ME724A
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MECHANICS OF BIOLOGICAL MEMBRANES
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Organization of animal cells; Structure and function of cell membrane; Role of fluid lipid bilayers in cell functionality; Experimental methods to study membranes; Self assembly of lipid bilayer, Brief review of differential geometry concepts; Development of elasticity models of membranes; Stable equilibrium shapes of red blood cells; shapes of phase separated fluid lipid bilayer vesicles; ; Adsorption of proteins to lipid membrane; Special topics from current research.
Lecturewise Breakup
I. Introduction (4 Lecture):
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Organization of animal cells (1 lecture)
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Structure and function of cell membranes (1 lecture)
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Role of fluid lipid bilayer in cell functionality and Experimental methods to study membranes (2 lecture)
II. Self assembly of lipid bilayer (5 lectures):
III. Review of differential geometry (8 Lecture):
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Introduction to membrane elasticity – stretching and bending (1 lecture)
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Differential geometry – curvilinear coordinates (1 lecture)
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Curvilinear coordinates on a surface (1 lectures)
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Covariant and contravariant derivatives (1 lecture)
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Mainardi-Codazzi relations (1 lecture)
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Ricci’s lemma, Surface divergence, Green’s theorem (3 lectures)
IV. Elasticity models for lipid bilayer (9 lectures):
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Development of elasticity models for lipid bilayer (3 lectures)
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Derivation of stress equilibrium equations of a lipid bilayer (1 lecture)
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Shape analysis of a red blood cell (3 lectures)
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Shape analysis of a two phase lipid bilayer vesicle (2 lectures)
V. Adsorption of proteins to membranes (7 lectures):
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Review of relevant thermodynamic concepts (2 lectures)
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Adsorption of proteins to flat surface using van der Waals and Bragg Willimas gas models (3 lectures)
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Adsorption of proteins to cylindrical and spherical membrane tubes (2 lectures)
VI. Additional topics – a few topics to be selected from below (7-9 lectures):
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Monge parameterization of surface and membrane fluctuations
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Adhesion of cells and vesicles to substrates
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Development of more refined fluid models for proteins based on protein-protein interactions and proteins shapes.
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Diffusion of proteins and domain in the membrane surface.
References:
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B. Alberts et al., Molecular Biology of the Cell, Garland Science, NY.
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J. N. Israelachvili, Intermolecular and Surface Forces: With Applications to Colloidal and Biological Systems, Academic Press, 1992 (second edition).
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R. Lipowsky and E. Sackmann, Structure and Dynamics of Membranes, Handbook of Biological Physics Vol. 1, Elsevier, Amsterdam, 1995.
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S. A. Safran, Statistical Thermodynamics of Surfaces, Interfaces, and Membranes Westview Press, 2003.
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Relevant journal articles.
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