BME 100 Computer project 1_nigel

BME 100 Computer project 1_nigel - BME 100 Computer Project...

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BME 100 Computer Project 1: Receptor mediated endocytosis of EGF BME 100 Computer project 1: Receptor mediated endocytosis of EGF Nigel Chou 1) When C L0 = 0, C L = 0 since no ligand is formed over time. Also, N c = 0 since no complex can be formed with no ligand. After canceling out zero terms, s R R rec R eR V N f k N k i + - + - = ) 1 ( 0 (2) i R R rec R R eR N f k f k N k )) 1 ( ( 0 deg - + - = (4) s R V N i + - + × - = ) 2 . 0 1 ( 08 . 0 ) 10 5 . 0 ( 03 . 0 0 5 1500 064 . 0 + - = i R s N V i R N )) 2 . 0 1 ( 08 . 0 ) 2 . 0 ( 0022 . 0 ( ) 10 5 . 0 ( 03 . 0 0 5 - + - × = 46742 . 23277 = i R N 242086 . 10 1500 ) 46742 . 23277 ( 064 . 0 = + - = s V 2) When numbers of surface receptor and intracellular receptor per cell (Figure 1) are plotted against time using the values of N Ri and V s calculated from the previous question, a horizontal line is obtained both molecules, showing that the levels of both types of molecules remain constant, thus validating the values obtained in question 1. 1
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BME 100 Computer Project 1: Receptor mediated endocytosis of EGF Figure 1: verification that the cell-surface and intracellular receptor levels are constant with initial conditions of part 1 3) main_q3.m calculates the percentage drop in C L for different values of n c by using ode45 to solve the five differential equations for a period of 30 minutes. The limitation with this code is that the value of n c cannot be varied automatically in main_q3.m that calls egfunq3.m , the function that defines the differential equation. Therefore, n c is determined by manually varying its value in the function file (egfunq3.m.m) and running main_q3.m to obtain for the resulting percentage drop. This can be done systematically by starting with an initial upper limit of 1 billion. After each try, the interval is halved, and after each halving if the percentage drop is <1%, the mid-point of the upper interval is used, whereas if the percentage drop is >1%, the mid-point of the lower interval is used for the next iteration. This is repeated until the percentage drop is just slightly under 1%. The value of n c is found to be 1.631 x 10 8 cells per L and gives a percentage change of -0.99986%) The change in C L over time is shown in Figure 2. 2
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BME 100 Computer Project 1: Receptor mediated endocytosis of EGF Figure 2: Plot of molar concentration of ligand (EGF) vs time for 30 minutes 4) Since C L is assumed constant at the given values, equation (1) is omitted and equations (2) to (5) are solved using the ode45 for a duration of 30 minutes with main_q4.m. The plots are shown in Figures 3, 4 and 5 for C L at 2.5 x 10 -11 M, 7 x 10 -10 M and 5 x 10 -9 M respectively. 3
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BME 100 Computer Project 1: Receptor mediated endocytosis of EGF Figure 3: Plot of number of each molecule per cell vs. time for 30 minutes for CL=2.5 * 10 -11 Figure 4: Plot of number of each molecule per cell vs. time for 30 minutes for CL=7 * 10 -10 4
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This lab report was uploaded on 04/09/2008 for the course BME 100 taught by Professor Yuan during the Fall '07 term at Duke.

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BME 100 Computer project 1_nigel - BME 100 Computer Project...

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