Unit information: Mathematical Modelling in Physiology and Medicine in 2016/17

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
Pre-requisites	Basic knowledge of non-linear systems, stability analysis and bifurcation theory e.g. EMAT33100 or equivalent
Co-requisites	None
School/department	School of Engineering Mathematics and Technology
Faculty	Faculty of Engineering

Description including Unit Aims

Description: This unit 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 biological networks and their functions.
6. an understanding of excitability and how this can describe neuron behaviour.

Teaching Information

Lectures and computer laboratory sessions.

Assessment Information

• Two assignments in the form of written report, each contributing 50% to the final mark.

• First Assignment assesses learning outcomes 1-3

• Second Assignment assesses learning outcomes 4-6

Reading and References

• Uri Alom Introduction to Systems Biology

• J. Keizer et al Computational Cell Biology

• J.Murray Mathematical Biology

• J.Keener and J.Sneed Mathematical Physiology