- Department: Mathematics
- Credit value: 20 credits
- Credit level: M
- Academic year of delivery: 2024-25
- See module specification for other years: 2023-24
In this module, students will learn how mathematics can be applied to study a variety of topics in soft matter in biological systems, such as viral capsid shells, liquid thin films, protein-ligand interactions, biological polymers, and membranes. Through the use of statistical mechanics, random walks, group graph and tiling theory and representation theory, the student will explore topics in biological soft matter ranging from protein buckling to the geometry and dynamics of protein shells of viruses.
Pre-requisite modules
Co-requisite modules
- None
Prohibited combinations
- None
Physics students can use Thermodynamics and Statistical Mechanics (PHY00013H) as a pre-requisite if necessary
Occurrence | Teaching period |
---|---|
A | Semester 1 2024-25 |
In this module, students will learn how mathematics can be applied to study a variety of topics in soft matter in biological systems, such as viral capsid shells, liquid thin films, protein-ligand interactions, biological polymers, and membranes. Through the use of statistical mechanics, random walks, group graph and tiling theory and representation theory, the student will explore topics in biological soft matter ranging from protein buckling to the geometry and dynamics of protein shells of viruses.
By the end of the module, students will be able to:
Apply the methods of Classical and Statistical Mechanics to describe a wide variety of biophysical systems
Explain viral geometry using groups, graphs, and tilings, including applications to vaccine design
Use the symmetry of an object to understand its biophysical properties, such as its dynamic behaviour
Use problem-solving skills and abilities developed in the module to treat problems using a set of different but complementary approaches
Apply mathematical skills and techniques in interdisciplinary contexts
The following topics will be covered:
Soft matter and biological materials as subjects of statistical mechanics (SM).
Mechanical equilibrium as energy minimisation problem. Protein buckling as a bifurcation.
Liquid films and membranes.
Fundamentals of Thermodynamics. Entropy. Free energy. Ideal gas.
Fundamentals of Statistical Mechanics.
Biological systems: optical trap, mechanosensitive ion channel, and ligand-receptor binding.
Polymers. Random walk and the entropic origin of elasticity.
Diffusion. Fluctuation-dissipation theorem.
Cayley’s theorem and symmetric group descriptions of viral geometry
Caspar-Klug tiling theory for viral shells, generalisation of viral tilings using Archimedean lattices, and applications to vaccine design
Coxeter theory, root systems and their applications to multi-shell models in viruses and chemistry applications.
Application to the study of biophysical properties of symmetric objects
Task | % of module mark |
---|---|
Closed/in-person Exam (Centrally scheduled) | 100 |
None
Task | % of module mark |
---|---|
Closed/in-person Exam (Centrally scheduled) | 100 |
Current Department policy on feedback is available in the student handbook. Coursework and examinations will be marked and returned in accordance with this policy.
R. Phillips et al. The physical biology of the cell. Garland science (2013).
S. J. Blundell and K.M. Blundell. Concepts in thermal physics. OUP (2010).
M. Doi. Soft matter physics. OUP (2013).
D.-G. De Gennes et al. Capillarity and Wetting Phenomena. Springer (2012).
Coxeter, Regular polytopes, Dover (1973)
Humphries, Reflection Groups and Coxeter Groups, Cambridge University Press (1990)
Senechal, Quasicrystals and Geometry, Cambridge University Press (2009)