Course Materials for MATH35032 Mathematical Biology, 2018-19

Lecturer: Prof. Oliver Jensen

This course unit has been developed from the version taught in previous years by Dr Mark Muldoon. Please feel free to contact me by email if you have any questions about the course.


Intended Learning Outcomes

Once you've successfully completed this module you should be able to:

  • Interpret differential equation models for populations, relating the expressions appearing in the model to processes that affect the population.
  • Formulate and analyse ordinary differential equation (ODE) models for the population of a single species, finding equilibrium populations and determining how their stability depends on parameters.
  • Analyse delay-differential equation (DDE) models for the population of a single species and use linear stability analysis to determine which values of the parameters induce oscillatory instabilities.
  • Analyse ODE models for the populations of two interacting species, finding equilibria and using information about their linear stability to characterise the long-term behaviour of the system.
  • Define a conserved quantity for a system of ODEs and, where possible, use such quantities to determine the long-term behaviour of both two-species ODE models and single-species models population models that include diffusion.
  • Construct the ODEs associated with a system of chemical reactions subject to mass-action kinetics and analyse them to discover conserved quantities.
  • Construct the Markov process associated with a system of chemical reactions and, for small numbers of reactions, analyse it to determine the long-term behaviour of the system.
  • Analyse two key models, Wolpert's Frech flag model and Turing's reaction-diffusion model, relating the solutions of the associated PDEs to the processes of pattern-formation in developing organisms.

Lecture Notes and Articles

The first half of the course will cover classical topics in mathematical biology, following sections of Jim Murray's famous text, Mathematical Biology I: An Introduction. This book is available online from within the University's network. For off-campus access, you can install software that will allow you to use all the Library's services via the University's Virtual Private Network (VPN).

Lecture notes will appear here.

Opportunities for feedback

The main channel for formal, written feedback in this module is the coursework. It will be a problem set similar to the ones provided on this page, but devoted to a novel application that uses the ideas from the course. You'll prepare written solutions and I'll mark them over the Easter Break, providing both written comments and a mark. In addition, the weekly examples classes provide further opportunities for verbal feedback and, for students who bring written solutions to the exercises, on-the-spot marking and written feedback as well.

Problem Sets & Solutions

Problem sets will be released throughout the course and will appear here

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The coursework will be due at 3:00 PM on Monday, 29 April. The coursework contributes 20% to your final mark for the module and will be marked out of 20. Potential topics: generation of nerve impulses; firefly synchronization; temperature control of circadian clocks

Week 3 Questionnaires

Watch here for a brief summary of and response to the Week 3 questionnaires

Coursework & Exams

Coursework   Exams

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Background reading

A hyperlinked version of the lists below is available from Manchester University Library's Link2Lists system.

For key mathematical ideas and techniques:
  • 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
  • Darren J. Wilkinson, Stochastic Modelling for Systems Biology (Chapman & Hall/CRC, 2006). ISBN 1-58488-540-8

For biological background:

  • Bruce Alberts, Alexander Johnson, Julian Lewis, Martin Raff, Keith Roberts and Peter Walter (2002) Molecular Biology of the Cell. 4th edition, Garland Science. ISBN 0-8153-4072-9
  • Uri Alon (2008) An Introduction to Systems Biology: Design Principles of Biological Circuits (Chapman & Hall/CRC, 2007). ISBN 1-58488-642-0
  • Terry A. Brown (2007) Genomes 3. Garland Science. ISBN 0-8153-4138-5
    The previous edition, Genomes 2, is available online from the National Center for Biotechnology Information (NCBI) Bookshelf
  • Eric H. Davidson (2006) The Regulatory Genome. Academic Press. ISBN 0-12-088563-8
  • Evelyn Fox Keller (2002) Making Sense of Life, Harvard University Press. ISBN 0-674-01250-X
  • Edda Klipp, Wolfram Liebermeister, Christoph Wierling, Axel Kowald, Hans Lehrach, Ralf Herwig (2009) Systems Biology: A Textbook. Wiley-Blackwell. ISBN 978-3-527-31874-2
  • Bernhard Ø. Palsson (2006) Systems Biology: Properties of Reconstructed Networks. Cambridge University Press. ISBN 0-521-85903-4
  • Ron Milo, Rob Philips (2016) Cell Biology by the Numbers. Taylor & Francis. ISBN 978-0-8153-4537-4

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