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Unit information: Mathematical Modelling in Physiology and Medicine in 2018/19

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Unit name Mathematical Modelling in Physiology and Medicine
Unit code EMATM0007
Credit points 10
Level of study M/7
Teaching block(s) Teaching Block 1 (weeks 1 - 12)
Unit director Dr. Marucci
Open unit status Not open

Basic knowledge of non-linear systems, stability analysis and bifurcation theory e.g. EMAT33100 or equivalent



School/department Department of Engineering Mathematics
Faculty Faculty of Engineering


Description: This unit is taught intensively in TB1 (as a FAT unit) and aims to introduce mathematicians and engineers to some of the latest thinking in cell biology, neuroscience, systems and synthetic biology. It also aims to introduce modern mathematical techniques based on differential equations for understanding the dynamics of biological systems via numerical continuation, using the software XPP-aut. It will be shown how to derive mathematical equations from the basic laws of mass action that describe biochemical reactions, and therefore how certain chemical motifs carry out certain dynamical functions. A range of topics including ion channels and synthetic gene regulatory networks will be introduced using a combination of simple and advanced techniques.

Aims: To give students an appreciation of how mathematical models can be useful to understand complex biological processes. To provide a point of entry into the modern research literature in cell biology, in systems and synthetic biology. To explore modern mathematical techniques based on differential equations for understanding the dynamics of biological systems.

Intended learning outcomes

By the end of this unit students will have:

  1. an understanding of cell biology in terms of DNA, RNA, enzymes and proteins and the complex interactions among them, including the dynamics of larger, but basic, functional components such as ion channels.
  2. an appreciation of different forms of solution to biochemical differential equations, and the ability to simulate them.
  3. the ability to derive differential equations from biochemical reactions using the law of mass action, and Michaelis-Menten kinetics.
  4. an appreciation for the range of approaches to modelling a biological system, their comparative features, and how to choose among them.
  5. a grasp of the concept of synthetic biological networks and their functions.
  6. an understanding of excitability and how this can describe neuron behaviour.
  7. knowledge of the software XPP-aut for numerical continuation.

Teaching details

Lectures and computer laboratory sessions.

Assessment Details

  • One homework in the form of written report, contributing 50% to the final mark, to assess the use of the continuation software (XPP-aut) on a biological network (i.e. assessing learning outcomes 2, 4-7).
  • Exam, contributing to 50% of the final mark, to assess the theory covered in the lectures (i.e. assessing learning outcomes 1-6).

Reading and References

  • Uri Alon Introduction to Systems Biology
  • J. Keizer et al Computational Cell Biology
  • J.Murray Mathematical Biology
  • J.Keener and J.Sneed Mathematical Physiology
  • Zoltan Szallasi,‎ Vipal Periwal,‎ J Stelling System Modeling in Cellular Biology