Tying knots with molecules, mutations and the emergence of new species, solving old mathematical problems – major EU funding for three JYU researchers

Three researchers from the Faculty of Mathematics and Science have been awarded a highly competitive Consolidator Grant from the European Research Council (ERC). The projects aim at developing more efficient catalysts by tying long molecules into knots, examining the effects of mutations in the emergence of new species, and solving problems in fractal geometry.

Fabien Cougnon, Ilkka Kronholm ja Tuomas Orponen.

Published

31.1.2023

More efficient catalysts by tying knots in molecules

Many people are annoyed by a headphone cord that got tangled in their pocket. Associate Professor of Synthetic Nanochemistry Fabien Cougnon's project investigates the same phenomenon – but on a much smaller scale. “The goal of this project is to develop a method to control the formation of entanglements at the molecular scale,” says Cougnon.

Long molecules like synthetic polymers or DNA often get entangled, which changes their shape, their mechanical properties, and their chemical properties. However, the formation of entanglements has proved to be extremely difficult to control. “Our idea is to exploit the formation of entanglements to manipulate the properties of synthetic molecules. This is an original idea that can have a huge impact in other fields of research, especially in the development of increasingly efficient catalysts,” Cougnon says. “It is also a lot of fun to try to tie knots with something as small as a molecule!”

Catalysts are small molecules that assist chemical transformations. They are essential to both fundamental research and the industrial production of synthetic compounds. Synthetic compounds are generally produced as the results of a series of several transformations. This process can be rather long and tedious because most catalysts can only carry out one specific type of chemical transformation. Each transformation must thus be performed one after the other, with the help of different catalysts, and the intermediate compounds must be purified at each step.

“It would be great to construct a single molecule containing several catalytic sites, which would be able to carry out the whole sequence of reactions, at the same time, in a single vessel. However, as the number of catalytic sites increases, the length of the entire molecule also increases. Long molecules tend to fold in uncontrollable ways, a phenomenon that interferes with their performance. By tying knots with long molecules containing several catalytic sites, we will become able to precisely control the relative position of each catalytic site to optimize their performance, a feat never accomplished before”, says Cougnon.

“This funding will allow us to push the boundary of knowledge and, hopefully, to produce large, knotted molecules usable for practical applications in catalysis in the future.” The funding will be mostly used to hire new researchers and purchase the chemicals necessary to pursue the project in the 5 coming years. This will considerably strengthen the project team, which has been in Jyväskylä for just over one year and is currently composed of 5 researchers and associate professor Cougnon.

How do mutations affect the emergence of new species?

Academy researcher Ilkka Kronholm’s project “Role of epistatic interactions in evolution” deals with genetic variation. In evolutionary biology, the operation of natural selection is fairly well understood, but the origin of genetic variation is less so. Variation is produced as a result of mutations, yet little is known about their properties.

“In this project, we are particularly interested in knowing how often new mutations interact with each other and what is the statistical distribution of these interactions” Kronholm explains. “Understanding the interaction between mutations adds to our knowledge and helps us to understand how populations adapt to changing conditions.”

It is well-established that interactions between mutations plays an important role, for example, in the emergence of new species, but the probability of these interactions is not known.

“On the basis of the results in this project we can better understand how new species arise in evolution,” says Kronholm. The experimental estimation of the interaction of mutations requires large amounts of data. In the project long-term evolution experiments are conducted with microbes, and the project’s five-year grant, worth almost 2 million euros, enables the collection of the necessary data.

Mathematicians solve old problems in fractal geometry

Assistant Professor of Mathematics Tuomas Orponen’s project aims to make progress in several well-known problems in geometric measure theory, including Vitushkin's conjecture from the 60s, and the Furstenberg set conjecture proposed by Tom Wolff in the 90s.

“There is a relatively short list of key open problems in my area: they are so old that they were already considered "vintage" when I was doing a PhD around 2010. Some of them date back 40-50 years. They are known to be connected with each other, and also with various other branches of mathematics, for example harmonic analysis. As long as these questions remain unsolved, they form a solid wall in the area: the only alternatives are to breach the wall, or to change fields completely,” explains Orponen.

“Cracks have finally started forming in the past 10 years, and at the same time the interconnectedness of the problems has turned from a formidable foe to a dear friend: progress in one question often rapidly leads to progress in others as well. There is now a vivid a sensation in the community that the old problems could fall in the next few years, and the field could finally develop past them. “

The project is basic research in mathematics, more specifically in geometric measure theory. The questions addressed by the project mostly deal with the geometry of fractal sets in the plane. “The term ‘fractal’ is a little vague, but it should evoke the idea of a ‘fractured’ set without any smoothness,” Orponen describes.

The size of fractals is typically measured in terms of their ‘dimension’. A line segment has dimension one, and the square has dimension two, but there exist multitudes of interesting fractals whose dimension is not an integer. It is a fundamental topic in geometric measure theory to study how the dimension of fractals is preserved, or perhaps distorted, under various maps, for example orthogonal projections.

“The ERC label is recognised around the world, and it will help attract good candidates for the postdoc and PhD researcher positions supported by the funding during the next 5 years. This is a great advantage of the ERC funding. The funding will also enable the organisation of an international conference at JYU, which will promote our department as a stronghold of research in geometric measure theory.”

Projects:

Fabien Cougnon, Chemistry: Entangled tertiary folds, 1 999 454 €
Ilkka Kronholm, Biological and Environmental Science: Role of epistatic interactions in evolution, 1 970 533 €
Tuomas Orponen, Mathematics: Multi-scale incidence geometry, 1 362 843 €