# ps_8 - 10nm Furthermore the contour length of each spectrin...

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MASSACHUSETTS INSTITUE OF TECHNOLOGY Molecular, Cellular and Tissue Biomechanics BEH.410 / 2.978J / 6.524J / 10.537J Problem Set #8 Issued: 4/30/03 Problem #1: Red Blood Cell Membrane Mechanics Below is a picture of the cortex of a red blood cell. Our goal is to develop a model to predict the membrane mechanics of this 2-dimensional array of crosslinked spectrin polymers. A simple model is to consider a 2-D rectangular array of polymers (spectrin) which are connected at defined nodes (the circles). Each one of the polymers has a persistence length L p , contour length of L and diameter d. Spectri n L e Junctional complex L a) Calculate the membrane shear modulus (K s ) for the model above. Note, it may be e helpful to consider the deformation of one unit cell. Also, for simplicity you can assume that the spectrin is not strongly stretched (L e <<L). b) Using optical tweezers researchers have found that the persistence length of spectrin is

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Unformatted text preview: 10nm. Furthermore, the contour length of each spectrin molecule is 200 nm and L e is approximately 70nm. Calculate the K s for the cortex using your model from part a). Comment on how this compares to the value mentioned in class for a red blood cell. 1 Photo removed due to copyright considerations. (Spectrin structure in red blood cell.) c) Now derive an expression for the membrane area expansion modulus K e for the model. d) Calculate the value of K e using the optical tweezer data. Comment on how this compares to the value of K e for a red blood cell. Problem #2 R.D. Kamm Manuscript, Chapter 2.1 Problem #1 Problem #3 R.D. Kamm Manuscript, Chapter 2.2 Problem #4 Problem #4 R.D. Kamm Manuscript, Chapter 2.3 Problem #1 Problem #5 R.D. Kamm Manuscript, Chapter 2.3 Problem #3 2...
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## This note was uploaded on 11/11/2011 for the course BIO 20.410j taught by Professor Rogerd.kamm during the Spring '03 term at MIT.

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ps_8 - 10nm Furthermore the contour length of each spectrin...

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