Individual components of biological materials include tiny motors that convert fuel into motion. This produces movement patterns, and the material shapes itself with coherent flows as a result of constant energy consumption. Such materials are referred to as “active matter.” Active matter theory, a scientific framework for understanding the shape, flows, and form of living materials, can be used to describe the mechanics of cells and tissues. The active matter theory is made up of numerous difficult mathematical equations.

Scientists from the Max Planck Institute of Molecular Cell Biology and Genetics (MPI-CBG) in Dresden, the Center for Systems Biology Dresden (CSBD), and the Technical University of Dresden have now developed an algorithm, implemented in open-source supercomputer code, that can solve the equations of active matter theory in realistic scenarios for the first time. These discoveries bring us one step closer to solving the century-old mystery of how cells and tissues take shape and designing artificial biological machines.

Biological processes and behaviors are frequently extremely complex. Physical theories offer a precise and quantitative framework for comprehension. The active matter theory provides a framework for understanding and describing the behavior of active matter, which is made up of individual components capable of converting chemical fuel (“food”) into mechanical forces.

Our approach can handle different shapes in three dimensions over time. Even when the data points are not evenly distributed, our algorithm employs a novel numerical approach that works seamlessly for complex biologically realistic scenarios to accurately solve the theory’s equations.

Abhinav Singh

Several Dresden scientists, including Frank Jülicher, director of the Max Planck Institute for the Physics of Complex Systems, and Stephan Grill, director of the MPI-CBG, were instrumental in developing this theory. The dynamics of active living matter can be described and predicted mathematically using these physics principles. These equations, however, are extremely complex and difficult to solve.

Therefore, scientists require the power of supercomputers to comprehend and analyze living materials. There are different ways to predict the behavior of active matter, with some focusing on the tiny individual particles, others studying active matter at the molecular level, and yet 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, TU Dresden Professor at the Center for Systems Biology Dresden (CSBD), research group leader at the Max Planck Institute of Molecular Cell Biology and Genetics (MPI-CBG), and Dean of the Faculty of Computer Science at TU Dresden, have now developed a computer algorithm to solve the equations of active matter. Their work was published in the journal “Physics of Fluids” and was featured on the cover. They present an algorithm that can solve the complex equations of active matter in three dimensions and in complex-shaped spaces.

“Our approach can handle different shapes in three dimensions over time,” says Abhinav Singh, a mathematician and one of the study’s first authors. “Even when the data points are not evenly distributed,” he continues, “our algorithm employs a novel numerical approach that works seamlessly for complex biologically realistic scenarios to accurately solve the theory’s equations.” We can finally understand the long-term behavior of active materials in both moving and non-moving scenarios using our approach, allowing us to predict their dynamics. Furthermore, the theory and simulations could be used to program biological materials or build nano-scale engines to extract useful work.”

The other first author, Philipp Suhrcke, a graduate of TU Dresden’s Computational Modeling and Simulation M.Sc. program, adds, “thanks to our work, scientists can now, for example, predict the shape of a tissue or when a biological material is going to become unstable or dysregulated, with far-reaching implications in understanding the mechanisms of growth and disease.”

**A powerful code for everyone to use**

The scientists developed their software using the open-source library OpenFPM, which is freely available for use by others. The Sbalzarini group created OpenFPM to democratize large-scale scientific computing. The authors first created a custom computer language that allows computational scientists to write supercomputer codes by specifying equations in mathematical notation and letting the computer do the rest of the work to generate correct program code. As a result, they don’t have to start from scratch every time they write a piece of code, effectively reducing code development times in scientific research from months or years to days or weeks, resulting in enormous productivity gains.

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

Ivo Sbalzarini, the study’s Principal Investigator, summarizes: “Ten years of our research went into creating this simulation framework and enhancing the productivity of computational science.” All of this has now been combined into a tool for understanding the three-dimensional behavior of living materials. Our code, which is open-source, scalable, and capable of handling complex scenarios, opens up new avenues for modeling active materials. This could finally explain how cells and tissues take shape, resolving a fundamental question of morphogenesis that has perplexed scientists for centuries. However, it may also help us design artificial biological machines with fewer components.”