Statistical approaches for the inference of drift and diffusion coefficients for a model describing directed cell migration

Rights statement
Awarding institution
  • University of Strathclyde
Date of award
  • 2022
Thesis identifier
  • T16217
Person Identifier (Local)
  • 201682418
Qualification Level
Qualification Name
Department, School or Faculty
  • The use of mathematical models has become a widespread and important aspect of cellular biology to describe cell migration and chemotaxis. Many of these models give results which qualitatively match experimental data well, but most are not calibrated to the data to quantitatively estimate the unknown parameters of interest. This thesis focuses on using statistical inference approaches to estimate the drift velocity and diffusion coeffcient of a simple drift-diffusion stochastic differential equation model describing directed cell movement. All approaches make use of the mean square displacement as a summary statistic of the trajectory data. When using least squares regression, the quality of the inference depends on the number of regression fitting points or the measurement time interval over which experiments are made, depending on the experimental protocol. Simple and effcient iterative algorithms are presented to estimate the optimal number of fitting points and measurement time interval, along with estimates of the drift and diffusion coeffcients. For inference using approximate Bayesian computation, the quality of the inference is again shown to depend crucially on the measurement time interval over which experiments are made. A number of different approximate Bayesian computation approaches are presented and compared, showing that the best approach changes depending on the value of the measurement time interval. Finally, a hybrid model describing cell migration and chemical diffusion is presented to investigate a process called self-generated gradient chemotaxis. Numerical simulation from the generative model using physiologically relevant parameter values produces data which agrees well with experimental data.
Advisor / supervisor
  • Husmeier, Dirk
  • Mackenzie, John
Resource Type