MIT 20 430j - Homework Set 3 (3 pages)

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Homework Set 3



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Homework Set 3

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Pages:
3
School:
Massachusetts Institute of Technology
Course:
20 430j - Fields, Forces, and Flows in Biological Systems
Fields, Forces, and Flows in Biological Systems Documents

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BEH 430 2 795 6 561 10 539 HST 544 Homework Set 3 Handed out Friday Oct 1 2004 Due Friday Oct 8 by 5pm Problem 3 1 Boyden Chamber Assay Consider the popular Boyden chamber assay for measuring leukocyte chemotactic response to a chemoattractant in which a quasi steady state linear attractant concentration gradient is established for a number of hours across a porous matrix see motivating paper Schagat T L et al Surfactant protein A differentially regulates peripheral and inflammatory neutrophil chemotaxis Am J Physiol Lung Cell Mol Physiol 284 2003 L140 L147 The matrix is situated between two reservoirs of media at the top and bottom of volumes Vt and Vb respectively The cells are placed on the top of the matrix to migrate from there x 0 to the bottom x L The cell density at the top of the matrix is sufficiently great that it remains approximately constant C0 Upon reaching the bottom of the matrix the cells quickly fall off onto a filter paper Thus the number of cells collected on the filter over any desired time period can be counted The experiment can be run with an attractant gradient of any magnitude either from bottomto top or top to bottom or with no gradient at all i e with uniform attractant concentration of any level across the matrix a Set up the appropriate leukocyte density conservation equation and boundary initial conditions to model this assay presuming that the experiment will be conducted largely during the timeperiod during which the attractant concentration gradient is roughly steady Also you can assume that the time scale of the experiment is sufficiently short that there is no leukocyte death and that the leukocyte density is sufficiently low that there attractant update is negligible b Assuming that the leukocyte random motility coefficient Dc and chemotaxis coefficient are constants independent of attractant concentration derive an expression for the number of cells collected on the bottom filter once they reach a steady state distribution



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