640:336:01 Dynamical Models in Biology
Spring 2015, Registration code 0115266

IMPORTANT NOTICE: Math 336 is being offered this Spring as an exception. It will most likely return to an only-Fall option next semester. Please do not plan your studies assuming the course will be offered again in a Spring Semester!!!

Class meets: Tuesdays and Thursdays 1:40-3:00, at: ARC-205 (Busch Campus)

link to sakai website

Text: link to pdf with instructor's online lecture notes.

this google drive folder has links to:

Make 100% sure that you know this material: the "Review of ordinary differential equations" appendix of the instructor's notes.
Since this course assumes familiarity with differential equations (its prerequisites are Calc4 math 252 and Linear Algebra), this last set of readings includes review notes on differential equations which may help refresh your mind, as well as a set of problems. This is review material. If you have difficulty working out the problems, you should not take this course!

Optional but strongly recommended reading: An introduction to molecular systems biology

Instructor: Eduardo Sontag, email: sontag@math (add .rutgers.edu if mailing from outside Rutgers)

Office Hours: Tuesdays and Thursdays 12:30-1:30, 724 Hill Center - but you should let me know in advance, by email or talking to me after class, if you will be coming in - also any other mutually convenient times, by appointment, and (almost) "24/7" communication by email.

Email: Important notices will be sent to you by email, to the address which the registrar provides for you (typically in the "eden" machine). You should set "forwarding" from that address if you wish to receive your emails in some other service (yahoo, gmail, etc). To ensure email delivery to instructor past spam filters, it is a good idea to add the following keyword: ALLOW336 (no spaces) to the subject line of any email sent to the instructor.

Class attendance: You are expected to attend every class and actively participate in discussions. There will be no make-ups for quizzes or exams.

"Cheat sheets" for exams: You will be allowed two two-sided pages in which you can summarize anything you want. Material there has to be written by you. You cannot paste material from slides and lecture notes.

Grade computation: My intention is to have three hourlies (25% of grade each) and no "final exam", but the last hourly will be scheduled for 1/2 the period of the final (start at 9:30 instead of 8AM) and might contain some material from the first two exams (topics that were not satisfactorily answered in exams 1 and 2). The other 25% of the grade will come from graded homework, projects, and quizzes. (I may adjust these percentages during the semester.) In addition, grades will be adjusted up, in "borderline" cases, to reflect class attendance and participation in discussions.

Computer Use

You should be able to use a computer for obtaining phase planes and numerical solutions of ordinary differential equations.
If you have not used computers for this purpose before, it is a good time to learn. ;-)

We will be using MATLAB. Please see the notes on "misc announcements" in the Google Drive folder linked above.
For the first two chapters (difference equations), it is best to use the MATLAB programs from Allman and Rhodes' book

Here is a useful file: odesolution_example.m
Download it into a directory in the MATLAB path, and execute it by typing odesolution_example in MATLAB. Edit it as needed (the example is a Van der Pol oscillator).

An interactive plotter is here: odem.m (Copyright 2009, Gabriel Alcantara).
Download it into a directory in the MATLAB path, and execute it by typing odem in MATLAB. Edit it as needed (the example is a Van der Pol oscillator).
Another simple option is to use the following Java Applet, which should run on any Java-enabled browser: JOde

If you prefer, you can use any other software which includes ODE solvers, such as Mathematica or Maple.

Noteworthy quotes:

"Complex assemblies of interacting proteins carry out most of the interesting jobs in a cell, such as metabolism, DNA synthesis, movement and information processing. These physiological properties play out as a subtle molecular dance, choreographed by underlying regulatory networks. To understand this dance, a new breed of theoretical molecular biologists reproduces these networks in computers and in the mathematical language of dynamical systems." (From "Network dynamics and cell physiology", by Tyson, Chen, and Novak, Nature Reviews in Molecular Cell Biology, 2001.)

"The slippery gooiness of biology is a consequence of its incredible complexity, consisting as it does of complex systems based upon chemistry. And chemistry obeys the rules of physics, which exists because of, and is consequently best described by, mathematics." (From an old "Mathematics in Biology" page at Brandeis.)

The important thing in science is not so much to obtain new facts as to discover new ways of thinking about them. (By Sir William Bragg, Physics Nobel Prize for X-ray crystallography.)

... mathematics ... was repugnant to me ... from my not being able to see any meaning in the early steps in algebra... This impatience was very foolish ... I have deeply regretted that I did not proceed far enough at least to understand something of the great leading principles of mathematics, for men thus endowed seem to have an extra sense. (From Charles Darwin's Autobiography, 1876 - I think we can assume he meant "people" ;-)

biomath major at Rutgers
Mathematical Biology web sites

back to Eduardo Sontag's Web page