Detecting metabolic regime switching using dilution-resolved growth data: mathematical modelling, statistical inference and uncertainty quantification

Overview

Microbial populations rarely grow according to a single fixed physiological program. As nutrients are consumed, waste products accumulate and environmental stress changes, cells can transition between distinct metabolic regimes associated with growth, maintenance, fermentation, respiration and survival. These transitions are biologically important and industrially relevant, but they are often difficult to detect directly from standard growth curve summaries such as maximum growth rate, lag time, carrying capacity or area under the curve.

This project will develop new mathematical and statistical methods for detecting metabolic regime switching from dilution-resolved yeast growth data. The central idea is that growth curves collected across a structured dilution series may contain quantitative signatures of underlying metabolic transitions. The challenge is to determine whether these signatures can be detected reliably, whether they correspond to biologically meaningful changes in cellular state, and whether they can be used to predict future growth behaviour under new conditions.

The project will focus on yeast systems that are important in both fundamental biology and biotechnology. Saccharomyces cerevisiae provides a well-characterised model system for studying yeast physiology, growth and transcriptomic state changes. Pichia pastoris provides an industry-relevant system used in biotechnology and microbial production. By working across these complementary systems, the project will investigate whether mathematical and statistical methods for detecting regime switching are organism-specific or transferable across related yeasts.

Research activities

The student will undertake a combination of mathematical modelling, computational simulation, statistical inference and data analysis. Activities may include:

• developing ordinary differential equation models for microbial growth with possible switching between metabolic regimes
• implementing numerical simulation and parameter estimation workflows in Julia, MATLAB, Python or R
• fitting candidate models to dilution-resolved growth data
• using likelihood-based methods to assess parameter identifiability and predictive uncertainty
• comparing switching and non-switching models using statistical and biological criteria
• developing or applying change-point detection methods to growth curve data
• exploring how model predictions depend on dilution, strain, nutrient availability and environmental condition
• producing reproducible code, figures and documentation
• interpreting mathematical and statistical results in the context of yeast biology and biotechnology.

Depending on the level of the project, the work may emphasise mathematical model development, statistical methodology, computational inference, biological data analysis, or a combination of these areas.

The first aim is to develop mechanistic and semi-mechanistic differential equation models for yeast growth that allow for metabolic regime switching. These models may include piecewise-smooth growth laws, continuous switching functions, hybrid dynamical systems or coupled models of biomass, nutrient availability and metabolic state. A key question will be how much model complexity is justified by the available data.

The second aim is to develop inference methods for estimating model parameters and assessing practical identifiability. This will involve likelihood-based parameter estimation, profile likelihood analysis, model comparison and prediction-focused uncertainty quantification. The goal is not simply to obtain good curve fits, but to determine which biological conclusions are genuinely supported by the data.

The third aim is to develop statistical methods for detecting and quantifying regime changes across large collections of growth curves. Possible approaches include change-point detection, hierarchical modelling, uncertainty quantification, model selection and robust inference methods that account for experimental replication and variation between dilution conditions.

The fourth aim is to integrate mathematical modelling, statistical inference and biological interpretation into a reusable workflow. This workflow will be used to identify which features of dilution-resolved growth are most informative for detecting metabolic transitions, and to assess whether early growth behaviour can be used to predict later cellular outcomes.

Outcomes

The first aim is to develop mechanistic and semi-mechanistic differential equation models for yeast growth that allow for metabolic regime switching. These models may include piecewise-smooth growth laws, continuous switching functions, hybrid dynamical systems or coupled models of biomass, nutrient availability and metabolic state. A key question will be how much model complexity is justified by the available data.

The second aim is to develop inference methods for estimating model parameters and assessing practical identifiability. This will involve likelihood-based parameter estimation, profile likelihood analysis, model comparison and prediction-focused uncertainty quantification. The goal is not simply to obtain good curve fits, but to determine which biological conclusions are genuinely supported by the data.

The third aim is to develop statistical methods for detecting and quantifying regime changes across large collections of growth curves. Possible approaches include change-point detection, hierarchical modelling, uncertainty quantification, model selection and robust inference methods that account for experimental replication and variation between dilution conditions.

The fourth aim is to integrate mathematical modelling, statistical inference and biological interpretation into a reusable workflow. This workflow will be used to identify which features of dilution-resolved growth are most informative for detecting metabolic transitions, and to assess whether early growth behaviour can be used to predict later cellular outcomes.

Outcomes include new mathematical and statistical tools for analysing dilution-resolved microbial growth data. Specific outcomes may include:

• a family of differential equation models for yeast growth with metabolic regime switching
• computational workflows for model fitting, model comparison and prediction
• practical identifiability analysis for key model parameters
• statistical tools for detecting and quantifying regime changes in growth curves
• figures and analyses comparing different yeast strains, dilution conditions and model structures
• a written thesis or research report
• preliminary results suitable for inclusion in a research manuscript.

A broader outcome of the project will be a clearer understanding of what can and cannot be inferred from growth curves alone. This is important because growth assays are scalable and relatively inexpensive, but their interpretation requires care. The project will help determine whether simple growth measurements can provide early indicators of deeper physiological and molecular change.

Skills and experience

This project would suit a master degree student or PhD student with a strong background in:

• applied mathematics
• mathematical biology
• statistics
• data science
• computational biology
• physics
• engineering
• a related quantitative discipline.

Useful experience includes:

• differential equations
• numerical simulation
• statistical inference
• parameter estimation
• uncertainty quantification
• scientific computing.

Experience with Julia, MATLAB, Python or R would be beneficial.

Prior knowledge of yeast biology is not essential, although an interest in biological applications is important.

Scholarships

You may be eligible to apply for a research scholarship.

Explore our research scholarships

Keywords

• applied mathematics
• computational mathematics
• mathematical biology

Contact

Contact supervisor for more information