**Biological Dynamics, APC/EEB/MOL/PHY 514**

**Fall 2004**

Lectures: Tuesdays, Thursdays, 1:30-2:50pm, starting Sept. 9 (org. meeting)

Carl Icahn Laboratory, Room 200

Computer Labs: Thursdays, 3:00-4:20PM, starting Sept. 16

BWF Computer Cluster (Carl Icahn Lab, Room 131)

Course Webpage: www.math.princeton.edu/apc514

This course is an introduction to the methods used to describe and understand biological dynamics using mathematical models and computer simulation. There will be four main units:

· **Section 1: Control of Gene Expression**, Curtis Callan (Physics), Saeed Tavazoie (Mol. Bio.)

· **Section 2: Ecological and Epidemiological Dynamics**, Simon A Levin (EEB), Jonathan Dushoff (EEB), Joshua
Weitz (EEB)

· **Section 3: Signaling, Chemotaxis, Cell Cycle Models**, Will Ryu (Lewis Sigler Institute), Ned Wingreen
(Mol. Bio.), Chao Tang (NEC)

· **Section 4: Morphogenesis, Spatial Patterns in
Development**, Stas Y. Shvartsman Chem.
Eng.), Eric F. Wieschaus (Mol. Bio.), Trudi Schupbach (Mol. Bio.),

perhaps guest lecturers) and a computer laboratory/ homework problem component.

** **

**Questions?
**The following is the contact
information for the course TA and for the principal lecturers in the different
sections:

*Course
Teaching Assistant (TA):*

* *

Kolia Sadeghi

Office: 221 Fine Hall

Phone: 258-5785

Email: ksadeghi@math.princeton.edu

Office: 334 Jadwin Hall Office: 245 Carl Icahn Lab

Phone: 258-4321 Phone: 258-0331

Email: ccallan@princeton.edu Email: tavazoie@princeton.edu

** Section
2**:

* *

** **Jonathan G. Dushoff Simon
Levin

Office: 201 Eno Hall Office: 203 Eno Hall

Phone: 258-6882 Phone: 258-6880

Email: jdushoff@princeton.edu Email: slevin@eno.princeton.edu

Joshua Weitz

Office: 201 Eno Hall

Phone: 258-6882

Email: jsweitz@princeton.edu

*Section
3:**Signaling, Chemotaxis,
Cell Cycle Models*

Ned Wingreen Will Ryu

Office: 347 Lewis Thomas lab Office: 119 Carl Icahn Lab

Phone: 258-8476 Phone: 258-8129

Email: wingreen@princeton.edu Email: wsryu@Princeton.edu

*Section
4:**Morphogenesis, Spatial
Patterns in Development*

* *

** **Stas Shvartsman Eric
Wieschaus

** **Office: 248 Carl Icahn Lab Office:
435 Moffett

Phone: 258-4694 Phone: 258-5383

Email: stas@princeton.edu Email: ewieschaus@molbio.Princeton.EDU

* *

No background in the relevant biology is required. However, a solid preparation in mathematics, including differential equations, integral calculus, and linear algebra is essential, as is some experience in using mathematics to model the real world. Graduate students with undergraduate degrees in mathematics, physics, electrical engineering, mathematical biology, and biophysics will have such backgrounds, as should Princeton seniors with these majors. Problem sets, which will frequently involve computer simulation exercises, are an important component of the course. Instruction and help will be available in a computer laboratory. Previous experience with computers is not essential, but the student will need to learn useful aspects of MATLAB and other programs for scientific computation.

There is no single book which covers all of the topics in this course. The following

general books, which will be useful at various times, have been requested for placement on reserve in Fine Library. Some of these books may be on reserve for other classes (see possible cross-listings below).

- B. Alberts et al, Molecular biology of the cell, 3rd edition, Reserve APC/EEB/MOL 514
- J. Watson et al, Recombinant DNA, 2
^{nd}edition, Reserve APC/EEB/MOL 514 - R. M. Anderson and R. M. May, Infectious diseases of humans: dynamics and
- control, Reserve APC/EEB/MOL 514
- H. C. Berg, Random walks in biology, Reserve APC/EEB/MOL 514
- F. Brauer and C. Castillo-Chavez, Mathematical models in population biology and epidemiology, Reserve APC/EEB/MOL 514
- L. Edelstein-Keshet, Mathematical models in biology, Reserve APC/EEB/MOL 514
- Goldbeter, Biochemical oscillations and cellular rhythms, Reserve APC/EEB/MOL 514
- T. G. Hallam and S. A. Levin, eds Mathematical ecology: an introduction, Reserve APC/EEB/MOL 514
- D. C. Hanselman, B. Littlefield Mastering MATLAB 6: a comprehensive tutorial and reference, Reserve APC/EEB/MOL 514
- N. J. Higham and D. J. Higham, MATLAB guide, Reserve APC/EEB/MOL 514
- D. Johnston and S. M-S. Wu, Foundations of cellular neurophysiology, Reserve APC/EEB/MOL 514
- J. P. Keener and J. Sneyd, Mathematical physiology, Reserve APC/EEB/MOL 514
- R. H. Kessin, Dictyostelium: evolution, cell biology, and the development of multicellularity, Reserve APC/EEB/MOL 514
- Koch, Biophysics of computation: information processing in single neurons, Reserve APC/EEB/MOL 514
- S. A. Levin, T. G. Hallam, and L. J. Gross (ed.) Applied mathematical ecology, Reserve EEB321
- J. D. Murray, Mathematical biology, 2nd edition, Reserve APC/EEB/MOL 514
- M. Nowak and R. M. May, Virus dynamics: mathematical foundations of immunology and virology, Reserve APC/EEB/MOL 514
- R. Pratap, Getting started with MATLAB 5: a quick introduction for scientists and

engineers, Reserve APC/EEB/MOL 514

- M. Ptashne, A genetic switch, Reserve MOL505
- Purves et al, Neuroscience, Reserve APC/EEB/MOL 514
- S. H. Strogatz, Nonlinear dynamics and chaos: with applications in physics, biology, chemistry, and engineering, Reserve APC/EEB/MOL 514
- G. H.Weiss, Aspects and applications of the random walk, Reserve APC/EEB/MOL 514

The lectures will often draw upon material in specific research articles, many of which are listed in the schedule. In most cases, pdf files of the articles will be posted on the course website. Where appropriate, a paper copy will be distributed in class or made available to be photocopied, location TBA.

There will be one to two homework sets per unit. These may involve computer simulations, and the necessary background will be provided in the lectures and in the

computer labs taught by the Course TA. Assignments will be put on the course

webpage. The homework will be due at the time given on the assignments, typically at the start of class, and must be handed in on time. Solution sets will be posted on the course webpage shortly after the due date.

As
a culminating experience, each registered student should describe a research
proposal based on the material covered in the lectures for APC514 in a *two
page* (no more!) proposal due (in pdf
format, via email to ksadeghi@math.princeton.edu)
*by 5 PM on Tues., January 11, 2005*.
We must be strict on this “Dean’s Date” deadline. The proposal should
describe the present state of knowledge, where there is a lack of
understanding, and how that gap could be filled by particular experiments,
mathematical analysis, or simulations with a *two month* research effort. The point is for the students to
move from the problem sets to asking their own questions, and to ask not only
what is a great question, but what is a more modest solvable question. We also
want to continue the building of a community of people interested in biological
dynamics, and hope through this ``proposal'' mechanism to enhance the future
interactions of the group of us on a variety of topics. We’ll have informal
presentations of the project ideas (~5 mins. per student) about a week later which
will provide a chance for friendly feedback and discussion. We’ll hand out
more details as the time comes closer.

Students will have the option of taking the course on a letter grade or pass/fail basis. Note, however, that pass/fail does not correspond to a “free ride,” and students are expected to complete all homework assignments in order to pass. The course grade will be based on homework assignments and the written and oral presentation of the course mini-project.

A roster including email addresses will be compiled at the first few lectures so that students can be contacted with important announcements and homework tips. (If you have a suggestion which you feel should be circulated to fellow students, please contact the Course TA, who will do so at his discretion.)

Computer labs will meet Thursdays 3:00-4:20 PM (starting Sept. 16) in the BWF computer cluster (CIL 131). The computer labs will cover supplemental material to the lectures. Students are also encouraged to ask questions about the lectures and homework assignments during the computer labs.

In addition to the computer labs, the Course TA will be available to answer questions

at times to be arranged. Also, feel free to email the Course TA with questions. The lecturers will also be available for consultation by appointment.

Each registered student will get a computer account on the BWF Linux cluster (CIL 131). MATLAB, a computing environment that combines numeric computation, graphics and visualization, and a high-level programming language is installed on these computers. MATLAB will be useful for the homework assignments and the computer tutorials.

**Schedule for APC/EEB/MOL 514, Fall 2004**

The journal articles cited in the reading list will, in general, be available for download from the course website. Books will be on reserve in Fine Library as will be some of the articles. The Sept. 9 class meeting will be devoted to organizational matters.

Unit 1: Control of Gene Expression

Lecturers: Curtis Callan (Physics), Saeed Tavazoie (Mol. Bio.)

Sept.
14^{th}. Lecture 1 (Tavazoie): High-level introduction to molecular
biology, genome organization, information flow in the cell, regulation of
cellular behavior, molecular networks.

- Recombinant
DNA (2
^{nd}ed.), Watson et al, Scientific American Books (1992), Chaps. 1-3

Sept.
16^{th}. Lecture 2 (Tavazoie): Core mechanisms of transcriptional
regulation, making observations, high-throughput technologies for measuring
mRNA expression, microarray analysis, finding patterns in expression data

- Watson et al, Recombinant DNA, Chaps. 4,9;
- Brown
& Botstein, Nature Genetics
**21,**33-37 (1999) - Quackenbush,
**2**: 418 – 427 (2001) - Eisen
et al., PNAS
**95**, 14863-14868 (1998)

Sept.
21^{st}. Lecture 3 (Callan): The dynamics and statistical mechanics of
transcription factor binding to specific sites on DNA. The bioinformatics and
statistical mechanics of identifying transcription factor binding sites.

- Robison et al, J. Mol. Biol.
**284**, 241-254 (1998) - Stormo
and Fields, Trends in Biol. Sci.
**23**, 109-113 (1998) - Gerland,
Moroz & Hwa, PNAS
**99**, 12015-12020 (2002) - Slutsky & Mirny, arXiv:q-bio.BM/0402005

Sept.
23^{rd}. Lecture 4 (Callan ): The dynamics of transcription factor control
of gene expression. Modeling of classic examples (phage and lac) of simple
genetic switches. Addressing the issues of small numbers, fluctuations,
stability.

- Ptashne. A genetic switch, Chaps 1-3.
- Elowitz et al, Science
**297**, 1183-1186 (2002) - Bialek, Stability and noise in biochemical switches, arxiv.org/cond-mat/0005235
- Sneppen et al, Phys Rev
**E65**, 0519143-0519149 (2002)

Sept.
28^{th}. Lecture 5 (Tavazoie): Systematic approaches for mapping
transcriptional regulatory interactions, expression patterns and motifs, linear
modeling, Bayesian networks, combinatorial regulation

- Segal et al, Nature Genetics
**34**, 166-176 (2003) - Gardner
et al., Science
**301**, 102-105 (2003) - Beer
& Tavazoie, Cell
**117**, 185-198 (2004)

Sept.
30^{th}. Lecture 6 (Callan): TBD. Discussion of the problems of
modeling gene regulation networks? Discussion in greater depth of issues from
Lects. 3 and 4?

- Kellis
et al, Nature
**423**241 (2003) (yeast phylogenetic footprinting)

Unit 2: Ecological and Epidemiological Dynamics

Lecturers: Johnathan Dushoff (EEB), Simon Levin (EEB) and

Joshua Weitz (EEB)

Oct. 5^{th} , Lecture
2 (Weitz):. An introduction to the
theoretical foundations of scaling: dimensional analysis, self-similarity, the
Pi-theorem, methods to construct scaling hypotheses, and the scaling collapse
in practice. This will be followed by an overview of scaling in biology,
drawing from examples in terrestrial and marine systemswith emphasis on the
structure and function of organisms.

- Barenblatt and Monin (PNAS, 80: 3540-2, 1983), "Similarity principles for the biology of pelagic animals".
- The Ecological Implications of Body Size (R.H. Peters, Cambridge University Press, 1986) pp. 164-183.
- Scaling: Why is Animal Size so Important (K. Schmidt-Nielsen, Cambridge University Press, 1984) pp. 56-74.

Oct. 7^{th} , Lecture
3 (Weitz): Application of scaling to problems in ecology with emphasis on
recent developments in the study of the allometric scaling of metabolic rate.
Empirical and theoretical studies of the scaling of metabolic rate will be reviewed,
along with attempts to unify observations of the organization of ecological
communities (population density, size distributions, stoichiometric relations)
via fundamental principles of energy use.

- Macrophysiology: large-scale patterns in physiological traits and their ecological implications. Chown S.L.; Gaston K.J.; Robinson D. Functional Ecology, April 2004, vol. 18, iss. 2, pp. 159-167(9)
- West, G.B., Brown, J.H. and Enquist, B.J. A general model for the origin of allometric scaling laws in biology. Science 276: 122-6 (1997).
- Dodds, P.S., Rothman, D.H., and Weitz, J.S. Re-examination of the ``3/4-law'' of metabolism. J. Theor. Biol. 209: 9-27 (2001).

Oct. 12^{th} ,
Lecture 1 (Levin): Ecosystems and the biosphere as complex adaptive systems: a study of the interplay among processes operating at
diverse scales of space, time and organizational complexity. The key to such a
study is an understanding of the interrelationships between microscopic
processes and macroscopic patterns, and the evolutionary forces that shape
systems. In particular, for ecosystems and socioeconomic systems, much interest
is focused on broad scale features such as diversity and resiliency, while
evolution operates most powerfully at the level of individual agents. Understanding
the evolution and development of complex adaptive systems thus involves
understanding how cooperation, coalitions and networks of interaction emerge
from individual behaviors and feed back to influence those behaviors.

- S.A.Levin: Complex adaptive systems: Exploring the known, the unknown and the unknowable, Bull. Amer. Math. Soc. 40 (2003), 3-19
- Levin, S. A. and S. W. Pacala. 1997. Theories of simplification and scaling of spatially distributed processes. In D. Tilman and P. Kareiva (eds.), Spatial Ecology: The Role of Space in Population Dynamics and Interspecific Interactions, pp. 271-295. Princeton University Press, Princeton, NJ

Oct. 14^{th} ,
Lecture 4 (Levin): On the evolution of
culture and other diseases. We will introduce the dynamics of disease, and draw
analogies for the dynamics of social norms.

- Earn, DJD, Dushoff, J., Levin, SA, 2002. "Ecology and evolution of the flu." Trends in Ecology and Evolution 17, 334-340
- Durrett, R., S.A.Levin 2004 Can stable social groups be maintained by homophilous imitation alone? JEBO In press

Oct.
19^{th}, Lecture 5 (Dushoff): Introduction to the dynamics of
infectious diseases

- F. Brauer and C. Castillo-Chavez, Mathematical models in population biology and epidemiology, Springer, 2000, Reserve APC/EEB/MOL 514.
- L. Lloyd and R. M. May. Spatial heterogeneity in epidemic models. J. Theor. Biol. 179: 1-11 (1996).

Oct. 21^{st}, Lecture
6 (Dushoff): Pathogen evolution and dynamics

- Plotkin, Dushoff and Levin. Hemagglutinin sequence clusters and the antigenic evolution of influenza A virus. PNAS April 30 2002 vol.99(9) 6263-6268.
- J. B. Plotkin, J. Dushoff and H. B. Fraser. Detecting selection using a single genome sequence of M. tuberculosis and P. falciparum. Nature, 428:942-945, 2004.

Unit 3: Signaling, Chemotaxis,Cell Cycle Models

Lecturers: Will Ryu (Lewis Sigler Inst.), Ned Wingreen (Mol. Bio.),

Chao Tang (NEC)

Nov.
2^{nd} , Lecture 1 (Ryu): General overview of bacterial chemotaxis:
historical perspective, how bacteria swim, general chemotactic strategy,
genetics and biochemistry, information flow.

- Blair DF. How bacteria sense and swim. Annu Rev Microbiol. 1995;49:489-522.
- Berg HC. Chemotaxis in Bacteria. Annu Rev Biophys Bioeng.1975;4:119-36.
- Adler J. Chemotaxis in Bacteria. Annu Rev Biochem. 1975;44:341-356.
- Berg HC. and Brown DA. Chemotaxis in Escherichia coli analyzed by three-dimensional tracking. Nature. 1972;239:500-504.

Nov.
4^{th} , Lecture 2 (Ryu): Physics of chemotaxis: Life at low Reynolds
number, limits and benefits of diffusion, physics of chemoreception.

- Purcell EM. Life at low Reynolds number. Am. J. Phys. 1977;45:3-11.
- Berg HC. Random walks in biology. 1993. Princeton University Press.
- Berg HC, Purcell EM. Physics of chemoreception. Biophys. J. 1977; 20, 193-219.

Nov.
9^{th} , Lecture 3 (Ryu): Biophysical measurements and models of
chemotactic response (I): response to temporal gradients, impulse response,
adaptation, sensitivity.

- Spudich JL, Koshland DE, Quantitation of the sensory response in bacterial chemotaxis. Proc. Natl. Acad. Sci. USA. 1975;72:710-713.
- Block SM, Segall JE, Berg HC. Impulse responses in bacterial chemotaxis. Cell 1982;31:215-226.
- Segall JE, Block SM, Berg HC. Temporal comparisons in bacterial chemotaxis. 1986;83:8987-8991.

Nov. 11^{th} ,
Lecture 4 (Wingreen): Biophysical measurements and models of chemotactic
response (II): robustness, sensitivity revisited.

- Sourjik V, Berg HC. Receptor sensitivity in bacterial chemotaxis. Proc. Natl. Acad. Sci. 2002;99:123-127.
- Cluzel P, Surette M, Leibler S. An ultrasensitive bacterial motor revealed by monitoring signaling proteins in single cells. Science.
- Alon U, Surette MG, Barkai N, Leibler S. Robustness in bacterial chemotaxis. Nature. 1999;397:168-171.

Nov.
16^{th}, Lecture 5 (Wingreen): Modeling min-protein oscillations.

- K. Huang, Y. Meir, N. Wingreen, Dynamic structures in
*Escherichia coli*: Spontaneous formation of MinE rings and MinD polar zones, Proc Natl Acad Sci U S A. 2003 Oct 28;100(22):12724-8.

Nov.
18^{th}, Lecture 6 (Tang): Cell cycle of the budding yeast.

- Fangting Li, Tao Long, Ying Lu, Qi Ouyang, and Chao Tang, The yeast cell-cycle network is robustly designed, Proc Natl Acad Sci. 2004 101: 4781-4786.

Unit 4: Spatial Patterns in Development

Lecturers: Trudi Schupbach (Mol. Bio.), Eric Wieschaus (Mol. Bio.),

Stas Shvartsman (ChemE & Genomics)

`Nov. 23`^{rd} and 30th, Lectures 1-2 (Shvartsman): Cell-cell communication networks in development. Feedback in pattern formation. Examples from Drosophila development.

Dec.
2^{nd} Lecture 3 (Wieschaus) Overview of development and key questions
requiring quantitative models; development of the body plan in *Drososphila*.

Dec.
7^{th}, Lecture 4 (Schupbach): *Drosophila* oogenesis.

Dec.
9^{th}, Lecture 5 (Shvartsman): Transcriptional profiling of developing
systems.

References:

· Gurdon JB, Bourillot PY. Morphogen gradient interpretation. Nature. 2001, 413(6858):797-803.

· Freeman M. Feedback control of intercellular signaling in development. Nature. 2000, 408(6810):313-9.

· Pires-daSilva A, Sommer RJ. The evolution of signaling pathways in animal development. Nat Rev Genet. 2003;4(1):39-49.