12:090:280:01 Mathematics as Biology's New Microscope
Rutgers, Spring 07

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

NOTE: I sent an email to the class on 8 April (Sunday), to discuss plans for the rest of the semester. If you have no received that email, let me know ASAP.

Calendar

• 16 Jan
  Lecture: A quick introduction to molecular systems biology
• 23 Jan
  Student presentation (presented by Sofia Machado): Scale-free networks in cell biology, Albert R., J Cell Sci. 2005 4947-57.
  Lecture: Second part of intro to molecular systems bio.
• 30 Jan
  Student presentation: second part of S.Machado's presentation.
  Guest speaker: Prof. Nina Fefferman, Department of Public Health, School of Medicine, Tufts University. Social behavior in insects, and swarming in bee populations (see this link for details).
• 6 Feb
  Student presentation (presented by Son Nguyen): Generation of oscillations by the p53-Mdm2 feedback loop: A theoretical and experimental study, Ruth Lev Bar-Or, Ruth Maya, Lee A. Segel, Uri Alon, Arnold J. Levine, and Moshe Oren, Proc. Natl. Acad. Sci. USA, 97, 11250-11255, 2000.
• 13 Feb
  Student presentation (presented by Ankit Shah): Essential nonlinearities in hearing, Eguiluz, V. M., Ospeck, M., Choe, Y., Hudspeth, A. J. & Magnasco, M. O. Physical Review Letters 84, 5232-5235, 2000.
  Guest speaker: Todd Riley, Rutgers BioMaPS and Institute for Advanced Studies. An introduction to synthetic biology.
• 20 Feb
  Lecture: Chapter 1 of text, Iterations of one-dimensional maps; equilibria, cobwebs.
  Guest speaker: Dr. Robert Dinerstein, Sanofi-Aventis Pharmaceuticals, Bridgewater, NJ. Drug discovery and math modeling in the pharma industry, and a discussion of careers.
• 27 Feb
  Lecture: rest of Chapter 1 of book, computer examples, periodic orbits, chaos.
  Student presentation (presented by Koshi Itagaki): Using mathematics to understand HIV immune dynamics, Kirschner D. AMS Notices pp. 191-202, February 1996.
• 6 Mar
  Student presentation (presented by Samar Shah): Luminescence control in the marine bacterium Vibrio fischeri: an analysis of the dynamics of lux regulation, Journal of Molecular Biology 296, 1127-1137, 2000.
  Guest speaker: Professor Alan Weinstein (MD), Physiology and Biophysics, and Medicine, Cornell Medical School. Kidney modeling: proximal tubule and cell homeostasis, and medical applications to potassium transport.

  (Spring Break)

  
  

• 20 Mar
  Guest speaker: Dr. Jonathan Dushoff, Ecology, Princeton. Ecology and modeling of influenza epidemics.
• 27 Mar
  Lecture: continue of Chapter 2 of book.
  Guest speaker: Professor Troy Shinbrot, Biomedical Engineering, Rutgers. Cellular morphogenesis.
• 3 Apr
  Lecture: rest of Chapter 2 of book. Perhaps start chapter 3.
  Guest speaker: Professor Fred Roberts, DIMACS and Mathematics, Rutgers. Epidemiology (or bioinformatics; topic TBA)
• 10 Apr
  Student presentation (presented by David Hammer): chapter 7 of book: epidemiology models
  Student presentation (presented by Timothy Ni): The growth and form of tunnelling networks in ants, Jerome Buhla, Jacques Gautrais, Jean Louis Deneubourg, Pascale Kuntz, and Guy Theraulaz
  Lecture:start discussing Chapters 4/5 of book (base substution models for DNA, phylogenetic trees)
• 17 April: flood day
• 24 Apr and make-up day:
  Student presentation (presented by Hinal Patel): The coherent feedforward loop serves as a sign-sensitive delay element in transcription networks, Mangan S., Zaslaver A., Alon U
  Student presentation (presented by Charles Chi): Chapter 3 (systems of difference equations) of book.
  Student presentation (presented by Rich Scibetti): Chapter 6 (genetics) of book.
  Student presentation (presented by Vinayak Thakur): Chapter 2 (Boolean systems) of L. Glass' book.
  Guest speaker: Dr. Deborah J. Aks, Center for Cognitive Science (RuCCS), Rutgers. Tools to explore dynamics of visual and biological behaviors.

Book

Mathematical Models in Biology, by Elizabeth S. Allman and John A. Rhodes.
Here is a zip file with all Matlab programs used in the book.

Web resources

• Links to Math Biology sites

Some Reading Materials:

• Notes on mathematical biology. (These are written for Rutgers Math 336, which assumes knowledge of differential equations. They are placed here only in case you are interested and have the appropriate background. No knowledge of differential equations is expected for this course. We may use parts of these notes, for instance those dealing wth chemical kinetics and enzymes.)
• Notes on genetics, sequence alignments, profile HMM's. (These are written for Rutgers Math 338 by Dr. Ocone. We may use some of that material.)
• Some papers for possible class discussion and/or projects collected here.
• Boolean systems, Chapter 2 of Glass' book (low quality scan)

Unconfirmed Guest Speakers (tentative list):

• Professor Stanley Dunn, Biomedical Engineering, Rutgers.
  Date and Topic: TBA. (Probably: imaging in medicine.)
• Professor Philip Holmes, Mechanical and Aerospace Engineering and Applied Math, Princeton.
  Date and Topic: TBA. (Probably: insect locomotion.)

Course Announcement:

Indeed, the Life Sciences are in the midst of a major revolution in quantitative theoretical formulations, not unlike the transformation that physics underwent in the 17th century. The need for interdisciplinary training in quantitative biology has been widely recognized, as evidenced by frequent position papers appearing in journals such as Nature and Science, and the establishment of graduate programs in the field at major universities (including Rutgers).

Unfortunately, our educational system tends to separate students into "quants" (math, physics, engineering) and others, so the majority of students are never given the opportunity to grasp the beauty and power of mathematical ideas in biology. The goal of this seminar is to expose Rutgers students, regardless of major, to this fascinating field, early on in their careers.

There are a very large number of possible topics to be covered, and the syllabus will evolve based on student's interest and input. Some of the possible topics include the mathematics behind phylogenetic trees, sequence alignment methods, shotgun sequencing, dynamics of cell signaling networks including memories, switches, and oscillators, chemotaxis, pattern formation, neural transmission, Markov chains for population models, and epidemiology.

In order to make the course accessible to a wide audience, there will be no prerequisites except high-school "precalculus"; any necessary mathematical concepts will be introduced as needed. While computers may be used as an aid in understanding, such as running simulations of dynamical processes, the emphasis will be on intuitive and fundamental understanding. Dr. Eduardo Sontag is a Professor of Mathematics, and is also in the Graduate Faculties of the Departments of Computer Science and of Electrical and Computer Engineering, and the BioMaPS Institute for Quantitative Biology, and directs the BioMathematics Interdisciplinary Undergraduate Major. He has published widely and won several international awards, as well as the 2002 Rutgers' Trustees Award for Research and the 2005 Rutgers Teacher/Scholar Award. (More info on his webpage)