Undergraduate Teaching 2023-24

Engineering Tripos Part IIB, 4G1: Mathematical biology of the cell, 2023-24

Engineering Tripos Part IIB, 4G1: Mathematical biology of the cell, 2023-24

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Module Leader

Dr Thierry Savin


Dr T Savin, Dr T O'Leary

Timing and Structure

Michaelmas term. 16 lectures (including 2 examples classes). Assessment: Coursework 100%


The aims of the course are to:

  • introduce to sub cellular processes and the role of thermal fluctuations
  • shift from the classical biology approach to a more physical description
  • illustrate mathematical/computing approaches to study regulatory networks and biomolecular dynamics
  • provide background knowledge on stochastic processes


The course covers topics in stochastic processes and statistical mechanics with application to examples from biology. No background in biology is assumed.

Introduction (Savin)

  • Cells are a very well organized machinery
  • But molecular processes are subject to fluctuations, i.e. stochasticity
  • How is it possible?

Mathematical formalism (Savin)

  • Probabilities & Random Variables
  • Stochastic Processes
  • Master Equation, Fokker-Plank Equation

Regulation of gene expression (O'Leary)

  • Gene expression analysis
  • Stochastic gene expression
  • Stochastic simulations

Cell structural organization (Savin)

  • Biomolecules (DNA, cytoskeleton)
  • Statistical physics for biology
  • Polymer mechanics
  • Transport processes in cells



Coursework Format

Due date

& marks

Coursework activity #1: Analysis of noise in prokaryotic gene expression

Cells often express genes in low copy numbers, leading to substantial variability in protein. In this coursework you will build a simple model of gene expression, analyse it mathematically and simulate a stochastic version of the model.

Learning objective:

  • understand how to estimate fluctuation size in a stochastic system and limitations of analytic estimates;
  • be able to implement stochastic simulations;
  • interpret biological data and predictions that simulations yield.

Individual report

Anonymously marked

Posted Fri week 5
Due Fri week 7


Coursework activity #2: Modelling DNA’s mechanical response

The mechanical properties of DNA and other biological filaments are important factors for cell functions. In this coursework you will simulate a DNA molecule using a bead-spring chain model undergoing thermal fluctuations, and compare your results with the theory and existing experimental data.

Learning objective:

  • understand models and Brownian dynamics of biological polymer;
  • code and carry out the simulations; statistically analyse the data;
  • interpret the simulations output in comparison with theory and experimental data.

Individual report

Anonymously marked

 Posted Fri week 8
Due Fri two weeks later




Please see the Booklist for Group G Courses for references for this module.

Examination Guidelines

Please refer to Form & conduct of the examinations.

Last modified: 30/05/2023 15:32