# MA256 Introduction to Systems Biology

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

**TA**:

**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]

**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**