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From July 7 to 11, the CRM became a hub for collaborative problem-solving during the XI Iberian Modeling Week, an international training initiative that brought together nearly 30 students from diverse academic backgrounds to tackle real-world challenges using mathematical modeling. Through hands-on work on industrial problems, ranging from public transport and biomedical diagnostics to urban planning and renewable energy, the participants not only applied their skills, but also experienced the power of teamwork and interdisciplinary thinking.

For five days, the CRM classrooms echoed not with lectures but with the buzz of teamwork. From July 7 to 11, 2025, the Centre de Recerca Matemàtica hosted the eleventh edition of the Iberian Modeling Week (IMW), a training experience where mathematics steps outside the classroom and into the messy, fascinating world of real-world problems.

Organised by the CRM, in collaboration with math-in (Spain) and PT-MATHS-IN (Portugal), the IMW brought together nearly 30 students from across Europe (from Barcelona to Lisbon, from Hamburg to L’Aquila) to tackle the applications of mathematics head-on. And not all of them came from a pure mathematics background. Among the participants were students of physics, chemistry, artificial intelligence, biomedical engineering, and aerospace engineering, bringing with them diverse perspectives and problem-solving strategies.

“It was incredible to work on a problem that’s actually useful for society,” said Álvaro Garrido, a participant from the University of L’Aquila, in Italy. “We often study theory, but here we had to make something work under real conditions; with data, with deadlines, with ambiguity.” Over the course of the week, participants worked in teams under the guidance of researchers and industry mentors, navigating challenges that ranged from public transport optimisation to biomedical diagnostics.

Each challenge had a real industrial or societal angle. One group modeled the optimal allocation of buses throughout a city’s daily cycle, factoring in not only trip duration and passenger demand but also synchronisation strategies to minimise fuel use and waiting times. Another team worked on the physics of blood flow, refining the Windkessel model to better understand hemodynamic changes during venous occlusion using real data from non-invasive spectroscopy.

A third team worked on a problem as timely as it was complex: how to place climate shelters in cities to ensure maximum accessibility for vulnerable populations during extreme heat events, using Barcelona as a case study. They used demographic and geographic datasets to develop algorithms that balanced social equity with spatial efficiency. Meanwhile, a fourth team wrestled with the trade-off between energy harvesting and flow efficiency in asphalt solar collectors, a problem at the crossroads of renewable energy, fluid dynamics, and infrastructure design.

For Angelica Chanvoedou Abaga, a student at Universidad Rey Juan Carlos, the IMW was more than just an academic experience. “You don’t just learn how to model,” she explained. “You learn to communicate with people from different countries, from different fields. That’s what made this week so valuable.”

Throughout the week, participants learnt how to translate the language of mathematics into tools for change. The modeling week emphasised collaboration and critical thinking. It also offered a glimpse into how mathematics connects with everything: engineering, public health, urban planning, and climate resilience.

“I didn’t expect to enjoy it this much,” admitted Natan Sisoev, a mathematics student from Universitat Autònoma de Barcelona. “But working side by side with others, finding new ways to look at a problem, it reminded me why I wanted to study this in the first place.”

Friday marked the final presentations. Each group stood before their peers and mentors to explain what they’d built: the models they’d refined and the solutions they proposed. And, just as importantly, the open questions that remained.

“Presenting our results to the other teams was a really interesting experience,” said Andrés Uranga, from Universidad de Sevilla. “It was impressive to see how each group approached the problem differently.”

For David Romero, director of the Knowledge Transfer Unit at CRM, this is precisely the point: “This kind of activity puts students in touch with problems that aren’t polished or prepared for a textbook. They’re raw, they’re real, and that forces them to think.” He added: “At CRM, we believe deeply in the connection between knowledge and society. That’s why we organise things like this; to make sure talent doesn’t stay isolated in theory.”

Emilio Carrizosa, professor at Universidad de Sevilla and president of Math-in, echoed this sentiment: “Events like this one are essential. They show that mathematics can, and should, leave the university walls and go solve real-world problems.” But beyond the technical skills, he emphasised what students take with them: “It’s not just about solving a problem. It’s about learning how to work in a team, how to explain your ideas, and how to listen. That’s what they’ll carry with them into any career.”

The IMW was not an isolated event, it preceded the European Study Group with Industry (ESGI), creating a powerful continuity: first the students, then the professionals, tackling problems side by side in the same space. This back-to-back setup maximised opportunities for networking.

Behind the scenes, the activity was coordinated by the Knowledge Transfer Unit at the CRM: Lucía Escudero, Marc Homs-Dones, Manel Mas, and David Romero, who served as the mentors for the four working groups. Their work, in collaboration with representatives from Spanish and Portuguese universities and industrial platforms, ensured that both the scientific content and the organisational logistics of the IMW ran smoothly and effectively.

Inside each one of your cells, there’s enough DNA to stretch more than two metres if laid out end-to-end. Yet somehow, all this DNA fits into a tiny structure called the cell nucleus, so intricately folded and tightly packed that it makes origami seem simple by comparison. But scientists are learning that this incredible folding isn’t just a clever trick to save space; it may also help cells make critical decisions about what kind of cells they become and how they behave.

A study published in the Bulletin of Mathematical Biology by researchers Daria Stepanova (CRM), Meritxell Brunet Guasch (University of Edinburgh), Helen M. Byrne (University of Oxford), and Tomás Alarcón (ICREA–CRM) explores how DNA’s 3D folding influences gene activity. They discovered that the shape of DNA, and how molecules interact with it, may be key to determining whether genes are switched “on” or “off.”

This switching of genes on and off without changing the DNA code is known as epigenetics. Epigenetic changes occur through chemical marks that attach to the DNA molecule or to proteins called histones, around which DNA wraps. Think of these marks as sticky notes placed along the DNA: they don’t change the instructions in our genetic code, but they tell cells which parts of those instructions to read or ignore. These notes are crucial for guiding a cell’s identity, allowing it to specialise into muscle, nerve, skin, or blood cells, even though every cell begins life with the same DNA.

However, a key mystery remains: sometimes these epigenetic marks form smooth patterns across the genome, while other times they become strikingly uneven or “rugged,” marked by abrupt shifts between areas where genes are active and areas where they’re silenced.

Until now, exactly how and why these complex, rugged patterns emerge has not been well understood.

A Virtual Lab Built with Mathematics

To solve this mystery, the research team created a mathematical model, a kind of “virtual lab,” that allows them to test biological rules and see what patterns emerge through computer simulations. Their model specifically explored the interactions between key histone modifications and the enzymes responsible for adding (“writing”) or removing (“erasing”) these chemical marks.

The model considers epigenetic modifications (H3K27me3, H3K4me3, H3K27ac) on histone H3 residues. It divides chromatin into fixed-size genomic regions characterised by these modifications, linked through reinforcing and inhibitory enzyme-driven feedback.

What set their approach apart was the inclusion of two critical elements usually overlooked in other studies. First, they included the actual 3D folding structure of chromatin (DNA wrapped around histones) because how chromatin folds changes which parts of the genome interact. Second, they factored in the limited availability and competition among enzymes. These enzymes constantly “fight” over which sites on the chromatin they modify, creating a microscopic molecular tug-of-war.

“There are not so many models of epigenetic regulation, especially those which also account for chromatin conformation; therefore, previous models have been formulated in a more simplified setting.” As Stepanova explains, “enzyme competition can be important in shaping epigenetic landscapes. It is a more realistic assumption than a constant or uniform concentration of enzyme along the chromatin. Chromatin is folded, and enzyme molecules are ‘floating’ around, ready to bind to any genomic site in their vicinity.” Moreover, she notes, this enzyme competition can “break the symmetry and eventually lead to the emergence of rugged epigenetic patterns.”

By combining chromatin folding and enzyme competition, the team found that remarkably uneven patterns emerged. When distant segments of DNA come into close contact due to folding, they influence each other’s epigenetic states. At the same time, because the enzymes needed to modify these regions are limited, only some areas get marked, leaving others untouched. The result is a patchwork, or rugged landscape, of active and inactive zones that mirrors what scientists see in real cells.

Stepanova further highlights why identifying these rugged and uniform regimes is crucial: “Epigenetic marks are known to have self-reinforcing feedback mechanisms, promoting the addition of the same or similar marks in neighbouring chromatin regions. If the region is extended, these loops would make the entire region uniform. This does not coincide with reality, since we know that, especially in differentiated cells, there are chromatin regions which are silenced and chromatin domains which are active.”

She notes that this raises an important question: “What is the ‘stopping factor’ that maintains the boundaries between these activating and inhibitory regions?” Their research provides “a possible explanation for one of the factors contributing to the emergence of alternating silenced and active genomic regions.”

Interestingly, the team’s model also captured another aspect observed in real cells called bivalent chromatin. These are regions carrying both activating and silencing epigenetic regulators at once, like genes being kept on standby, ready to quickly turn “on” or “off” in response to specific signals. These bivalent states help cells transition smoothly from uniform epigenetic landscapes to more rugged patterns, or vice versa.

Bridging Scales

The researchers designed their model to function effectively across different scales, from individual gene regions to larger chromatin structures known as Topologically Associating Domains (TADs). This mesoscale approach is particularly important. “Higher-order structures, such as loops and small TADs, can be visualised more precisely, and we can investigate how these structures influence the formation of epigenetic patterning,” Stepanova explains. “If we go to large scales of the entire chromosome, these details are also lost. In my view, the mesoscopic approach is ideal for exploring epigenetic landscapes.”

Stepanova also highlights the unique advantages mathematics offers in studying epigenetics. “Using mathematical modelling, we can investigate various aspects of biological processes which cannot be manipulated, visualised, isolated, measured, or controlled in an experimental setting,” she notes. While experimental studies are powerful, they can be costly and time-consuming. Theoretical modelling, she points out, is essentially cost-free, though closer collaboration with biologists is essential.

As an example of this type of collaboration, Stepanova mentions the current work of her master’s student Roger Bosch, who is investigating how various methods of processing chromatin conformation data affect our understanding of epigenetic patterns. These techniques aim to remove experimental artefacts and clarify the true chromatin folding patterns. However, Stepanova remarks, “It is still unclear how much these methods give us a prettier picture and how much they genuinely bring us closer to the accurate structure of cellular DNA.”

Questions like these underline both the importance and potential of integrating theoretical modelling closely with experimental research to improve our understanding of biological data.

Citation:

Stepanova, D., Brunet Guasch, M., Byrne, H.M. et al. Understanding How Chromatin Folding and Enzyme Competition Affect Rugged Epigenetic Landscapes. Bull Math Biol 87, 59 (2025). https://doi.org/10.1007/s11538-025-01434-0