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3D simulation of active matter in a geometry similar to a dividing cell. Credit: Singh et al. Physics of Fluids (2023) / MPI-CBG

Biological materials are made of individual components, including tiny motors that convert fuel into motion. This creates patterns of movement, and the material molds itself into coherent flows through constant energy consumption. These continuously activated materials are called active matter.

The mechanics of cells and tissues can be described by active matter theory, a scientific framework for understanding the shape, flow, and form of living materials. Active matter theory consists of many challenging mathematical equations.

Scientists at the Max Planck Institute for Molecular Cell Biology and Genetics (MPI-CBG) in Dresden, the Center for Systems Biology Dresden (CSBD) and TU Dresden have now developed an algorithm, implemented in an open-source supercomputer code, that can for the first time solve the equations of active matter theory in realistic scenarios.

These solutions bring us a big step closer to solving the centuries-old enigma of how cells and tissues acquire their shape and to designing artificial biological machines.

Biological processes and behaviors are often very complex. Physical theories provide a precise and quantitative framework for understanding them. Active matter theory offers a framework for understanding and describing the behavior of active matter – materials composed of individual components capable of converting a chemical fuel (“food”) into mechanical forces.

Several Dresden scientists were instrumental in developing this theory, among others Frank Jülicher, director of the Max Planck Institute for the Physics of Complex Systems, and Stephan Grill, director of the MPI-CBG.

With these principles of physics, the dynamics of active living matter can be described and predicted by mathematical equations. However, these equations are extremely complex and difficult to solve. Therefore, scientists need the power of supercomputers to understand and analyze living materials.

There are different ways to predict the behavior of active matter, with some focusing on tiny individual particles, others studying active matter at the molecular level, and still others studying active fluids on a large scale. These studies help scientists see how active matter behaves at different scales in space and over time.

## Solving complex mathematical equations

Scientists from the research group of Ivo Sbalzarini, professor at TU Dresden at the Dresden Center for Systems Biology (CSBD), research group leader at the Max Planck Institute for Molecular Cell Biology and Genetics (MPI-CBG) and Dean of the Faculty of Computer Science at TU Dresden has now developed a computer algorithm for solving the equations of active matter. His work was published in the magazine *Fluid Physics* and appeared on the cover. They present an algorithm that can solve complex equations of active matter in three dimensions and in complexly shaped spaces.

“Our approach can handle different shapes in three dimensions over time,” says one of the study’s first authors, Abhinav Singh, a mathematician studied.

“Even when data points are not regularly distributed, our algorithm employs a new numerical approach that works perfectly for complex biologically realistic scenarios to accurately solve the theory’s equations. Using our approach, we can finally understand the long-term behavior of materials assets in moving and immobile scenarios to predict their dynamics. Furthermore, the theory and simulations could be used to program biological materials or create nanometer-scale engines to extract useful work.”

The other first author, Philipp Suhrcke, graduate of TU Dresden’s Computational Modeling and Simulation, M.Sc. program, says: “Thanks to our work, scientists can now, for example, predict the shape of a fabric or when a material biology will become unstable or dysregulated, with far-reaching implications for understanding the mechanisms of growth and disease.”

## A powerful code for everyone to use

The scientists implemented their software using the OpenFPM open source library, which means it is freely available for third-party use. OpenFPM is developed by the Sbalzarini group to democratize large-scale scientific computing.

The authors first developed a custom computer language that allows computer scientists to write supercomputer code by specifying the equations in mathematical notation and letting the computer do the work to create correct program code. As a result, they no longer need to start from scratch every time they write code, effectively reducing code development time in scientific research from months or years to days or weeks, delivering huge productivity gains.

Due to the enormous computational demands of studying three-dimensional active materials, the new code is scalable on shared and distributed memory multiprocessor parallel supercomputers, thanks to the use of OpenFPM. Although the application is designed to run on powerful supercomputers, it can also be run on regular office computers to study two-dimensional materials.

The study’s principal investigator, Ivo Sbalzarini, says: “Ten years of our research were dedicated to creating this simulation framework and increasing the productivity of computational science. All of this now comes together in a tool for understanding the three-dimensional behavior of living materials .”

“Open source, scalable, and capable of handling complex scenarios, our code opens new avenues for modeling active materials. This could finally lead us to understanding how cells and tissues achieve their shape, addressing the fundamental question of morphogenesis that has intrigued scientists for centuries. But it could also help us design artificial biological machines with a minimal number of components.”

**More information:**

Abhinav Singh et al, A numerical solver for active hydrodynamics in three dimensions and its application to active turbulence, *Fluid Physics* (2023). DOI: 10.1063/5.0169546

The open source OpenFPM framework is available at github.com/mosaic-group/openfpm_pdata

Pietro Incardona et al, OpenFPM: A scalable open framework for particle and particle mesh codes on parallel computers, *Computer Physics Communications* (2019). DOI: 10.1016/j.cpc.2019.03.007

**Diary information:**

Fluid Physics