“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)

Handouts

Assignments

  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.

Books

Keshet2005
Mathematical Models in Biology
L. Edelstein-Keshet
deVries2006
A Course in Mathematical Biology
G. de Vries and T. Hillen and M. Lewis and J. Muller and B. Schonfisch

Papers

Armstrong1980
Competitive Exclusion
R. A. Armstrong and R. McGehee
The American Naturalist  115  15-170  (1980)
Ayyaswamy2004
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)
Beltrami:1995zr
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)
Bialek2005
Physical limits to biochemical signaling
W. Bialek and S. Setayeshgar
Proc. Natl. Acad. Sci.  102  10040-10045  (2005)
Bier2000
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)
Brandman2005
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)
Brookmeyer2005
Modelling the incubation period of anthrax
R. Brookmeyer and E. Johnson and S. Barry
Statistics in Medicine  24  531-542  (2005)
Cho2003
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)
Eaton2007
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)
Economou:2012fk
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)
Elowitz2000
A synthetic oscilatory network of transcriptional regulators
M. B. Elowitz and S. Leibler
Nature  403  335-338  (2000)
Elowitz2006
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)
Epstein:1996kx
Nonlinear Chemical Dynamics: Oscillations, Patterns, and Chaos
I. R. Epstein
Journal of Physical Chemistry  100  13132-13147  (1996)
Fisher1937
The wave of advance of advantageous genes
R. A. Fisher
Annals of Eugenics  7  355-369  (1937)
Gillespie1977
Exact Stochastic Simulation of Coupled Chemical Reactions
D. T. Gillespie
The Journal of Physical Chemistry  81  2340-2361  (1977)
Grierer1972
A Theory of Biological Pattern Formation
A. Grierer and H. Meinhardt
Kybernetic  12  30-39  (1972)
Goldbeter:1981ys
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)
Goldsztein2005
Transport of Nutrients in Bones
G. H. Goldsztein
SIAM Journal on Applied Mathematics  65  2128-2140  (2005)
Guo2000
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)
Hughes2002
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)
James2000
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)
Jesty:1993ly
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)
Kashtan2004
Topoligical generalizations of network motifs
N. Kashtan and S. Itzkovitz and R. Milo and U. Alon
Physical Review E  70    (2004)
Keener1987
Propagation and Its Failure in Coupled Systems of Discrete Excitable Cells
J. P. Keener
SIAM Journal on Applied Mathematics  47  556-572  (1987)
Khammash2004
Systems Biology: From Physiology to Gene Regulation
M. Khammash and H. El-Samad
IEEE Control Systems Magazine    62-76  (2004)
Kimura1962
On the probability of fixation of mutant genes in a population
M. Kimura
Genetics  47  713-719  (1962)
Levine:2001fk
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)

Lewis1977
Thresholds in development
J. Lewis and J. M. W. Slack and L. Wolpert
Journal of Theoretical Biology  65  579 - 590  (1977)
Lewis2003
Autoinhibition with Transcriptional Delay: A simple mechanism for the zebrafish somitogenesis oscillator
J. Lewis
Current Biology  13  1398-1408  (2003)
Longtin1990
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)
Ludwig1978
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)
Mogilner2005
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)
Nahmad:2009fk
Dynamic Interpretation of Hedgehog Signaling in the Drosophila Wing Disc
M. Nahmad and A. Stathopoulos
PLoS Biology  7  1-15  (2009)
Novak:2008fk
Design principles of biochemical oscillators
B. Novak and J. J. Tyson
Nature Reviews Molecular Cell Biology  9  981-991  (2008)
Othmer1999
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)
Paliwal2004
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)
Peskin:1993fk
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)
Pinto:1996fk
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)

Purcell1976
Life at Low Reynolds Number
E. M. Purcell
American Journal of Physics  45  3-11  (1977)
Reed1997
Algebraic Structure of Genetic Inheritance
M. L. Reed
Bulletin of the American Mathematical Society  34  107-130  (1997)
Reed2004
Why is Mathematical Biology So Hard?
M. C. Reed
Notices of the American Mathematical Society  51  338-342  (2004)
Santillan:2004fk
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)
Samoilov2005
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)
Samoilov2006
Deviant effects in molecular reaction pathways
M. S. Samoilov and A. P. Arkin
Nature Biotechnology  24  1235-1240  (2006)
Shouval2002
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)
Shouval2002b
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)
Solomonoff:1951uq
Connectivity of Random Sets
R. Solomonoff and A. Rapoport
Bulletin of Mathematical Biophysics  13  1-10  (1951)
Sprott2004
Dynamical Models of Love
J. C. Sprott
Nonlinear Dynamics, Psychology, and Life Sciences  8  303-313  (2004)
Sprott2005
Dynamical Models of Happiness
J. C. Sprott
Nonlinear Dynamics, Psychology, and Life Sciences  9  23-36  (2005)
Strogatz1990
Synchronization of Pulse-Coupled Biological Oscillators
R. E. Mirollo and S. H. Strogatz
SIAM Journal on Applied Mathematics  50  1645-1662  (1990)
Tabak2000
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)
Tyson1993
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)
Tyson2003
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)
VanVreeswijk1994
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)
Weiss:1997vn
The Hill equation revisited: uses and misuses
J. N. Weiss
The FASEB Journal  11  835-841  (1997)
Wyller:2007fk
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)
Yang:2005uq
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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