HW2 - BIOE 398BS: Quantitative Human Systems Physiology...

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BIOE 398BS: Quantitative Human Systems Physiology Spring 2008 Bioengineering, University of Illinois at Urbana-Champaign 1 Two parts: First is paper problem. Second is Matlab simulation. Due: Feb. 01, 2008 at the beginning of class. 1. * We are going to calculate the size of a cell given the information below. Note that the number of macromolecules and their average charge is not given, so use N to represent the number of charges due to macromolecules. Some of the solution will be put in terms of N. Include units in your answers. Use the following data about a cell g Na = 3.5 μ mho/cm 2 , g K = 250 μ mho/cm 2 , [Na + ] o = 150 μ mol / cm 3 , (Note: this is 150 mM) [K + ] o = 5 μ mol / cm 3 , (Note: this is 5 mM) q = 1.6 x 10 -19 coulombs, kT/q = 25 x 10 -3 volts. The external solution is electrically neutral, so [Na + ] o + [K + ] o = [Cl - ] o Let v = electric potential and V = cell size. Note: μ mho = 10 -6 (coulomb/sec)/volt, a mho is the basic unit of conductance (the reciprocal of resistance, measured in ohms), the coloumb is a standard unit of charge, and 1 μ mol = 10 -6 x (6 x 10 23 ) ions. a.) Assume that the pumping rate of the NA+/K+ pump is optimal (p opt ), which given by the following equation: p opt = (kT/q 2 )(g Na g K /( g Na + g K )) log(([Na + ] o g K ) / (g Na [K + ] o ). This represents the optimal pumping rate to achieve the smallest cell volume, V, and electrical potential, v. Calculate the pumping rate and describe what it means. b.) Assuming that p=p opt , evaluate v, V, [NA + ] i , [K + ] i , [Cl - ] i . Note: some of the solutions will be a function of N. c.) Which terms are a function of N and what does that mean about cell size versus growth? d.) Calculate E Na , E K , E Cl . * Adapted from Hoppensteadt and Peskin text.
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BIOE 398BS: Quantitative Human Systems Physiology Spring 2007 Bioengineering, University of Illinois at Urbana-Champaign 2 2. Simulation of Action Potential We will be simulating the electrical activity of a patch of membrane of a neuron in response to a step change in voltage and an applied electrical current. We will be
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HW2 - BIOE 398BS: Quantitative Human Systems Physiology...

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