I am a PhD candidate based in London. I study stochastic processes and game theory to better understand intra-tumour heterogeneity and resistance evolution in cancers. More broadly, I like to use mathematics to understand nature. Before my PhD, I did my BSc and MSc in Physics at ETH Zurich.
Cancers are driven by genetic and non-genetic mechanisms. However, the majority of genetic mutations have no effect on the cancer cell fitness. Those neutral mutations are accumulated over time and lead to distinct patterns that can be observed in sequencing data. We predict mutational patterns using mathematical models and compare those to sequencing data to make inferences on the evolutionary dynamics of cancer.
Evolutionary game theory (EGT) provides a framework to study the interactions between multiple entities. As such, EGT is used to study interactions of cancer cells with other cancer cells, the tumor-microenvironment or treatment. The latter has led to development of Stackelberg evolutionary game (SEG) theory. In SEG theory, a rational leader (the clinician) optimizes an objective (quality of life of the patient) under consideration of the eco-evolutionary dynamics of the followers (the cancer cell population). Current efforts go into fitting the model to data and test the feasibility of evolutionary therapies, e.g. adaptive therapy.
Evolutionary theory in constant well-mixed populations was thoroughly analysed in the past decades. However, less is known about expanding or spatially structured populations. Recent studies show that both population growth and spatial structure have profound influence on evolution. We investigate the emergence and the spread of mutations in time and space using mathematical models with the ultimate goal of gaining new biological insights.
On the patterns of genetic intra-tumour heterogeneity before and after treatment
Alexander Stein, Benjamin Werner
bioRxiv, 2024
Link: https://www.biorxiv.org/content/10.1101/2024.10.10.617575v1
Selective sweep probabilites in spatially expanding populations
Alexander Stein, Ramanarayanan Kizhuttil, Maciej Bak, Robert Noble
bioRxiv, 2023
Link: https://doi.org/10.1101/2023.11.27.568915
Stackelberg evolutionary game theory: how to manage evolving systems
Alexander Stein, Monica Salvioli, Hasti Garjani, Johan Dubbeldam, Yannick Viossat, Joel Brown, Kateřina Staňková
Philosophical Transactions of the Royal Society B, 2023
Public Goods Games in Disease Evolution and Spread
Christo Morison, Małgorzata Fic, Thomas Marcou, Javad Mohamadichamgavi, Javier Redondo Antón, Golsa Sayyar, Alexander Stein, Frank Bastian, Hana Krakovská, Nandakishor Krishnan, Diogo L. Pires, Mohammadreza Satouri, Frederik J. Thomsen, Kausutua Tjikundi, Wajid Ali
Dynamic Games and Applications, 2025
Poster at the conference London Mathematical Biology Conference 09/2024, London (United Kingdom) of the project On the patterns of genetic heterogeneity in cancers before and after treatment.
Talk at the Conference for Mathematical Models in Ecology and Evolution 07/2024, Vienna (Austria) with the title On the properties of genetic intra-tumour heterogeneity before and after treatment
Talk at the seminar Modeling and Theory in Population Biology 05/2024, online with the title A mathematical analysis of the mutational landscape in cancer before and after treatment.
Poster at the conference Mutations in time and space 04/2024, Edinburgh (Scotland) of the project The ubiquity of clonal interference in cancer and other range expansions.
Talk at the seminar for the special issue of Royal Society Publishing Half a century of evolutionary games: a synthesis of theory, application and future directions 05/2023, Online presenting the paper Stackelberg evolutionary game theory: how to manage evolcving systems
Poster at the Conference Mathematical and Computational Methods in Cancer and Biology 03/2023, New York (USA) with the title Understanding the relationship between genetic intra-tumour heterogeneity and evolutionary therapies
Talk at the seminar for Integrated Mathematical Oncology 02/2023, Tampa (USA) with the title Exploring the relationship between genetic intra-tumour heterogeneity and evolutionary therapies
Talk at the Conference for Mathematical Models in Ecology and Evolution 07/2022, Reading (UK) with the title Intra-tumour heterogeneity during evolutionary therapies
October 2024 - present: Ella Jones, (Australian) summer project (joint supervision with Maria Kleshnina)
July-September 2023: Ramanarayanan Kizhuttil, summer project resulting in a co-authored publication (joint supervision with Rob Noble)
Spring semester 2021: Private tutoring in (i) Data analysis for Biologists (ii) Introduction to Quantum Mechanics (iii) Statistics for Political Science
Autumn semster 2020: Introduction to Quantum Mechanics, Department of Physics, ETH Zurich
Spring semester 2020: Modelling of pedestrian flows (Modellieren von Fuss und Veloverkehr), Department of Civil, Environmental and Geomatic Engineering, ETH Zurich
Norman Bailey, The elements of stochastic processes (great introduction to branching processes)
Rick Durrett, Branching processes in cancer (summary of theory and applications of birth-death processes to cancer)
Martin Nowak, Evolutionary dynamics (motivated me to study evolution using maths)
Nicolas Bacaër, A short history of mathematical population dynamics (fun read introducing famous equations and a bit of their history)
Michael Hochberg, Editor's Guide to Writing and Publishing Science (recommended for beginning PhDs to learn about science culture)