General mathematical frame for open or closed biomembranes (Part I): Equilibrium theory and geometrically constraint equation

Journal of Mathematical Biology

Volumn 51, Issue 4, 2005, Pages 403-413

  Yin, Yajun ^a   Yin, Jie ^a   Ni, Dong ^a  

^a TSINGHUA UNIVERSITY   (China)

Author keywords

Biomembranes; Differential equation; Equilibrium; Geometrically constraint equation

Indexed keywords

ARTICLE; BIOLOGICAL MODEL; BIOMECHANICS; CELL SHAPE; CYTOLOGY; ERYTHROCYTE; HUMAN; IN VITRO STUDY; MATHEMATICS; MEMBRANE; PHYSIOLOGY; PRESSURE; THERMODYNAMICS;

BIOMECHANICS; CELL SHAPE; ERYTHROCYTES; HUMANS; MATHEMATICS; MEMBRANES; MODELS, BIOLOGICAL; PRESSURE; THERMODYNAMICS;

EID: 26444612695     PISSN: 03036812     EISSN: 14321416     Source Type: Journal    
DOI: 10.1007/s00285-005-0330-x     Document Type: Article

References (16)

1. Boal, D.: Mechanics of the Cell. London: Cambridge University Press, 2002
2. Ou-Yang, Z.C., Liu, J.X., Xie, Y.Z.: Geometric Methods in the Elastic Theory of Membranes in Liquid Crystal Phases. Word Scientific, 1999
3. Ou-Yang, Z.C., Helfrich, W.: Bending Energy of Vesicle Membranes: General Expressions for the First, Second and Third Variations of the Shape Energy and Applications to Spheres and Cylinders. Phys. Rev. A. 39, 5280-5288 (1989)
4. Leibler, S.: Curvature instability in membranes. J. Phy. (Paris) 47, 507-516 (1986)
5. Mukhopadhyay, R., Lim, H., Wortis, M.: Echinocyte shapes: bending, stretching, and shear determine spicule shape and spacing. Biophys. J., 82, 1756-1772 (2002)
6. Lim, H., Wortis, M., Mukhopadhyay, R.: Stomatocyte-discocyte- echinocyte sequence of the human red blood cell: Evidence for the bilayer-couple hypothesis from membrane mechanics. Proc. Natl. Acad. Sci. USA, 99 (26), 16766-16769 (2002)
7. Bessis, M., Weed, R.I., Leblond, P.F. (eds.): Red cell shape: Physiology, Pathology, Ultrastructure. Springer, Heidelberg, 1973
8. Iglič, A.: A possible mechanism determining the stability of speculated red blood cells. J. Biomech., 30, 35-40 (1997)
9. Saitoh, A., Takiguchi, K., Tanaka, Y., Hotani, H.: Opening-up of liposomal membranes by talin. Proc. Natl. Acad. Sci. 95, 1026-1030 (1998)
10. Capovilla, R., Guven, J., Santiago, J.A.: Lipid membranes with an edge. Phys. Rew. E. 66, 021607-(1-6) (2002)
11. Tu, Z.C., Ou-Yang, Z.C.: Lipid membranes with free edges. Phys. Rev. E. 68, 061915-(1-7) (2003)
12. Yin, Y., Yin, J.: Geometrical Constraint Equation and Geometrically Permissible condition for Vesicles. Chin. Phys. Lett., 21 (10), 2057-2058 (2004)
13. Yin, Y., Chen, Y., Ni, D., Shi, H., Fan, Q.: Shape equations and curvature bifurcations induced by inhomogeneous rigidities in cell biomembranes. J. Biomech., Digital Object Identifier (DOI), 2005
14. Yin, Y.: Integral Theorems Based on A New Gradient Operator Derived from Biomembranes (Part I), Tsinghua Science and Technology. 10 (3), 369-372 (2005)
15. Yin, Y.: Integral Theorems Based on A New Gradient Operator Derived from Biomembranes (Part II): Deduced Transformations and Applications. Tsinghua Science and Technology, 10 (3), 373-377 (2005)
16. Naito, H., Okuda, M., Ou-yang, Z.C.: Preferred equilibrium structures of a smectic-A phase grown from an isotropic phase: Origin of focal conic domains. Phys. Rev. E. 52(2), 2095-2098 (1995)