“The lack of real contact between mathematics and biology is either a tragedy, a scandal, or a challenge, it is hard to decide which.”
Gian-Carlo Rota (1986)

“To understand [biological mechanisms], one must immerse oneself in the messy, complex details of the biology; that is, you must work directly with biologists.”
Michael Reed (2004)



  1. Syllabus
  2. Reading List
  3. Article Summary Template
  1. Week 01 homework: Choose initial paper.
  2. Week 01: T:Reed2004
  3. Week 01: F:Tyson2003
  4. Week 02: T:Goldbeter1981, Th:Ludwig1978, F:Paliwal2004
  5. Week 03: Short Homework
  6. Week 03: Th:Tabak2000, F:Elowitz2000
  7. Week 04: Midterm Project Proposal
  8. Week 04: Th:Brookmeyer2005, F:Novak2008
  9. Week 05: T:James2000, Th:Longtin1990, F:Peskin1993
  10. Week 06: Th:Shouval2002b, F:Beltrami1995
  11. Week 07: --Projects--
  12. Week 08: M:Santillan2004, T:Yang2005, Th:Levine2001, F:Pinto1996
  13. Week 09: --Projects--
  14. Week 010:

The following is a complete list of books and papers which may be discussed in this course. Those papers which are most appropriate for student presentations and projects are in the Reading List. Last updated: 2013.04.05.


Mathematical Models in Biology
L. Edelstein-Keshet
A Course in Mathematical Biology
G. de Vries and T. Hillen and M. Lewis and J. Muller and B. Schonfisch


Competitive Exclusion
R. A. Armstrong and R. McGehee
The American Naturalist  115  15-170  (1980)
Modeling of Phosphate Ion Transfer to the Surface of Osteoblasts under Normal Gravity and Simulated Microgravity Conditions
K. Mukundakrishnan and P. S. Ayyaswamy and M. Risbud and H. H. Hu and I. M. Shapiro
Annals New York Academy of Sciences  1027  85-98  (2004)
Mathematical analysis of activation thresholds in enzyme-catalyzed positive feedbacks: Application to the feedbacks of blood coagulation
E. Beltrami and J. Jesty
Proc. Natl. Acad. Sci.  92  8744-8748  (1995)
Physical limits to biochemical signaling
W. Bialek and S. Setayeshgar
Proc. Natl. Acad. Sci.  102  10040-10045  (2005)
How yeast cells synchronize their glycolytic oscillations: a perturbation analytic treatment
M. Bier and B. M. Bakker and H. V. Westerhoff
Biophysical Journal  78  1087-1093  (2000)
Interlinked Fast and Slow Positive Feedback Loops Drive Reliable Cell Decisions
O. Brandman and J. E. F. Jr. and R. Li and T. Meyer
Science  310  496-498  (2005)
Modelling the incubation period of anthrax
R. Brookmeyer and E. Johnson and S. Barry
Statistics in Medicine  24  531-542  (2005)
Experimantal Design in Systems Biology Based on Parameter Sensitivity Analysis Using a Monte Carlo Method: A Case Study for the {TNF}$\alpha$ -Mediated {NF}-$\kappa$ B Signal Transduction Pathway
K.-H. Cho and S.-Y. Shin and W. Kolch and O. Wolkenhauer
Simulation  79  726-739  (2003)
Evolution of Allosteric Models for Hemoglobin
W. A. Eaton and E. R. Henry and J. Hofrichter and S. Bettati and C. Viappiani and A. Mozzarelli
IUBMB Life  59  586-599  (2007)
Periodic stripe formation by a turing-mechanism operating at growth zones in the mammalian palate
A. D. Economou and A. Ohazama and T. Porntaveetus and P. T. Sharpe and S. Kondo and M. A. Basson and A. Gritli-Linde and M. T. Cobourne and J. B. A. Green
Nature Genertics  33  348-351  (2012)
A synthetic oscilatory network of transcriptional regulators
M. B. Elowitz and S. Leibler
Nature  403  335-338  (2000)
An excitable gene regulatory circuit induces transient cellular differentiation
G. M. Süel and J. Garcia-Ojalvo and L. M. Liberman and M. B. Elowitz
Nature  440  545-550  (2006)
Nonlinear Chemical Dynamics: Oscillations, Patterns, and Chaos
I. R. Epstein
Journal of Physical Chemistry  100  13132-13147  (1996)
The wave of advance of advantageous genes
R. A. Fisher
Annals of Eugenics  7  355-369  (1937)
Exact Stochastic Simulation of Coupled Chemical Reactions
D. T. Gillespie
The Journal of Physical Chemistry  81  2340-2361  (1977)
A Theory of Biological Pattern Formation
A. Grierer and H. Meinhardt
Kybernetic  12  30-39  (1972)
An amplified sensitivity arising from covalent modification in biological systems
A. Goldbeter and J. Daniel E. Koshland
Proc. Natl. Acad. Sci.  78  6840-6844  (1981)
Transport of Nutrients in Bones
G. H. Goldsztein
SIAM Journal on Applied Mathematics  65  2128-2140  (2005)
A hydrodynamic mechanosensory hypothesis for brush border microvilli
P. Guo and A. M. Weinstein and S. Weinbaum
American Journal of Physiology - Renal Physiology  279  F698-F712  (2000)
The Theoretical Population-Level Impact of a Prophylactic Human Papilloma Virus Vaccine
J. P. Hughes and G. P. Garnett and L. Koutsky
Epidemiology  13  631-639  (2002)
Luminescence Control in the Marine Bacterium Vibrio fischeri: An Analysis of the Dynamics of lux Regulation
S. James and P. Nilsson and G. James and S. Kjelleberg and T. Fagerström
Journal of Molecular Biology  296  1127-1137  (2000)
Mathematical Analysis of a Proteolytic Positive-Feedback Loop: Dependence of Lag Time and Enzyme Yields on the Initial Conditions and Kinetic Paramaters
J. Jesty and E. Beltrami and G. Willems
Biochemistry  32  6266-6274  (1993)
Topoligical generalizations of network motifs
N. Kashtan and S. Itzkovitz and R. Milo and U. Alon
Physical Review E  70    (2004)
Propagation and Its Failure in Coupled Systems of Discrete Excitable Cells
J. P. Keener
SIAM Journal on Applied Mathematics  47  556-572  (1987)
Systems Biology: From Physiology to Gene Regulation
M. Khammash and H. El-Samad
IEEE Control Systems Magazine    62-76  (2004)
On the probability of fixation of mutant genes in a population
M. Kimura
Genetics  47  713-719  (1962)
Mathematical Modeling of the Onset of Capillary Formation Inititating Angiogenesis
H. A. Levine and B. D. Sleeman and M. Nilsen-Hamilton
J. Math. Biol.  42  195-238  (2001)

Thresholds in development
J. Lewis and J. M. W. Slack and L. Wolpert
Journal of Theoretical Biology  65  579 - 590  (1977)
Autoinhibition with Transcriptional Delay: A simple mechanism for the zebrafish somitogenesis oscillator
J. Lewis
Current Biology  13  1398-1408  (2003)
Noise and critical behavior of the pupil light reflex at oscillation onset
A. Longtin and J. G. Milton and J. E. Bos and M. C. Mackey
Physical Review A  41  6992-7005  (1990)
Qualitative analysis of insect outbreak systems: The spruce budworm and forest
D. Ludwig and D. D. Jones and C. S. Holling
Journal of Animal Ecology  47  315-332  (1978)
Efficient Chromosome Capture Requires a Bias in the 'Search-and-Capture' Process during Mitotic-Spindle Assembly
R. Wollman and E. N. Cytrynbaum and J. T. Jones and T. Meyer and J. M. Scholey and A. Mogilner
Current Biology  15  828-832  (2005)
Dynamic Interpretation of Hedgehog Signaling in the Drosophila Wing Disc
M. Nahmad and A. Stathopoulos
PLoS Biology  7  1-15  (2009)
Design principles of biochemical oscillators
B. Novak and J. J. Tyson
Nature Reviews Molecular Cell Biology  9  981-991  (2008)
Stripe formation in jevenile Pomacanthus explained by a generalized Turing mechanism with chemotaxis
K. J. Painter and P. K. Maini and H. G. Othmer
Proc. Natl. Acad. Sci.  96  5549-5554  (1999)
Responding to Directional Cues: A Tale of Two Cells
S. Paliwal and L. Ma and J. Krishnan and A. Levchenko and P. A. Iglesias
IEEE Control Systems Magazine    77-89  (2004)
Cellular Motions and Thermal Fluctuations: The Brownian Ratchet
C. S. Peskin and G. M. Odell and G. F. Oster
Biophysical Journal  65  316-324  (1993)
A Quantitative Population Model of Whisker Barrels: Re-Examining the Wilson-Cowan Equations
D. J. Pinto and J. C. Brumberg and D. J. Simons and G. B. Ermentrout
Journal of Computational Neuroscience  3  247-264  (1996)

Life at Low Reynolds Number
E. M. Purcell
American Journal of Physics  45  3-11  (1977)
Algebraic Structure of Genetic Inheritance
M. L. Reed
Bulletin of the American Mathematical Society  34  107-130  (1997)
Why is Mathematical Biology So Hard?
M. C. Reed
Notices of the American Mathematical Society  51  338-342  (2004)
Why the Lysogenic State of Phage lambda Is So Stable: A Mathematical Modeling Approach
M. Santillan and M. C. Mackey
Biophysical Journal  86  75-84  (2004)
Stochasitc amplification and signaling in enzymatic futile cycles through noise-induced bistability with oscilations
M. S. Samoilov and S. Plyasunov and A. P. Arkin
Proc. Natl. Acad. Sci.  102  2310-2315  (2005)
Deviant effects in molecular reaction pathways
M. S. Samoilov and A. P. Arkin
Nature Biotechnology  24  1235-1240  (2006)
A unified model of {NMDA} receptor-dependent bidirectional synaptic plasticity
H. Z. Shouval and M. F. Bear and L. N. Cooper
Proc. Natl. Acad. Sci.  99  10831-10836  (2002)
Converging evidence for a simplified biophysical model of synaptic plasticity
H. Z. Shouval and G. C. Castellani and B. S. Blaise and L. C. Yeung and L. N. Cooper
Biological Cybernetics  87  383-391  (2002)
Connectivity of Random Sets
R. Solomonoff and A. Rapoport
Bulletin of Mathematical Biophysics  13  1-10  (1951)
Dynamical Models of Love
J. C. Sprott
Nonlinear Dynamics, Psychology, and Life Sciences  8  303-313  (2004)
Dynamical Models of Happiness
J. C. Sprott
Nonlinear Dynamics, Psychology, and Life Sciences  9  23-36  (2005)
Synchronization of Pulse-Coupled Biological Oscillators
R. E. Mirollo and S. H. Strogatz
SIAM Journal on Applied Mathematics  50  1645-1662  (1990)
Modeling of Spontaneous Activity in Developing Spinal Cord Using Activity-Dependent Depression in an Excitatory Network
J. Tabak and W. Senn and M. J. O'Donovan and J. Rinzel
The Journal of Neuroscience  20  3041-3056  (2000)
Numerical analysis of a comprehensive model of M-phase control in Xenopus oocyte extracts and intact embryos
B. Novak and J. J. Tyson
Journal of Cell Science  106  1153-1168  (1993)
Sniffers, buzzers, toggles and blinkers: dynamics of regulatory and signaling pathways in the cell
J. J. Tyson and K. C. Chen and B. Novak
Current Opinion in Cell Biology  15  221-231  (2003)
When Inhibition not Excitation Synchronizes Neural Firing
C. van Vreeswijk and L. F. Abbott and G. B. Ermentrout
Journal of Computational Neuroscience  1  313-321  (1994)
The Hill equation revisited: uses and misuses
J. N. Weiss
The FASEB Journal  11  835-841  (1997)
Turing instability and pattern formation in a two-population neuronal network model
J. Wyller and P. Blomquist and G. T. Einevoll
Physica D  225  75-93  (2007)
An Enzyme Mechanism Language for the Mathematical Modeling of Metabolic Pathways
C.-R. Yang and B. E. Shapiro and E. D. Mjolsness and G. W. Hatfield
Bioinformatics  21  774-780  (2005)

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