EPSRC Reference: 
EP/T031573/1 
Title: 
Using catastrophes, dynamics & data analysis to uncover how differentiating cells make decisions 
Principal Investigator: 
Rand, Professor DA 
Other Investigators: 

Researcher CoInvestigators: 

Project Partners: 

Department: 
Mathematics 
Organisation: 
University of Warwick 
Scheme: 
Standard Research 
Starts: 
01 July 2021 
Ends: 
30 June 2024 
Value (£): 
446,283

EPSRC Research Topic Classifications: 
Nonlinear Systems Mathematics 
Statistics & Appl. Probability 

EPSRC Industrial Sector Classifications: 
No relevance to Underpinning Sectors 


Related Grants: 

Panel History: 

Summary on Grant Application Form 
A landscape model consists of a parameterised family of potential functions together with a Riemannian metric. The dynamical system associated with this is given by the corresponding gradient vectorfield. Any MorseSmale dynamical system with only rest point attractors and any system that admits a filtration admits such a representation except in a small neighbourhood of attractors and repellers. Such landscape models are of great interest in Developmental Biology because they correspond to Waddington's famous epigenetic landscapes but can also be rigorously associated with network models of the relevant genetic systems.
When used to model the dynamics of a cell the parameters of the landscape correspond to signals being received by the cell. These can be due to morphogens in the cell's environment or signals coming from other cells. When these signal are altered, the landscape changes and this can cause bifurcations which destroy the attractor governing a cell's state and this can lead to a change in the cell's state. This is cellular differentiation, the way by which cell can change their cell type and specification. For example, stem cells differentiate in this way eventually to provide cells for all the tissue types in the body.
The formation of the vertebrate trunk provides an important example of how cell fate decisions in developing tissues are made by signal controlled gene regulatory networks. Our biological collaborators have been studying part of this, namely the time course of differentiation of mouse embryonic stem cells to anterior neural or neuralmesodermal progenitors using such multidimensional single cell data. These experiments and the associated mathematical analysis has suggested that underlying this system is a highly nontrivial landscape of a complexity significantly greater than any published. This will be a key exploratory system that we will use to develop our ideas and we will work closely with the Briscoe and Warmflash labs to do this. However, it is important to stress that the purpose of this proposal is to focus strongly on developing mathematical ideas and tools and not just to be embedded in a particular biological project. On the other hand, access to stateofthe art data is very important. It ensures biological relevance and work with real data, rather than simulated data, raises real mathematical challenges.
More and more powerful biological tools are becoming available to study such processes but the increasing amount and complexity of the data produced and the fact that the processes are carried out by complex systems means that new mathematical tools are need to help understand what is going on. In particular, biologists can now measure the numbers of multiple molecules in each of tens of thousands of cells in a single experiment.
The key aim of this project is to increase our understanding of landscape models and combine this with stateoftheart statistical techniques to provide new tools to analyse such data and to use it to probe the mechanisms of cellular differentiation and cellular decisionmaking in some important biological systems.
The project involves deep collaboration with biological labs both in terms of data and biological ideas. It will be an excellent example of data science since it involves informatics (bioinformatics), statistics, mathematics (analysis, geometry & probability), hp computing and science (biology). It provides a new method of date dimension reduction a key theme in data science.

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Organisation Website: 
http://www.warwick.ac.uk 