Mathematical Biology - Math 4780/6780, Engg 8110

Instructor: Caner Kazancı
Offices: Driftmier Engineering Center, Room 410, and Boyd Graduate Studies, Room 525.
Office hours: Wednesdays between 11:00am-12:00pm, and anytime by appointment.
Course Information: You can download the syllabus here.
Topics: Population dynamics, sensitivity analysis, phase-plane analysis, biochemical kinetics, metabolic pathways, approximate kinetics, bifurcation analysis, stochastic simulation methods, Langevin equation, chemical master equation, biochemical networks, Neuroscience, Gene Regulation, Genetic Networks and Systems Biology.
Text Book: A course in Mathematical Biology, Vries, Muller, Hillen, Schonfisch, Lewis. Other books of interest:

• Essential Mathematical Biology, Nicholas F. Britton.
• Handbook of Stochastic Methods, C. W. Gardner
• Computational Cell Biology, C. Fall, E Marland, J. Wagner, J. Tyson
• Systems Biology in Practice, E. Klipp, R. Herwig, A. Kowald, C. Wierling
• Nonlinear Dynamics and Chaos, Steven. H. Strogatz
• Mathematical Biology I, J. D. Murray

Objective: The course will provide students with the mathematical and computational tools necessary to understand, model, analyse and modify a variety of biological and ecological systems and their dynamics.
Prerequisites: It is highly recommended that students have taken a prior differential equations course, as well as a matrix algebra course. We will use Matlab and XPP for simulation and analysis, however no prior knowledge or experience is necessary.

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Announcements

• Group final presentations are scheduled for Thursday, May 3, in the following order:
  • Group 1 - Laura, Tierney, Tonya.
    Looking for Evidence of Critical Slowing Down in the Bobwhite Quail Population Model
  • Group 2 - Amir, Grant, Joydeep.
    
  • Group 3 - Scott, Tian, Timothy
    Toward a quantative understanding of sugar mixture fermentation using E. coli
  • Group 4 - Daniel, Farres, Rene.
    
  • Group 5 - Ahmad, Jonathan, Vallery.
    The qualitative analysis of biological clock in bread mold
  • Group 6 - Margaret, Nibiao, Tiffany.
    Metabolic cooperation and competition between intestinal bacteria.
  • Group 7 - Andrew, Shunli, Yuheng.
    
  A couple of important points:
  • Send me your finalized project titles if you have not done so.
  • The reports are due before the start of the presentations.
  • I need an e-mail from each group on Thursday by 5pm with a zipped attachment including the following: Presentation, Report, All computer codes that you used for your project, Manuscript(s) closely related to your project (if there are any).
• Here you can download metropolis.m, compute_error0.m, compute_error1.m, compute_error2.m, compute_error3.m, solve_system.m, my_system.m.
• Final presentations are scheduled for Thursday, May 5, between 12pm-3pm, at the same room (Driftmier 312).
• Here you can download abm_wolfram0.m, abm_wolfram1.m, abm_wolfram2.m and abm_life_game.m.
• An example for bifurcations using XPP: bifurcation.ode
• You should've received a group e-mail to encourage you to form groups. The e-mail contained the project ideas discussed today, and your e-mail addresses. If you have not received this e-mail yet, let me know ASAP.
• Here you can download competition.ode and sir_epidemic.ode.
• Here is the main webpage of XPP. You can install XPP for Windows from here. It's free!
• Emacs is a powerful text editor. You can download the Windows version from here and the various Mac OS versions are available here. Most Linux distributions come with Emacs. If you don't have it, use your package manager to get and install it automatically.
• To print in XPP, go to "Graphic stuff -> Postscript". To print in Auto, go to "File -> Postscript". You will end up with a postscript file (with *.PS extension), which is similar to a PDF file. You can view and print this file as described here.
• The assignment is now due Thursday by 4pm at Congcong (Cindy) Han's mailbox at Mathematics Department (Boyd Graduate Studies, 4th floor, mailbox room).
• Use of laptops, netbooks, tablet PC's, iphones, ipads, android devices, and cellphones are not permitted, unless you have a documented disability that requires you to use one. If this is the case, you need to contact and inform me about your situation beforehand. This means that you should not have an open laptop in front of you unless you have talked to me before.
• Chapter 1 of the textbook is provided below, in case you have not purchased it yet.

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Homework Assignments

• Homework Set 1
• Homework Set 2
• Homework Set 3

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Syllabus

Date	Reading	Topics	Notes
Jan 13	1.1, 1.2, 1.3	Introduction to Mathematical Biology	Overview
Jan 18	2.1, 2.2.1	Population dynamics, Discrete time models	Lecture 1
Jan 20	2.2.2, 2.2.3	Stability, long term behavior, and chaos	Lecture 2
Jan 25	2.3.1, 2.3.2, 2.3.3	Multi-step and coupled dicrete-time systems	Lecture 3
Jan 27	2.3.2, 2.3.3	Stability of multi-dimensional discrete-time models	Lecture 4
Feb 1	3.1	Continuous time models I: Ecosystem models	Lecture 5
Feb 3	3.3.1, 3.3.2, 3.3.3	Epidemic model and chemical reaction systems	Lecture 6
Feb 8	3.4.1	Phase plane analysis	Lecture 7
Feb 10		Phase plane analysis of the competition model
Feb 15	3.4.2	Stability analysis of continuous time models
Feb 17		Using XPP for simulation and analysis	Lecture 8
March 3-5		Enzymatic reactions, inhibition, approximate kinetics	Lecture 9
March 8	5.1, 5.2	Stochastic models, Markov chains	Lecture 10
March 10	5.1, 5.2	Gillespie's Stochastic Algorithm	Lecture 11
March 22-24		Chemical Master and Fokker-Planck Equations	Lecture 12
March 29-31		Numerical solutions for ODE systems using Matlab	MM.m, logistic.m AB_C.m AB_C_Langevin.m
April 7-12	6.1.1, 6.1.2	Agent based modeling, Cellular automata	Lecture 13
April 14	7.1, 7.2	Parameter estimation	Lecture 14

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