Cells make decisions—whether to become a heart cell, a cancer cell, or self-destruct—and a new mathematical framework aims to map the invisible landscapes that guide those choices. Current single-cell techniques can show *what* a cell becomes, but not *how* it decides. This project tackles that gap by turning the old metaphor of a "developmental landscape"—a sloping terrain where cells roll downhill into their fates—into a rigorous mathematical tool. The researchers have already applied it to several developing organisms. Their method reveals the underlying dynamics: how signals reshape the landscape and alter a cell's trajectory, rather than just mapping the final destination. If successful, this work will give biologists a powerful new lens for interpreting the torrent of data from single-cell experiments. That could sharpen understanding of stem cell reprogramming—why some cells resist becoming a desired type—and of cancer, where cells make pathological decisions to proliferate or metastasise. The project is fundamental science: it builds the mathematical foundations and machine-learning tools needed to fit these landscapes to real data, including systems with oscillations. Past work on similar dynamical systems has underpinned breakthroughs in neuroscience and ecology; this one could do the same for cell biology.
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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.
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