final - Massachusetts Institute of Technology Biological...

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Massachusetts Institute of Technology Biological Engineering Division Department of Mechanical Engineering Department of Electrical Engineering and Computer Science BEH.410/2.798J/6.524J/10.539J Molecular, Cellular & Tissue Biomechanics, Spring 2003 Second quiz Distributed: Friday, May 9, 2003 Due: 5:00 PM, Wednesday, May 14, 2003 You are to complete this quiz on your own, without any consultation anyone except for the two instructors or the course TA. If you have any questions, don’t hesitate to ask us. If anyone raises questions that we feel would be of general interest, we will post the question and our response on the class website, so be sure to check periodically. You are free to use any resource materials you feel might be useful. There are three problems on the exam with the points as indicated. Please be sure to explain your reasoning as fully as possible. Write everything in the exam booklet, not on the exam or on separate pages. Solutions will be available at the time you turn in the exam.
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Problem #1 MEMBRANE MECHANICS (35 Points) The lipid membrane of a large vesicle in solution will fluctuate due to thermal motion. It is possible that such fluctuations could result in a “pinching off’ of the membrane to form two smaller vesicles as shown in the figure below. a) (10 pts) What is the change in the total bending energy in going from a system containing one large vesicle (radius = 30 m m) to a system containing a slightly smaller vesicle and a very small vesicle (radius = 1 micron)? Assume a value of K b = 10 kT and negligible change in total volume during the pinching process. b) (5 pts) Do you expect to find many small vesicles in an ensemble if the system above is at thermal equilibrium and the pinching process is reversible? Assume that there is a small change in total volume which is just enough to prevent the membrane from being in a state of tension after the pinching process (ie only bending energy is important). Lipid membrane tethers can be created by exerting a force at a point on the surface of a
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final - Massachusetts Institute of Technology Biological...

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