Dynamical landscapes of cell fate decisions

Understanding how cells respond to signals and make decisions to switch state or choose a cell fate is a central concern of biological and medical research and key to being able to exploit the immense potential of, for example, stem cells and new cancer therapies. Recent developments in single-cell transcriptomics, proteomics and imaging have opened up exciting opportunities to probe these decision-making mechanisms in much deeper ways but there is a great unmet need for powerful analytical approaches and tools to understand this data. We are proposing a new approach to cellular decisions based on a formalization of the Waddington landscape metaphor into a rigorous mathematical tool for constructing landscapes and fitting them to cell fate data. This has been successfully applied to several developmental systems. The key difference this new approach makes to the understanding of cellular decision-making is that whereas current single-cell methods can identify the topology of the process, our method in addition uncovers the underlying dynamical structure and the way the signals the cell receives alters the decision. The underlying mathematics is concerned with understanding the structure of generic parameterised families of relatively simple dynamical systems which represent the gene regulatory networks that describe the dynamic and complex circuits formed by the signals and the downstream transcriptional responses controlling the location and timing of the cell fate decisions. Since these systems always flow downhill, by analogy with Waddington's landscape, they have become known as \emph{dynamical landscapes}. Our strategy is to firstly classify these landscapes on the basis of various complexity criteria and use this classification to determine which has the most plausible qualitative correspondence to the experimental data. Then we use stochastic simulation algorithms such as ABC particle filters to fit the normal form of the model to the data and choose between the alternative hypothesised models. In this grant we aim to develop both the mathematical foundations of dynamical landscapes and the data science component of our approach which uses machine learning and AI to link the models to the dynamic single cell data. In collaboration with our project partners we also will extend the range of the development systems analysed in this way and as part of this we will extend the theory to include systems involving oscillations.