#mathematical model

Paths to Pathogens

At a crossroads, we may receive conflicting advice “keep your options open” or “go all in”. It appears cells weigh up similar decisions when faced with multiple paths to take. Navigating routes around hexagonal cells in this zebrafish tail fin, macrophages, a type of immune cell highlighted in orange, consider two approaches. Investigating many paths at once helps to explore the local environment but slows progress. Or do they go all in with, choosing a path? Less dawdling means migration is faster, but it might lead to a 'wrong' choice. Researchers developed a mathematical model to simulate these strategies, finding cells will make different choices depending on obstacles and chemical clues to the 'right' path. Adapting the model may predict the migration of cancer cells or macrophages in our own immune system, possibly finding, as we do, that most choices have pros and cons – and sometimes all roads lead to Rome.

Written by John Ankers

Video from work by Jiayi Liu and colleagues

Cell Communication & Migration Laboratory, Institute of Biochemistry & Molecular Cell Biology, University Medical Center Hamburg-Eppendorf, Hamburg, Germany; Department of Chemical & Biological Physics, Weizmann Institute of Science, Rehovot, Israel

Video contributed by the authors and originally published with a Creative Commons Attribution 4.0 International (CC BY 4.0)

Published in Science Advances, January 2026

A History of Mathematics | November

We have decided to share more interesting facts from the history of mathematics. We have been doing this for three months (August, September and October) and it is a great way to find out more about some great mathematicians, but also remind ourselves about some great mathematical concepts. We are continuing with the same idea in November. Thank you for all your support in this project. Hope you…

Community Property

A welcoming community accepts that some people are more sociable than others – it seems the same is true for bacteria. Here different species (with genetic tweaks to make them glow in different colours) are thriving together. Their ‘structured’ living environment – a tiny ecosystem full of nooks and crannies – gives them a choice of privacy and society, helping local communities (rounded shapes) to bloom. Using mathematical models, researchers predict designs that allow social bacteria to exchange chemical signals, while others enjoy isolation – the overall community grows in population and diversity. Along with the alarming conclusion that bubble-like crevices in kitchen sponges make ideal bacterial homes, researchers can use these insights to grow vibrant microscopic communities, potentially spotting ways to tackle harmful biofilms in public spaces like hospitals.

Written by John Ankers

Image by Andrea Weiss, Zach Holmes and Yuanchi Ha, Duke University

Research by Feilun Wu and colleagues, Department of Biomedical Engineering, Duke University, Durham, NC, USA

Image copyright held by the original authors

Research published in Nature Chemical Biology, February 2022

Predicted Move

Crawling through a new environment, a cancer cell reaches out. In this simulation an invadopodium (top) pokes out like a nose, leading the cell into the surrounding extracellular matrix. Driving the simulation, a complex mathematical model helps researchers ponder simple questions – how do invadopodia work? How can we stop them? They find moving parts in the cell’s cytoskeleton (coloured lines) balance internal and external forces: as the cell prods upwards, bursts of myosin (red) activity help to keep the nucleus in place while proteins at the tip of the invadopodium nibble away at chemicals in the matrix (black). Repeated cycles of these movements direct the cell’s persistent creep. While these dynamics mirror those of real cancer cells, the model also predicts ways in which drugs might snarl up this complex machinery, slowing or stopping metastasis.

Written by John Ankers

Video from work by Min-Cheol Kim and colleagues

Departments of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA

Video originally published with a Creative Commons Attribution 4.0 International (CC BY 4.0)

Published in Scientific Reports, January 2022