Final Assignment (Pancreatic Duct Simulation): 304, 2010
Task: Develop a simulation of a simple pancreatic duct draining into the duodenum.
Work in teams of no more than 3 people.
1. The pancreatic duct will be made up of 13 volume cells. The right most 3 volume cells will secrete Trypsinogen.
Assume in each volume element that protein is evenly mixed.
2. The duodenum will comprise of 5 volume elements with the second volume element connected to the left most
volume element of the pancreatic duct.
3. The bottom three elements of the duodenum will contain Enterokinase.
Notes:
1. Trypsinogen and Trypsin can freely diffuse between the volume elements.
2. Enterokinase cannot diffuse between elements but is present in a fixed quantity in the last 3 cells of the
duodenum.
3. Trypsin is an enzyme that catalyzes the irreversible conversion of Trypsinogen to Trypsin. The Vmax of the
Trypsin will equal the concentration of Trypsin (yes you read it right).
4. Enterokinase is an enzyme that catalyses the irreversible conversion of Trypsinogen to Trypsin
5. Diffusion of protein molecules from one volume element to the next will be first order with the same
diffusion constant for each volume element (See figure above)
6. Trypsinogen will be secreted at a constant rate in the 3 right most cells.
7. The cell numbering system refers to the columns in your simulation data file. The first column of the data file
should be time. The second column should be a pair of numbers related to cell number 1. The first number
of the pair will indicate the concentration of Trypsinogen and the second column to Trypsin. The remaining
columns are the same but with reference to the numbering in the above figure.
Aim 1: Using a suitable programming environment (eg Matlab) construct a differential equation model of this system.
Use your program to generate the simulation data, that is how the proteins change in concentration in the individual
volume elements over time. Use a space to separate the columns (no commas, semicolons or tabs!).
Aim 2: Graphically present the data in a series of screen shots showing the diffusion of protein down the duct. Use Blue
to indicate a low concentration and red to indicate a high concentration for Trysinogen and use Green to indicate a low
concentration and yellow to indicate a high concentration of Trypsin.
Turn Over
Pick constants that give the most interesting results.
Consider setting up Aim 1 for next Monday, or at least write out the differential equations you will use and we can go
over them in class.
Next Monday we will also consider how to do Aim 2 unless you have figured some way to do it already.
An initial version of the visualization software is now available on the GoPost at the Catalyst grade book.