MATH35032: Mathematical Biology—Online Course Materials

The first 5-6 weeks of the term will be devoted to what one might describe as mathematical biology in the classical style and the lectures will follow sections of Jim Murray's famous text, Mathematical Biology I: An Introduction. This book is available online, though only from within the University's network (e.g. in the campus clusters or in the halls), but if you want to access it from off campus, you can install software that will allow you to use all the Library's servcies via the University's excellent Virtual Private Network (VPN).

Lecture Outlines, Notes and Articles

• Outlines for the lectures in Week 1
• Outlines for the lectures in Week 2
• Outlines for the lectures in Week 3

Weeks 1–5

As mentioned above, the lectures for Weeks 1–5 relate to Jim Murray's book Mathematical Biology I: An Introduction.

Week 6 (Thursday 7 & Friday 8 March)

The lectures for Week 6 are about the Principle of Competitive Exclusion. The scanned notes below include everything I doscussed in lecture, as well as some of the material that went into Problem 3.

• My scanned notes about competitive exclusion.
• A slide with two useful lemmas

Week 7 (Thursday 14 & Friday 15 March)

The lectures for Week 7 are mainly concerned with Metabolic Control Analysis (MCA), sometimes also called Metabolic Flux Analysis. The standard mathematical reference in the area is the paper by Christine Reder listed below, but the brief, recent summary by Hofmeyr is closer to the lectures. Chapters 6–16 of the book by Palsson go into much greater depth than either of the articles and include many applications that lie outside the scope of this course.

• My scanned notes about Metabolic Control Analysis.
• Jan-Hendrik S. Hofmeyr (2001), Metabolic control analysis in a nutshell. In T. M. Yi, M. Hucka, M. Morohashi and H. Kitano, eds. Proceedings of the 2nd International Conference on Systems Biology: 291–300.
• Christine Reder (1988) Metabolic control theory: A structural approach. Journal of Theoretical Biology, 135: 175–201.
• Bernhard  Ø. Palsson, Systems Biology: Properties of Reconstructed Networks (Cambridge University Press, 2006). ISBN 0-521-85903-4

Week 8 (Thursday 21 & Friday 22 March)

The lectures for Week 8 are mainly concerned with stochasticity in chemical reactions and the Gillespie algorithm, which was first described in the paper cited below. Our treatment will be more in the spirit of the recent pedagogical note by Des Nigham.

• My scanned notes about the Gillespie Algorithm.
• Notes for a computational project (offered i Scientific Computing) that includes a brief treatment of the same material.
• Daniel T. Gillespie (1977), Exact stochastic simulation of coupled chemical reactions, Journal of Physical Chemisty 81: 2340–2361.
• Des Higham (2008), Modeling and Simulating Chemical Reactions, SIAM Review 50: 347–368.

Week 9 (Thursday 18 & Friday 19 April)

The lectures for the latter part of Week 9 will be about Alan Turing's famous paper on morphogenesis.

• The Chemical Basis of Morphogenesis, Phil. Trans. Roy. Soc. Series B, Biological Sciences 237, 37–72.
• My scanned notes about the paper

The first link above works only from within the University's network, so if you want to read the paper elsewhere you'll need to download a PDF version while on campus and keep it on your P: drive or on a USB stick.

If you find yourself curious about the success—or lack thereof—of mathematical models in the study of development, I recommend a recent book,

Evelyn Fox Keller (2002), Making Sense of Life, Harvard University Press, ISBN: 0-674-01250-X,

from which I learned a lot about the role of models in biology. Keller is a theoretical physicist-turned-biologist who now studies the history and philosophy of science. In this book she is interested in why the styles of explanation preferred by physicists and mathematicians—of which Turing's model for morphogenesis is a prime example—have had such small impact on biology. To my taste her pithiest observation is

Indeed, the foremost meaning contemporary develomental biologists are likely to associate with the term model is neither a mechanical or classical model nor a set of equations: it is an organism.

Week 10 (Thursday 25 & Friday 26 April)

After concluding our discussion of Turing's paper I'll introduce Lewis Wolpert's “French Flag model” and discuss briefly the establishment of robust morphogen gradients through nonlinear morphogen degradation processes: a link to my notes appears below. Although we will not have time to study them closely, the two papers by Avigdor Eldar below come from Naama Barkai's group and describe a related, but somewhat more complex patterning system.

• My scanned notes about Wolpert's model
• A. Eldar, D. Rosin, B.-Z. Shilo and N. Barkai (2003), Self-Enhanced Ligand Degradation Underlies Robustness of Morphogen Gradients, Developmental Cell 5: 635–646.
• A. Eldar, B.-Z. Shilo and N. Barkai (2004), Elucidating mechanisms underlying robustness of morphogen gradients, Current Opinion in Genetics & Development 14: 435–439.

Week 11 (Thursday 2 & Friday 3 May)

The lectures in Week 11 refer to a circle of papers about regulatory motifs that came out of Uri Alon's group in the early noughties. The main ideas are are summarized in a set of slides, though if you are interested there is a lot more detail in in Alon's book.

• S. S. Shen-Orr, R. Milo, S. Mangan & U. Alon (2002), Network motifs in the transcriptional regulation network of Escherichia coli, Nature Genetics 31: 64–68.
• R. Milo, S. Shen-Orr, S. Itzkovitz, N. Kashtan, D. Chklovskii & U. Alon (2002), Network motifs: simple building blocks of complex networks, Science 298: 824–827.
• S. Mangan, A. Zaslaver and U. Alon (2003), The Coherent Feedforward Loop Serves as a Sign-sensitive Delay Element in Transcription Networks, Journal of Molecular Biology 334: 197–204.
• S. Mangan, S. Itzkovitz, A. Zaslaver and U. Alon (2006), The Incoherent Feed-forward Loop Accelerates the Response-time of the gal System of Escherichia coli, Journal of Molecular Biology 356: 1073–1081.

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Example Sheets

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Coursework and Exams

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Reading Matter

A hyperlinked version of the lists below is available from Manchester University Library's Link2Lists system.
I studied the following—more or less mathematically-minded—books while preparing this course.

• James D. Murray, Mathematical Biology I: An Introduction 3rd edition, (Springer, 2002). ISBN 0-387-95223-3
  
• James D. Murray, Mathematical Biology II: Spatial Models and Biomedical Applications 3rd edition, (Springer, 2002). ISBN 0-387-95228-4
  
• Lee A. Segel, Modeling dynamic phenomena in molecular and cellular biology (Cambridge University Press, 1984). ISBN 0-521-27477-X
• Uri Alon, An Introduction to Systems Biology: Design Principles of Biological Circuits (Chapman & Hall/CRC, 2007). ISBN 1-58488-642-0
• Darren J. Wilkinson, Stochastic Modelling for Systems Biology (Chapman & Hall/CRC, 2006). ISBN 1-58488-540-8

• Bernhard  Ø. Palsson, Systems Biology: Properties of Reconstructed Networks (Cambridge University Press, 2006). ISBN 0-521-85903-4
• Eric  H. Davidson, The Regulatory Genome (Academic Press, 2006). ISBN 0-12-088563-8
• Terry  A. Brown, Genomes 3 (Garland Science, 2007). ISBN 0-8153-4138-5
  The previous edition, Genomes 2, is available online from the National Center for Biotechnology Information (NCBI) Bookshelf, a service of the U.S.A's National Institutes of Health (NIH).
• Bruce Alberts, Alexander Johnson, Julian Lewis, Martin Raff, Keith Roberts and Peter Walter, Molecular Biology of the Cell 4th edition, (Garland Science, 2002). ISBN 0-8153-4072-9

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