Mathematics in the Fight Against Bacterial Diseases

Cover Photo: The mathematical model also enables classification of the spectrum of known defects and mutants of the E. coli bacterium. (Illustration: Pixabay)

Researchers from Matfyz, in collaboration with scientists from the Université de Lausanne and Harvard University, describe a mechanism of cell division in gram-negative bacteria. Several species of these bacteria exist and some are responsible for difficult-to-treat diseases such as pneumonia, meningitis, sepsis, or plague. The new mathematical model, published in the prestigious journal PNAS, gives unique insight into their division process and may thereby facilitate the development of antibiotics in the future.

A key target of anti-microbial therapy is synthesis and remodelling of the bacterial wall, that consists of a cross-linked polymer, also known as peptidoglycan or murein.

When bacterial cells multiply, they do so by division. During the division process, the peptidoglycan wall undergoes a complicated transformation of firstly constricting and secondly separating the origal bacterium into two viable bacteria. One crucial step is the growth of a septum which functions as a separating wall during the division process.

An animation showing the division of the so-called wild-type E. coli bacterium

In a previous study, some of the authors had collected data on the local structure of the bacterial division site of the wild type E. Coli bacterium and various mutants. These mutants contained deficiencies or overexpression of some of the components of the bacterial division apparatus, which in turn led to different division dynamics as well as an overall different morphology of the bacteria during and after the division process.

In this new study, published in the prestigious journal PNAS, scientists from Charles University show how to explain this plethora of data though an elegant model. The basis of this model is that both growth and restructuring processes are governed by the stress inside the bacterial wall. This stress in turn originates from elastic deformations, which are a response to the combination of the internal pressure of the bacterial cell, a constricting apparatus operating on an interior membrane and the changes of the material caused by growth.

The way bacterial growth and remodelling respond to stress is, according to the authors, what differentiates the individual mutants from one another. For example, one mutant might miss one of the enzymes responsible for restructuring the peptidoglycan polymer, and this will lower the response to the part of the stress which is responsible for driving fluidity.

With this simple approach, relying on only two parameters, it becomes possible to classify an entire spectrum of known defects and combinations of mutants of E. coli. This, in turn, validates the model of growth. It is now conceivable to interpret and classify for example the effect of a targeted inhibition of one or several growth enzymes on the bacterial wall, which should facilitate the development of new antibiotics.

“People, who are involved in mathematical modelling, often focus on understanding the properties of a given system of equations. But this time, we didn't have any equations, we only had images from our collaborators and our intuition to start with. It took us some time to understand the mechanisms, but we learnt a lot and eventually succeeded more than we expected. We are very grateful to our collaboration partners who gave us early access to their data. I think that modelling of mechanobiological phenomena is a very rewarding and still underexplored area of applied mathematics,“ says Dr. Christoph Allolio, co-author of the paper and head of a research group focusing on biomembrane remodelling at Mathematical Institute of Charles University.

Furthermore, the research group has already been applying modifications of the same concept to plants and other types of bacteria. “Our group will continue this research in the field of modelling growth processes but also keep working on our original focus of biomembrane remodelling to better understand morphogenesis of intracellular organelles and cellular entry pathways.“

This research was financed by Charles University's PRIMUS and UNCE grants.

P. Pelech, P.P. Navarro, A. Vettiger, L.H. Chao, & C. Allolio, Stress-mediated growth determines Escherichia coli division site morphogenesis, Proc. Natl. Acad. Sci. U.S.A. 122 (28) e2424441122, https://doi.org/10.1073/pnas.2424441122 (2025).

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