MERGE: biology through A+B

Mathematics and biology, an unexpected scientific duo? Not really. In Anglo-Saxon countries, bridges have existed between the two disciplines since the end of the 19th century. Charles Darwin's work paved the way for the emergence of statistical tools to analyze the data he had collected. In France, this association was hardly conceivable before the second half of the 20th century, biology having inherited Buffon's observations and classifications. It wasn't until the 50s and 60s, with the massive development of biological investigation tools, that scientists began accumulating data that needed to be interpreted.

Population dynamics 

Mathematics and biology, an unexpected scientific duo? Not really. In Anglo-Saxon countries, bridges have existed between the two disciplines since the end of the 19th century. Charles Darwin's work paved the way for the emergence of statistical tools to analyze the data he had collected. In France, this association was hardly conceivable before the second half of the 20th century, biology having inherited Buffon's observations and classifications. It wasn't until the 50s and 60s, with the massive development of biological investigation tools, that scientists began accumulating data that needed to be interpreted.

Population dynamics 

Mathematics and biology, an unexpected scientific duo? Not really. In Anglo-Saxon countries, bridges have existed between the two disciplines since the end of the 19th century. Charles Darwin's work paved the way for the emergence of statistical tools to analyze the data he had collected. In France, this association was hardly conceivable before the second half of the 20th century, biology having inherited Buffon's observations and classifications. It wasn't until the 50s and 60s, with the massive development of biological investigation tools, that scientists began accumulating data that needed to be interpreted.

Population dynamics

“Mathematics offers biologists models to explain things that cannot be observed directly,” emphasizes Marie Doumic, research director at Inria and head of the MERGE project team. At the Center for Applied Mathematics, MERGE - Understanding Mathematics for Evolution, Reproduction, Growth and Emergence - is rooted at the interface of the two disciplines and brings together some fifteen researchers under the banner of population dynamics. “Interdisciplinarity is our raison d'être. For us, it's an inexhaustible reservoir of new mathematical problems or new ways of looking at old problems. For biologists, it opens new ways of thinking and new avenues of research”. 

The project team is involved in the fields of aging and cancer, as well as modeling at different scales. “This latter field is of particular interest to us, as it covers both stochastic methods (editor's note: analysis of the evolution of random quantities) to describe phenomena on a microscopic scale, and so-called averaged methods on more macroscopic scales”, explains the researcher. 

Expanding knowledge

While the research carried out by MERGE members is similar in many respects, the variety of the work carried out is constantly adding to our knowledge and innovation. A project on the fragmentation of amyloid fibers, for example, led Marie Doumic to establish an innovative set of equations - based on a prey-predator interaction system dear to ecologists - to model the polymerization of these proteins involved in certain neurodegenerative diseases, and provide a scientific explanation for the biologists' observations. 

“These are exciting research topics. Through them, we are trying to build innovative mathematical objects at the service of biologists,” adds Sylvie Méléard, professor at CMAP and member of the Institut Universitaire de France.

The founder of the Chair in Mathematical Modeling and Biodiversity (MMB - in association with the Muséum national d'Histoire naturelle) is closely involved with microbiologists at the Ecole normale supérieure and oncologists at Hôpital Saint-Louis in Paris. “Using mathematical equations, I try to describe the behavior of cells over time (differentiation, division, death), to take into account the appearance of mutations and the behavior of mutants, and to present possible evolutionary scenarios to doctors and biologists,” explains Sylvie Méléard. For example, we can model the appearance and multiplication of mutant cells in an organism to optimize chemotherapy, or the evolution of a bacterial line in the face of a cocktail of antibiotics to combat antibiotic resistance. “But let's not kid ourselves. Biology is complex. It all takes time,” warns the mathematician. 

Sylvie Méléard is not the only one working on antibiotic resistance at MERGE. Gaël Raoul, also a researcher at CMAP, approaches the issue from the angle of spatial structure. In other words, his mathematical models consider how organisms occupy their environment and how they interact with it. Using partial differential equations and probabilistic methods, he studies the impact of antibiotic dosage or hospital hygiene procedures on the emergence of resistant or nosocomial bacteria. “I approach this work from a One Health perspective, i.e. considering human, animal and environmental health. This is a central theme in antibiotic resistance", explains Gael Raoul. The tools developed by the researcher could even help trace the life cycle of a bacterium. “A nosocomial illness caused by a microorganism is the result of a series of very rare events that can be mathematically traced back and thus anticipated or better understood”.

Recently, modeling spatial structure has also taken the researcher to the forests of French Guiana. The ONF (Office national des forêts) has noted the death of several patches of forest there, and is wondering not only about the trees' capacity to adapt to climate change, but also about the actions to be taken to preserve the forest in this context. To do this, the mathematician has to define an envelope of scenarios, which he will run through his mathematical models one by one. “This is robust optimization. Here, all eventualities are considered, including the most extreme ones, which are usually sidelined because they are considered unlikely,” explains Gaël Raoul. “The aim is to go beyond the numerical simulations that the ONF has already mastered, and to build a simple message that is easy to communicate to local players”.

Passengers

Today, the expertise of mathematicians is recognized and identified by biologists. The latter no longer hesitate to ask their colleagues to shed new light on their work. Over the past 20 years, Sylvie Méléard and her MMB Chair have made a major contribution to building a strong and vibrant “maths-bio” community. “We still need people to bridge the gap between the two fields, and MERGE is helping to do just that,” she stresses. “The team is at the crossroads of mathematics, biology, and medicine. We believe that theories built jointly with our colleagues can support our understanding of the living world and enable us to imagine answers to current problems", conclude Marie Doumic, Sylvie Méléard and Gaël Raoul.