
R.
,
1977
, “
Elastic Deformations of Red Blood Cells
,”
J. Biomechanics
, Vol.
10
, pp.
211
221
.
25.
Zhong-can
O.
, and
Helfrich
W.
,
1989
, “
Bending Energy of Vesicle Membrane: General Expressions for the First, Second, and Third Variation of the Shape Energy and Applications to Spheres and Cylinders
,”
Physical Review A
, Vol.
39
-
10
, pp.
5280
5288
.
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