Computational systems biologists and pure mathematicians have discovered that topology – the mathematical study of shapes and spaces – can reveal fundamental principles about how all of life is organised at the molecular level.
Lead researcher Professor Michael Stumpf says it’s something that's never been done before at such scale, and establishes a new way of seeing the building blocks of biology that can predict function and dysfunction.
Michael Stumpf is Professor for Theoretical Systems Biology in the School of BioSciences and the School of Mathematics and Statistics at the University of Melbourne. He is an ARC Laureate Fellow and co-Founder and Chief Scientific Officer of the University-spin-off company Cell Bauhaus.
The research was published in the journal Nature Communicaitons and among its impacts will be our understanding of the mechanism and treatment of disease, by allowing identification of structural weaknesses across millions of proteins simultaneously.
“Think of it like this,” Professor Stumpf explains. “Imagine a library of more than 214 million different protein blueprints that exist in life on Earth. We’ve developed a new way to analyse their 3D shapes, at once.
“So instead of just looking at what proteins are made of (like reading the ingredients list), we can study their actual architecture – the holes, loops, and cavities in their 3D structures.”
Co-author on the study is Alessia David, Associate Professor in Bioinformatics and Data Analysis in the Department of Life Sciences at Imperial College London.
Professor David says the study is a "clear example of how the application of sophisticated mathematical analyses of 3D protein structures can open new frontiers in our understanding of life on our planet”.
“The results of this study will be of paramount importance in deciphering how DNA variability in humans and other species can lead to evolution, adaptation, biodiversity and, ultimately, disease," she says.
Key findings
Key findings from the research include:
- Proteins from complex organisms (such as humans) have more intricate, sophisticated 'architectural features' than those from simpler life forms
- Proteins from heat-loving bacteria have smaller, more compact void spaces than those from organisms living at normal temperatures, meaning basically, they're built tighter to withstand extreme heat
- The mathematical patterns can predict which parts of proteins are most likely to give rise to problems when mutated, helping identify disease-causing genetic variants.
Professor Stumpf says the findings from this research represent a significant leap forward in understanding.
“Firstly, this is a scale revolution”, he says. “Previous topology studies looked at dozens or hundreds of proteins. Our research analysed 214 million – essentially the entire known protein universe. It's like going from studying individual houses to analysing the architecture of every building on the planet.”
It also creates a new mathematical lens for investigating protein architecture.
"The research applies topological data analysis (TDA), a mathematical approach that focuses on holes, loops, and connectivity patterns rather than precise measurements. This reveals features invisible to traditional methods of structural analysis.
"And there are cross-Kingdom insights. For the first time, we can see clear mathematical patterns that distinguish simple versus complex organisms at the protein level, adaptations for extreme environments (like heat tolerance), and disease-associated mutations across all of biology.
"And lastly, we’ve established practical prediction power. Unlike purely descriptive studies, this creates a tool that can predict functionally important protein regions and potential disease mutations.”
And according to Professor David the new discovery has revolutionised our ability to model proteins and has provided us with millions of 3D protein structures for several organisms.
"We have harnessed this new knowledge to study the protein universe at a scale never done before and provided new insight into how changes in the 3D structure of proteins can be used to identify harmful genetic mutations in humans and other species," she says.
Professor Stumpf says the research fills a crucial gap, meaning while we could previously predict protein structures we lacked tools to understand what all these structures mean functionally across the full spectrum of life.
Research impact
The research has wide-ranging impact, especially in the fields of medicine, biotech and biology.
“By understanding the topological "rules" that govern protein function, we can better predict which genetic mutations cause disease, design more effective drugs, and engineer better proteins for industrial applications. It's like having a universal blueprint reader for the machinery of life,” Professor Stumpf says.
Medical applications:
- Drug development: Identifying binding sites and functional regions more accurately across all known proteins
- Genetic medicine: Better prediction of which genetic variants cause disease
- Personalised medicine: Understanding how mutations affect protein function in individuals.
Biotechnology applications:
- Protein engineering: Designing more stable proteins for industrial applications
- Synthetic biology: Creating new proteins with desired topological features
- Climate adaptation: Understanding how organisms adapt proteins for extreme environments.
Evolutionary biology applications:
- Deep understanding: Revealing how complexity evolved at the molecular level
- Comparative biology: Understanding what makes multicellular life structurally different from microbes.
Next steps
Next steps in the research will include investigation of integration with function (connecting topological features to specific protein functions), drug design applications (using topology to identify new therapeutic targets), evolutionary studies (tracing how topological complexity evolved over time), and clinical translation (developing diagnostic tools based on topological analysis).
“This isn’t just academic curiosity,” Professor Stumpf says, “it’s really a step change in our knowledge.”
“For the first time, we can mathematically quantify what makes complex life forms (like humans) structurally different from simple organisms (like bacteria) at the protein level.
“This provides concrete evidence that biological complexity manifests in measurable topological features - essentially, life's complexity is written in the geometry of its proteins.”
Other co-authors
Banner illustration: Getty Images
First published on 18 September 2025.
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