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MA256 Introduction to Systems Biology

Lecturer: Annabelle Ballesta, Till Bretschneider, Nigel Burroughs and Sascha Ott,


Term(s): Term 3

Status for Mathematics students: List A

Commitment: 30 one hour lectures

Assessment: Two hour exam

Prerequisites: MA133 Differential Equations, MA250 PDE, ST111 Probability A, ST112 Probability B [Recommended: MA254 Theory of ODEs (taken in parallel or previously)]

Course content:

1. Clocks switches and signals - Dr. Annabella Ballesta
1.1 Modelling regulatory and signalling systems.
1.2 Relevant aspects of differential equations
1.3 Modelling the cell cycle

2. Oscillations in biological systems - Dr. Annabella Ballesta
2.1 Periodic orbits, limit cycles and index theory
2.2 Poincare-Bendixon Theorem and Dulac Negative Criterion
2.3 Nullcline method; Relaxation Oscillations
2.4 Hopf bifurcation
2.5 Jacobian patterns: activator-inhibitor models and substrate-depletion models
2.6 Time delays

3. Introduction to bioinformatics - Dr Sascha Ott
3.1 Position weight matrices
3.2 Modelling combinatorial binding of transcription factors
3.3 Using dynamic programming to compute a complex discrete probability distribution
3.4 Evaluating similarity of regulatory sequences
3.5 Sequence alignments
3.6 Needleman-Wunsch algorithm for optimal sequence alignments

4. Neuroscience - Professor Nigel Burroughs
4.1 Mathematics of basic neuronal electrophysiology
4.2 Response properties of one and two-variable neuron models
4.3 Calculation of the firing rate of integrate-and-fire neurons
[ neuroscience component site ]

5. Biological systems in space and time - Dr Till Bretschneider
5.1 Biological examples of reaction-diffusion systems
5.2 Mathematics of diffusion and principles of pattern formation
5.3 Numerical methods for solving parabolic PDEs

[Lecturenotes for Part 5, weeks 9 and 10]

Introduction to Mathematical Biology and Systems Biology. Modelling techniques (based on core module material).

To develop simple models of biological phenomena from basic principles.
To analyse simple models of biological phenomena using mathematics to deduce biologically significant results.
To reproduce models and fundamental results for a range of biological systems.
To have a basic understanding of the biology of the biological systems introduced.

H. van den Berg, Mathematical Models of Biological Systems, Oxford Biology, 2011
James D. Murray, Mathematical Biology: I. An Introduction. Springer 2007
Christopher Fall, Eric Marland, John Wagner, John Tyson, Computational Cell Biology, Springer 2002
James Keener, James Sneyd, Mathematical Physiology I: Cellular Physiology. Spinger (Interdisciplinary Applied Mathematics) 2008
M J Zvelebil: Understanding Bioinformatics, Garland Science, 2007
L. Edelstein Keshet, Mathematical Models in Biology, SIAM Classics in Applied Mathematics 46, 2005.

Additional Resources


Year 1 regs and modules
G100 G103 GL11 G1NC

Year 2 regs and modules
G100 G103 GL11 G1NC

Year 3 regs and modules
G100 G103

Year 4 regs and modules

Archived Material
Past Exams
Core module averages