642:613 Mathematical Foundations of Systems Biology
Rutgers, Fall 07, Course Index Number: 35072

(click icon for wiki)

Instructor:
Eduardo Sontag,
email:
sontag@math (add .rutgers.edu if
mailing from outside Rutgers)
Please add the following word: ALLOW1 (no spaces) to the subject line of any
email sent to me, so spam filters do not block it.

Class will meet Wednesdays 10-1, right before the BioMaPS seminar, in the
BioMaPS seminar room, Hill 260.
If you are not receiving emails from the instructor, please send him an email
to let him know. (Please check your
spam filters first.)

Class notes and other reading materials:

Schedule
-
05 Sep: Review of molecular biology. Setting up simple exponential growth and
logistic models. Recaling variables to reduce number of parameters.
-
12 Sep: Chemostat. Steady states. Stability. Other models.
-
19 Sep: More modeling examples: chemotherapy; Gompertz' law; compartmental
models. Geometric view: vector fields, nullclines, directions of flow.
Review of linear phase planes, trace-determinant plane. Stability in
chemostat: local and proof of global asymptotic equilibrium.
-
26 Sep: Chemical reaction networks. Enzyme kinetics. Michaelis-Menten.
-
03 Oct: Attending Internat. Conf. Systems Biology. Professor Anirvan
Sengupta lectured on stochastic chemical kinetics.
-
10 Oct: Finished MM. Started epidemiology.
-
17 Oct: Finished epi. Allosteric and competitive inhibition. Cooperative responses. Presentation by Tom Eck (agent-based models in cancer).
-
24 Oct: Hyperbolic and sigmoidal responses. Multi-stability. Morphogens and
cell differentiation as a multi-stable phenomenon. Intro to periodicity.
-
31 Oct: Limit cycles. Poincare'-Bendixson. Trapping regions. Example: van
der Pol.
-
07 Nov: Bendixson criterion. Introduction to bifurcations. Saddle-node.
Guest speaker: Dr. Muruhan Rathinam (U.Md.) lecture on stochastic chemical
dynamics and simulations.
-
14 Nov: Other real-eigenvalue bifurcations. Hopf bifurcations. Cubic
nullclines: relaxation oscillations, excitable systems. Behavior of neurons,
Hodgkin-Huxley model.
-
21 Nov: no class ("Friday classes")
-
28 Nov: Continue Hodgkin-Huxley model, and FitzHugh-Nagumo simplifications.
Student presentation:
- Mauro Lapelosa and Eliane Traldi (Tyson's "Sniffers, buzzers,...")
-
05 Dec:
student presentations:
- Brian Roche ("The growth and form of tunnelling networks in ants")
-
Nguyen Thanh Tung and Thang Nguyen
("Modeling and Simulation of Genetic Regulatory Systems: A Literature Review")
- Justin Bush ("Dynamics of a simple regulatory switch")
- Ricardo Collado ("Robustness and fragility of Boolean models for genetic
regulatory networks")
Start PDE's: fluxes and general formulation. Transport equation.
-
12 Dec: No class. Attending Conference on Decision and Control
-
19 Dec: (after end of official classes, make-up of 12 Dec class)
student presentations:
-
Alex Chan ("A mathematical model of rat distal convoluted tubule. I. Cotransporter function in early DCT")
-
Fensidi Tang ("Dynamic behavior in mathematical models of the tryptophan operon")
-
Julie Tsitron and Peter Stivers ("Essential nonlinearities in hearing" and
"Auditory sensitivity provided by self-tuned critical oscillations of hair
cells")
-
Ariella Sasson and Tom Eck (java applet for stochastic simulations)

Course Announcement:
Life, whether at the level of the genome, cells, organs, organisms, or
populations, can only be understood when seen as the result of interactions
among multiple components. Whether dealing with signal transduction pathways
in cells and their disruption in cancer, neuronal networks in brain function,
the spread of epidemics in populations, or ecosystem responses to climate
change, the typical "reductionist" approach to learning and doing biology is
not powerful enough to describe, analyze, and interpret such complex
behaviors. Quantitative (i.e, mathematical!) formalisms, concepts, tools, and
models are required.
Indeed, one could say that 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.
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 dynamics of cell signaling networks including
memories, switches, and oscillators, chemotaxis, pattern formation, neural
transmission, synthetic biology, reverse engineering of gene and protein
networks, Markov chains for population models, epidemiology, and the
mathematics behind phylogenetic trees, sequence alignment methods, and shotgun
DNA sequencing.
The course will consist of instructor's lectures, student discussion of research
papers, and perhaps have some guest speakers.

Level and Background:
As I expect that many or even the majority of students taking the course will
come from programs other than math (BioMaPS, various Engineering departments,
chemistry, genetics, physics, computer science, etc), I will not impose any
explicit course prerequisites. At a minimum, however, students should
have a working familiarity with linear algebra, differential equations, and
basic probability, at the level of an advanced undergraduate or beginning
graduate student.
