Books, URLs, and Software
for Teaching Mathematical Biology to Undergraduates
Lower Division Textbooks
Adler, F., Modeling the Dynamics of Life, 2nd Ed. (Brooks/Coles, 1998))
Allman, E. & Rhodes, J., Mathematical Models in Biology: An Introduction
(Cambridge U. Press, 2004)
Mahaffy, J. & Chavez-Ross, A., Calculus: a Modeling Approach for the Life
Sciences (Pearson, 2004)
Neuhauser, C., Calculus for Biology and Medicine (Prentice Hall, 2000)
Smith, D. & Moore, L., Calculus: Modeling and Applications (Houghton Mifflin,
1996)
Upper Division Textbooks
Berg, H.C., Random Walks in Biology (Princeton Univ. Press, 1993)
Blanchard, P., Devaney, R.L. & Hall, G.R., Differential Equations, 2 nd Ed. (Brooks
Cole, 2002)
Brauer, F. & Castillo-Chavez, C., Mathematical Models in Population Biology and
Epidemiolgy (Springer, 2001)
Britton, N., Essential Mathematical Biology (Springer, 2003)
Edelstein-Keshet, L., Mathematical Models in Biology (SIAM Classics in Applied
Math, Vol 46).
Hoppensteadt, F. & Peskin, C., Modeling and Simulation in Medicine and Life
Sciences, 2nd Ed. (Springer, 2001)
Kaplan, D. & Glass, L., Understanding Nonlinear Dynamics (Springer, 1995)
Maynard Smith, J., Mathematical Ideas in Biology (Cambridge U. Press, 1968)
Segel, L., Modeling Dynamic Phenomena in Molecular and Cellular Biology
(Cambridge U. Press, 1984)
Strogatz, S., Nonlinear Dynamics and Chaos (Perseus Books, 1994)
Strogatz, S., Sync: The Emerging Science of Spontaneous Order (Hyperion,
2003)
Taubes, C.H., Modeling Differential Equations in Biology (Prentice Hall, 2000)
Graduate-level Textbooks
Beuter, A., et al., Eds., Nonlinear Dynamics in Physiology and Medicine
(Springer Verlag, 2003)
Fall, C., Marland, E., Wagner, J. & Tyson, J., Eds., Computational Cell Biology
(Springer Verlag, 2004)
Goldbeter, A., Biochemical Oscillations and Cellular Rhythms (Cambridge U.
Press, 1997)
Heinrich, R. & Schuster, S., The Regulation of Cellular Systems (Chapman &
Hall, 1996)
Keener, J. & Sneyd, J., Mathematical Physiology (Springer, 1998)
Kuznetsov, A., Elements of Applied Bifurcation Theory (Springer)
Lauffenburger, D. & Linderman, J., Receptors: Models for Binding, Trafficking
and Signaling (Oxford Univ. Press, 1993)
Murray, J.D., Mathematical Biology, Vols I and II (Springer, 2004)
Segel, L.A., Mathematical Models in Molecular and Cellular Biology (Cambridge
Univ. Press, 1983)
URLs
www.math.ubc.ca/people/faculty/keshet/keshet.htm
Follow links to UBC Calculus Online. Look especially at “this year’s labs”.
www.nsf.gov/crssprgm/reu
Research Experiences for Undergraduates. Click on “Search for an REU Site”
and then on “Mathematical Sciences”.
www.bioquest.org
The BioQUEST Curriculum Consortium supports educators interested in the
collaborative development of biology curricula that encourage the use of
simulations, tools and databases in the life sciences.
http://www.smb.org/
The Society for Mathematical Biology. Check out the Books pages. Also,
Instructional Resources at http://www.smb.org/education/instructional.shtml
http://www.esmtb.org
The European Society for Mathematical and Theoretical Biology.
http://math.rice.edu/~dfield/dfpp.html
On-line versions of the Matlab tools: DFIELD and PPLANE.
Software
XPP-Aut
www.math.pitt.edu/~bard/xpp/xpp.html
Simulation and analysis of nonlinear dynamical systems. Includes bifurcation
analysis by AUTO. Also available in a Windows version (WinPP) without AUTO.
Accompanied by a great handbook “Simulating, Analyzing and Animating
Dynamical Systems: A Guide to XPPAUT for Researchers and Students,”
available at www.siam.org/books/index.htm.
Berkeley Madonna www.berkeleymadonna.com
Modeling and analysis of dynamic systems.
Gepasi
www.gepasi.org
A software package for modeling biochemical reaction systems.
Research Articles and Reviews
General
Jungck, J.R., “Ten equations that changed biology: mathematics in problemsolving biology curricula,” Bioscene 23:11-36 (1997)
Lazebnik, Y., “Can a biologist fix a radio? -- Or, what I learned while studying
apoptosis,” Cancer Cell. 2:179-82 (2002)
Tyson, J.J., “A precarious balance,” Curr Biol. 14:R262-3 (2004)
Bray, “Protein molecules as computational elements in living cells,” Nature 376:
307 (1995)
DNA Topology
Sumners, D.W., “Lifting the curtain: using topology to probe the hidden action of
enzymes,” Notices AMS (May, 1995)
Bauer, W.R., Crick, F.H.C. & White, J.H., “Supercoiled DNA,” Sci. Am. 243:100113 (July, 1980)
Protein Interaction Networks
Tyson, J.J., Chen, K.C. & Novak, B., “Sniffers, buzzers, toggles and blinkers:
dynamics of regulatory and signaling pathways in the cell,” Curr Opin Cell Biol.
15:221-31 (2003)
Tyson, J.J., Csikasz-Nagy, A., Novak, B., “The dynamics of cell cycle regulation,”
Bioessays 24:1095-109 (2002)
Tyson, J.J., Chen, K.C. & Novak, B., “Network dynamics and cell physiology,”
Nat Rev Mol Cell Biol. 2:908-16 (2001)
Tyson, J.J., “Biochemical Oscillations,” in Computational Cell Biology (Fall et al.,
Eds., Springer Verlag, 2004), Chap. 9
Genetic Regulatory Networks
Keller, A.D., “Model genetic circuits encoding autoregulatory transcription
factors,” J. Theor. Biol. 172:169–185 (1995)
Cherry, J.L. & Adler, F.R., “How to make a biological switch,” J. Theor. Biol.
203:117-133 (2000)
Savageau, M., “Design principles for elementary gene circuits: elements,
methods and examples,” Chaos 11:142-159 (2001)
Hasty, J, McMillen, D., Isaacs, F. & Collins, J., “Computational studies of gene
regulatory networks: in numero molecular biology,” Nat Rev Genet 2:268-279
(2001)
Gardner, T., Cantor, C. & Collins, J., “Construction of a genetic toggle switch in
Escherichia coli,” Nature 403:339-342 (2000)
Elowitz, M. & Leibler, S., “A synthetic oscillatory network of transcriptional
regulators,” Nature 403:335-338 (2000)
Glycolytic Oscillations
Higgins, J., “The theory of oscillatory chemical reactions,” Ind. Eng. Chem. 59:1862 (1967)
Selkov, E.E., “Self-oscillations in glycolysis. 1. A simple kinetic model,” Eur. J.
Biochem. 4:79-86 (1968)
Goldbeter, A., & Lefever, R., “Dissipative structure for an allosteric model.
Applications to glycolytic oscillations,” Biophys. J. 12:1302-1315 (1972)
Teusink, B., et al., “Can yeast glycolysis be understood in terms of in vitro
kinetics of the constituent enzymes? Testing biochemistry,” Eur. J. Biochem.
267:5313-5329 (2000)
Hynne, F., Dano, S. & Sorensen, P.G., “Full-scale model of glycolysis in
Saccharomyces cerevisiae,” Biophys. Chem. 94:121-163 (2001)
ATP Synthesis
Elston, T., Wang, H. & Oster, G., “Energy transduction in ATP synthesis,” Nature
391:510-513 (1998)
Wang, H. & Oster, G., “Energy transduction in F1 motor of ATP synthase,”
Nature 396:279-282 (1998)
Cyclic-AMP Oscillations
Goldbeter, A. & Segel, L.A., “Relay and oscillations of cAMP in Dictyostelium,”
PNAS 74:1543-1547
Martiel, J.P. & Goldbeter, A., “A model based on receptor desensitization for
cyclic AMP signaling in Dictyostelium cells,” Biophys. J. 52:807-828 (1987)
Tyson, J. & Murray, J., “Cyclic AMP waves during aggregation of Dictyostelium
amoebae,” Development 106:421-426 (1989)
Calcium Oscillations
Goldbeter, A., Dupont, G. & Berridge, M., “Minimal model for signal-induced Ca2+
oscillations and for their frequency encoding through protein phosphorylation,”
PNAS 87:1461-1465 (1990)
Keener & Sneyd, Chapter 5
Fall et al., Chapter 5
Circadian Rhythms
Goldbeter, A., “A model for circadian oscillations in the Drosophila period protein
(PER),” Proc R Soc Lond Ser B 261:319-324 (1995)
Leloup, J. & Goldbeter, A., “Modeling the molecular regulatory mechanism of
circadian rhythms in Drosophila,” Bioessays 22:84-93 (2000)
Tyson, J., Hong, C., Thron, D. & Novak, B., “A simple model of circadian rhythms
based on dimerization and proteolysis of PER and TIM,” Biophys. J 77:24112417 (19990
Cell Signaling
Hanahan, D. & Weinberg, R., “The hallmarks of cancer,” Cell 100:57-70 (2000)
Hoffman, A., Levchenko, A., Scott, M. & Baltimore, D., “The IkB-NF-kB signaling
module: temporal control and selective gene activation,” Science 298:1241-1245
(2002)
Lahav, G., et al., “Dynamics of the p53-Mdm2 feedback loop in individual cells,”
Nat. Genet. 36:147-150 (2004)
Tyson, J., “Monitoring p53’s pulse,” Nat. Genet. 36:113-114 (2004)
Ciliberto, A., Novak, B. & Tyson, J., “Steady states and oscillations in the
p53/Mdm2 network,” Cell Cycle 4:488-493 (2005)
Ferrell, J. & Machleder, E., “The biochemical basis for an all-or-none cell fate
switch in Xenopus oocytes,” Science 280: 895-895 (1998)
Xiong, W. & Ferrell, J., “A positive-feedback-based bistable ‘memory module’ that
governs a cell fate decision,” Nature 426:460-465 (2003)
Eissing, T., et al., “Bistability analysis of a caspase activation model for receptorinduced apoptosis,” J. Biol. Chem. 279:36892-36897 (2004)
Bacterial Chemotaxis
Bray, D., Bourret, R. & Simon, M., “Computer simulation of the phosphorylation
cascade controlling bacterial chemotaxis,” Mol Biol Cell 4:469-482 (1993)
Barkai, N. & Leibler, S., “Robustness in simple biochemical networks,” Nature
387:913-917 (1997)
Yi, T., Huang, Y., Simon, M. & Doyle, J., “Robust perfect adaptation in bacterial
chemotaxis through integral feedback control,” PNAS 97:4649-4653 (2000)
Cell Cycle
Tyson, J. & Novak, B., “Regulation of the eukaryotic cell cycle: molecular
antagonism, hysteresis, and irreversible transitions,” J Theor Biol 210:249-263
(2001)
Tyson, J. & Novak, B., “A model for restriction point control of the mammalian cell
cycle,” J Theor Biol 230:563-579 (2004)
Tyson, J. & Novak, B., “Cell cycle controls,” in Computational Cell Biology (Fall et
al., Eds., Springer Verlag, 2004), Chapter 10
Novak, B. & Tyson, J., “Numerical analysis of a comprehensive model of Mphase control in Xenopus oocyte extracts and intact embryos,” J Cell Sci
106:1153-1168 (1993)
Chen, K., et al., “Integrative analysis of cell cycle control in budding yeast,” Mol
Biol Cell 15:3841-3862 (2004)
Borisuk, M. & Tyson, J., “Bifurcation analysis of a model of mitotic control in frog
eggs,” J Theor Biol 195:69-85 (1998)
Sha, W., et al., “Hysteresis drives cell-cycle transitions in Xenopus laevis egg
extracts,” PNAS 100:975-980 (2003)
Pomerening, J., Sonntag, E. & Ferrell, J., “Building a cell cycle oscillator:
hysteresis and bistability in the activation of Cdc2,” Nat Cell Biol 5:346-351
(2003)
Cross, F., et al., “Testing a mathematical model of the yeast cell cycle,” Mol Biol
Cell 13:52-70 (2002)
Turing Patterns
Segel, L.A. & Jackson, J.L., “Dissipative structures,” J. Theor. Biol. 37:545-559
(1972)