MRes Projects

During the CoMPLEX MRes year, I have done three six-week case presentations and a summer project, each being supervised by two scientists: one from life sciences and one from mathematical/physical sciences. These projects have given me a taste of different fields of research and have familiarised me with the complexities of interdisciplinary studies. Below, you can read more about my projects:


Summer Project: A Mathematical Approach to Tissue Development

Supervisors: Prof Mark Miodownik, Dr Jeremy Green

Abstract: In the past few years, an increasing number of models for tissue development have been published in the literature. While many of these models studied the features of a tissue with a restricted size, only a few focused on the properties of the growing tissue.

Directional growth of the tissue plays an important role in the development of the embryo and its organs. The model tissue in this research is mouse palatal epithelium. Recent findings have revealed that non-proliferative mechanisms should account for its anteroposterior growth [Unpublished data from the Green lab].

This research is an attempt to identify the amount of contribution of different growth mechanisms in directional growth of the tissue. A 2D vertex model of the growing tissue will be developed for this purpose. This model will then be used to find explanations for the role of different growth mechanisms, arising from anisotropic tension, in tissue elongation.

[Download PDF]

[Download simulations of the tissue growth under isotropic and anisotropic tension.]

CP 3: Reverse Engineering of the Actin Cortex with Speckle Microscopy and Smart Capture

Supervisors: Dr Guillaume Charras, Dr Gabriel Brostow

Abstract: In 1939, W H Lewis was one of the pioneers to suggest the presence of a ”superficial plasmagel” at the membrane of the cell, which contributed to its locomotion (Bray and White, 1988). Although the light microscopy at that time was unable to identify this layer, it is now well known that this layer is the actin cortex, a meshwork of actin filaments, responsible for determining the shape and movement of the cell (Alberts et al, 2008).

Although many of the actin binding proteins and their functions have been determined, much still remains to be discovered. Images obtained from Fluorescent Speckle Microscopy (FSM) can provide a lot of information about the assembly of the cell cortex, as well as the actin dynamics. However, it is not possible to extract these information from FSM images without an accurate tracking algorithm.

In the following essay, a new tracking algorithm will be developed and used to track actin speckles.

[Download PDF]
[Download sample videos of tracking actin speckles using the particle filter]

The main part of the speckle tracking code is adapted from the particle filter code developed by Dr Gabriel Brostow and Cristina Garcia-Cifuentes. You can find their code here.

CP 2: Integration of Multimodal Spectroscopy Data through Modelling

Supervisors: Dr Ilias Tachtsidis, Dr Nicola Robertson

Abstract: Hypoxia-Ischaemia, a condition characterised by inadequate blood flow and oxygen concentration, is one of the major causes of brain injury in newborn infants (Vannucci, 1990). One approach to study the encephalopathy following the hypoxia-ischaemia is mathematical modelling.

The BrainPiglet model is a simplified model of circulation and metabolism in the brain (Moroz et al, 2012). Although being successful in studying anoxic piglets, the model has failed to make accurate predictions of the changes in brain metabolism during hypoxia-ischaemia. It has been proposed that inclusion of pH in the model would help improve these predictions (Moroz et al, 2012). In the following essay, a novel method will be proposed to calculate the pH from 31P MRS measurements. The BrainPiglet model will then be modified to accept the calculated pH as input. Finally, comparisons will be made among the results obtained from the experiments, the modified and the original model.

[Download PDF]

CP 1: Evolution of Cell Division

Supervisors: Prof Buzz Baum, Prof Mark Miodownik

Abstract: It is widely accepted that in order for a cell to maintain its average size through several divisions, a coordination between the cell growth and cell division should exist. However, the details of this coordination is not well understood. In the recent years, several attempts have been made to propose a generic model that explains the details of the process of cell growth and its coordination with cell division. Most of these models were developed using nonlinear dynamics and mathematical modelling.

Cellular automata have been used to study the growth of a population of cells. However, they have not been used in studying the growth of an individual cell. In the following essay, I will introduce the previous mathematical and computational approaches to the problem. I will also propose a model, which combines cellular automata with genetic algorithm in order to study the growth of an individual cell.

[Download PDF]