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# HW4 - Department of Chemical Engineering University of...

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Department of Chemical Engineering ChE 170 University of California, Santa Barbara Fall 2010 Problem Set No. 4 Due: Monday, 11/18/10 at the start of class Objective : To understand the thermodynamic and kinetic laws governing membrane structure, transport, and function. Review problems You should pay special attention to these questions after reading. Note that the answers are given in the back of the book. Formulate your answers fully first and then check them. This can be a significant aid in your understanding of the material, and similar questions may be asked on the final. You do not need to provide written answers in the solutions you hand in. ECB 11-8 ECB 11-9 ECB 11-11 ECB 12-9 ECB 12-10 ECB 12-11 ECB 12-14 Problem 1 Consider the model of a random walk discussed in class, g1766g1870 g3041 g2870 g1767g3404g1866g1864 g2870 g3436g3404 g1872 g2028 g1864 g2870 g3440 We can also use this basic approach to estimate the size of an unstructured long polymer like DNA. In this case, we model DNA as the path taken by a random walk. Instead of the walk taking a random step every small unit of time g2028 , we can think of the DNA strand as taking a new random direction (step) every g1865 base pairs. The number of base pairs we have to traverse before DNA can take a random new direction is related to its flexibility, and is roughly 300 base pairs. The length of a DNA molecule is about 3.4 Å per base pair and the length of a rigid unit 3.4g1865 Å. With this analogy, compute the root-mean-squared end-to-end distance, g3493g1766g1870 g2870 g1767 , of an unstructured DNA strand that is 50 million base pairs long. This number roughly corresponds to the human chromosome 19. Compare this to the length of the chromosome when condensed for cell division, ~2 g2020g1865 .

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Problem 2 Glucose transport across the plasma membrane into the intracellular space has been identified as the limiting step in the delivery of this energy source to muscle cells. So-called GLUT membrane transporter proteins bind to and facilitate transport of glucose into the cell. In particular, impairment of this transport mechanism is strongly implicated in patients with type 2 diabetes and modern research efforts are attempting to understand how such impairment occurs [Shepherd and Kahn, New England Journal of Medicine 341, 248 (1999)].
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