Mathematical Methods in Biophysics - MAT00095M
- Department: Mathematics
- Credit value: 20 credits
- Credit level: M
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Academic year of delivery: 2024-25
- See module specification for other years: 2023-24
Module summary
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.
Related modules
Additional information
Physics students can use Thermodynamics and Statistical Mechanics (PHY00013H) as a pre-requisite if necessary
Module will run
Occurrence | Teaching period |
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A | Semester 1 2024-25 |
Module aims
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.
Module learning outcomes
By the end of the module, students will be able to:
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Apply the methods of Classical and Statistical Mechanics to describe a wide variety of biophysical systems
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Explain viral geometry using groups, graphs, and tilings, including applications to vaccine design
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Use the symmetry of an object to understand its biophysical properties, such as its dynamic behaviour
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Use problem-solving skills and abilities developed in the module to treat problems using a set of different but complementary approaches
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Apply mathematical skills and techniques in interdisciplinary contexts
Module content
The following topics will be covered:
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Soft matter and biological materials as subjects of statistical mechanics (SM).
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Mechanical equilibrium as energy minimisation problem. Protein buckling as a bifurcation.
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Liquid films and membranes.
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Fundamentals of Thermodynamics. Entropy. Free energy. Ideal gas.
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Fundamentals of Statistical Mechanics.
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Biological systems: optical trap, mechanosensitive ion channel, and ligand-receptor binding.
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Polymers. Random walk and the entropic origin of elasticity.
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Diffusion. Fluctuation-dissipation theorem.
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Cayley’s theorem and symmetric group descriptions of viral geometry
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Caspar-Klug tiling theory for viral shells, generalisation of viral tilings using Archimedean lattices, and applications to vaccine design
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Coxeter theory, root systems and their applications to multi-shell models in viruses and chemistry applications.
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Application to the study of biophysical properties of symmetric objects
Indicative assessment
Task | % of module mark |
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Closed/in-person Exam (Centrally scheduled) | 100 |
Special assessment rules
None
Indicative reassessment
Task | % of module mark |
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Closed/in-person Exam (Centrally scheduled) | 100 |
Module feedback
Current Department policy on feedback is available in the student handbook. Coursework and examinations will be marked and returned in accordance with this policy.
Indicative reading
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R. Phillips et al. The physical biology of the cell. Garland science (2013).
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S. J. Blundell and K.M. Blundell. Concepts in thermal physics. OUP (2010).
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M. Doi. Soft matter physics. OUP (2013).
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D.-G. De Gennes et al. Capillarity and Wetting Phenomena. Springer (2012).
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Coxeter, Regular polytopes, Dover (1973)
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Humphries, Reflection Groups and Coxeter Groups, Cambridge University Press (1990)
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Senechal, Quasicrystals and Geometry, Cambridge University Press (2009)