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Unformatted text preview: Computational Methods in Biology (Spring 2011) Assignment 2 (due in class on Feb. 18) The Rules This assignment and most of the others in this course will involve computer simu lations. What do I expect you to turn in? I'd like the following: (1) Handwritten or wordprocessed text describing what you are doing, how you did it, and the results you got. I ask many questions, and I expect you to answer these. When I grade I will be looking to see if each question has been satisfactorally an swered. Use complete sentences and make your work easy to follow. (2) Labelled gures. Include things such as gure number, axis labels, bifurcations, types of branches (stationary or periodic), nullclines ( xnullcline or ynullcline), and equilibrium points (what type?). In some cases I will ask for a handdrawn gure, and this is what you should turn in. In other cases I will ask for a computerdrawn gure (the XMGR graphing package is what I use to make gures, I'll show you how to use it if you ask). In other cases I won't specify. (3) Make it look good. Wading through disorganized and unclear work does not put me in a good mood. Ask yourself whether you would want to grade it! (4) Turn it in on time. You can, however, turn it in up to two days late with a 20% reduction in grade. After that I won't accept it. 1 2 The free software package XPPAUT , written by Bard Ermentrout at the University of Pittsburgh, is a great tool for analyzing continuous dynamical systems. In this rst problem I will talk you through many of the things you need to know to use this package (on the SUNs) to do phase plane and bifurcation analysis. [Versions of this software are written for unix, linux, and even Windows machines. You can download it from Bard's web page.] The example problem will be a model of oscillatory glycolysis developed in 1972, called the GoldbeterLefever model . This descibes in a very simple way how the molecule ATP is converted to ADP by the enzyme phosphofructokinase. This enzy matic function is described by \". The ATP input rate to the system is and the ADP degradation rate is . Parameter is a time constant. 1. [10 points] The GoldbeterLefever model ( Biophysical Journal , vol. 12, pp. 1302{ 1315, 1972) is dATP dt = [  ( ATP,ADP )] / dADP dt = [( ATP,ADP ) ADP ] / . where ( ATP,ADP ) = ATP (1 + k ADP ) 2 , and , , k , and are parameters. We will use k = 20 and = 500 throughout the assignment, and various values for and . (a) The computer code for the GoldbeterLefever model, goldbeter.ode , can be downloaded from my website (www.math.fsu.edu/ bertram/course software). If you look in this le you will see how easy it is to enter ODEs and associated information into this program. On the SUNs start up xpp using the command \xppaut gold beter.ode". Notice the buttons on the top of the xpp screen. Clicking on these will open other windows that will allow you to do things like change the values of the system parameters.system parameters....
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This note was uploaded on 11/27/2011 for the course MAC 2312 taught by Professor Zhang during the Fall '07 term at FSU.
 Fall '07
 Zhang
 Calculus

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