Mathematical and statistical methods for change point detection in precision fermentation

Overview

Precision fermentation uses microorganisms such as yeast to produce valuable biological products for food, biotechnology and synthetic biology. A major challenge is that microbial growth and production can change when cells switch between different metabolic regimes. These changes may occur because of nutrient depletion, stress responses, dilution conditions, or shifts in how cells allocate resources between growth and product formation.

This PhD project will develop new mathematical and statistical methods for detecting these metabolic change points from experimental data. The project will be motivated by dilution-resolved microbial growth experiments, with a focus on yeast systems relevant to biotechnology and precision fermentation. The main aim is to build mathematical models that can identify when a population changes its growth or metabolic behaviour, quantify uncertainty in those predictions, and provide insight into the biological mechanisms that drive these changes.

The project is designed for students with a strong background in:

• mathematics
• applied mathematics
• statistics
• physics
• engineering
• computational science.

Prior experience in biology is not essential.

The biological system provides the motivation and data, but the central focus of the project is mathematical modelling, statistical inference and scientific computation.

Research activities

Research questions

The project will address questions such as:

• How can change points in microbial growth data be detected reliably?
• Can mathematical models distinguish between gradual changes and sudden metabolic transitions?
• Which features of microbial growth curves are most informative about underlying metabolic changes?
• How can uncertainty in noisy biological data be propagated into model-based predictions?
• Can dynamical systems models provide useful mechanistic insight into precision fermentation processes?
• How should dilution-resolved experiments be designed to maximise information about metabolic regime switching?

Mathematical and statistical approaches

The project will combine mathematical modelling, statistical inference and scientific computing. The student will develop and analyse models based on ordinary differential equations, stochastic processes and statistical change-point methods. These models will be used to describe microbial growth, nutrient use and switching between different metabolic regimes.

A major component of the project will involve parameter estimation and inverse problems. The student will investigate which model parameters can be inferred from available data, which parameters are practically non-identifiable, and how uncertainty in parameter estimates affects predictions. This will naturally lead to questions in identifiability analysis, model comparison, uncertainty quantification and optimal experimental design.

Depending on the student's interests, the project could also involve Bayesian inference, likelihood-based methods, hierarchical statistical models, stochastic simulation, partial differential equation models, or machine-learning-assisted model discovery.

Student activities

The student will be involved in:

• developing mathematical models of microbial growth and metabolic switching
• analysing ordinary differential equation and stochastic models
• implementing numerical simulations in Julia, MATLAB or Python
• fitting models to experimental growth-curve data
• developing statistical methods for change-point detection
• comparing competing models of metabolic regime switching
• quantifying uncertainty in parameters, predictions and detected change points
• working with experimental collaborators to interpret model predictions
• preparing figures, reports and research manuscripts.

The project will involve a strong balance between mathematical formulation, computational implementation and interpretation of real biological data.

Outcomes

This project sits at the interface of applied mathematics, statistics, computation and biotechnology. It is motivated by real experimental data, but the main intellectual challenge is mathematical: how can we infer hidden changes in biological behaviour from noisy time-series observations?

For a mathematics student, the project offers a strong combination of modelling, analysis, computation and inference. It provides an opportunity to work on a modern interdisciplinary problem while keeping mathematics at the centre. The broader goal is to develop mathematical and statistical tools that help make biological systems more predictable, particularly in precision fermentation and biotechnology.

Expected outcomes

The project is expected to produce:

• new mathematical models for precision fermentation data
• new statistical methods for detecting metabolic change points
• computational tools for simulation, inference and prediction
• uncertainty-aware predictions of microbial growth and metabolic switching
• improved understanding of how dilution-resolved experiments can reveal metabolic transitions
• research publications in mathematical biology, applied mathematics, computational biology or biotechnology-focused journals.

The project may also contribute to larger collaborative research programs involving experimental yeast biology, biotechnology and predictive modelling.

Skills and experience

This project is suited to a student with a strong background in:

• mathematics
• applied mathematics
• statistics
• physics
• engineering
• computational science.

The student does not need prior experience in microbiology or fermentation, although an interest in biological applications is important.

Useful background includes one or more of the following:

• differential equations
• dynamical systems
• numerical methods
• probability and statistics
• optimisation
• mathematical biology
• scientific computing
• Bayesian inference
• data analysis.

The ideal student will enjoy building models, writing code, analysing data and thinking carefully about how mathematics can be used to understand complex biological systems.

Scholarships

You may be eligible to apply for a research scholarship.

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Keywords

• applied mathematics
• computational mathematics
• mathematical biology

Contact

Contact the supervisor for more information.