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MA256 Introduction to Systems Biology

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

TA:

Term(s): Term 2

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]

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

Objectives:
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.

Books:
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

 

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Year 1 regs and modules
G100 G103 GL11 G1NC

yr2.jpg
Year 2 regs and modules
G100 G103 GL11 G1NC

yr3.jpg
Year 3 regs and modules
G100 G103

yr4.jpg
Year 4 regs and modules
G103

Archived Material
Past Exams
Core module averages