Peer into the heart of a living cell, and you are not looking at a static blueprint, but a bustling, fluid metropolis. Cytoplasm streams, filaments assemble and tear apart, and the entire structure churns with a purpose that is both chaotic and exquisitely ordered. This is the world of active matter. These are not passive materials; they are the very engines of life, consuming energy to sculpt embryos, heal wounds, and drive the relentless migration of cells. Life, in its most intimate form, is a current in motion.

What you just saw is a collection of polar microtubule fibers and motors working to stream the currents but failing to stir up motion in smaller droplets.

For decades, the physics describing these living currents were elegant but formidable equations of active hydrodynamics and remained trapped on paper [1,2]. They were a physicist’s dream but a biologist’s nightmare, a set of partial differential equations so sprawling and interconnected that one reviewer aptly called them “terrifyingly complex.” For example, one component/equation governing the nonlinear flow in a 7 equation system:

While these equations held the key to understanding the machinery of life, they were computationally inaccessible. The rigid, specialized software of the past was simply too brittle. It could not capture the intricate dance of these equations in the complex, three-dimensional geometries of actual biology. The language of physics had no fluent translator for the world of the cell.

My doctoral research set out to build that translator. The breakthrough was not a brute-force increase in computing power, but a radical change in philosophy inspired by the power of abstractions. We decided to build a framework that could cleanly separate the physics (the what) from the numerics (the how) and the high-performance supercomputer code (the where). This “separation of concerns” was our Rosetta Stone, a way to create a universal language between the abstract world of mathematics and the messy, beautiful reality of biological form.

The core of this new translator is metaprogramming i.e., software that, in a sense, writes itself. We engineered an embedded domain-specific language (eDSL) within the distributed computing library called OpenFPM [3,4], enabling a system that allows researchers to write equations in code nearly exactly as they appear on a blackboard. The framework handles the rest, automatically translating these high-level expressions into thousands of lines of optimized, parallel code for modern data centers and supercomputers. This dramatically lowered the barrier to entry. Suddenly, a physicist or biologist could focus entirely on their scientific question, leaving the Herculean task of high-performance parallel solver implementation to the computer.

This newfound flexibility unleashed our ability to experiment. We integrated and expanded a novel, mesh-free numerical scheme, the Discretization-Corrected Particle Strength Exchange (DC-PSE) method [5,6]. Instead of relying on rigid computational grids that shatter when faced with the fluid shapes of biology, our particle-based approach thrived in complexity. It allowed us to compute with high-order accuracy on any imaginable geometry, from a sphere to a peanut-shaped dividing cell. For the first time, computations that had previously stalled became elegantly solvable, scaling efficiently across thousands of CPU cores.

With these computational floodgates opened, biology revealed its secrets. Our three-dimensional simulations uncovered phenomena entirely absent from flatter, simpler models. We witnessed the first numerical realization of a 3D “active Fréedericksz transition,” a point where the living fluid spontaneously erupts into motion (movie below) [7]. As we pushed the system further, we discovered a stunning zoo of behaviors: from spontaneous flow transitions and traveling waves to a rich, spatiotemporal chaos [5]. Most remarkably, we observed a topological phase transition akin to the famous BKT transition of 2D physics, a deep insight into the universal laws that could be governing the organization of life, an insight only made possible by a tool that could finally speak the right language [8, 9].

Yet, solving the equations was only half the battle. If our discoveries remained locked behind inaccessible software, the scientific impact would be muted. We committed to making our framework a powerful sandbox for discovery, accessible to all. The payoff has been immediate. By combining our simulations with analytical theory, we could provide quantitative predictions for phenomena observed in labs. We uncovered principles linking a cell’s geometry to the stability of its chaotic interior, offering a physical reason for the prevalence of spherical forms in biology as shown in the movie below.

Labs focused on microscopy can now prototype experiments virtually, testing the effect of a change in cell shape or activity in a matter of hours, not months.

The true power of this new language became clear when we applied it to the very shapes that life itself inhabits as shown in the movie below. The underlying physics, an extension of the same Ericksen-Leslie theory that gave us the liquid crystals in our colorful displays, could now be explored in its native biological context. Just as we once engineered the flow of molecules to create LCDs, we could now simulate the flow of life. Our algorithms and software allowed simulations from simple cylindrical tubes to the complex peanut shape of a dividing cell.

In these intricate domains, we discovered that geometry was not a passive stage but an active player in the drama. The 3D active Fréedericksz transition generalized to spherical shapes and was confirmed experimentally to tame the wild currents, suppressing the onset of chaotic turbulence [10]. This hinted why cellular structures, like organelles could be predominantly spherical.

Ultimately, this project’s most significant contribution may be cultural. Our work demonstrates how advanced computational tools, when designed for accessibility, can fundamentally expand biological inquiry. By placing the power of theoretical physics and high-performance computing directly into the hands of biologists, we have helped democratize the scientific process. Our open-source framework is now being used by researchers worldwide to investigate everything from 3D cytoskeletal dynamics to the engineering of novel active materials.

This is the new paradigm: computational physics and biology are no longer isolated disciplines but a dynamic, creative partnership. What began as an intimidating mathematical challenge has been transformed into a collaborative toolkit for simulating, predicting, and understanding the currents of life. Having learned to read life’s hidden choreography, we are now taking the first steps toward learning how to rewrite it.

[1] M. C. Marchetti, J. F. Joanny, S. Ramaswamy, T. B. Liverpool, J. Prost, M. Rao, and R. A. Simha, “Hydrodynamics of soft active matter,” Rev. Mod. Phys., vol. 85, pp. 1143–1189, July 2013. Publisher: American Physical Society.

[2] F. Jülicher, S. W. Grill, and G. Salbreux, “Hydrodynamic theory of active matter,” Rep. Prog. Phys., vol. 81, p. 076601, June 2018.

[3] A. Singh, P. Incardona, and I. F. Sbalzarini, “A c++ expression system for partial diferential equations enables generic simulations of biological hydrodynamics,” European Physical Journal E, vol. 44, 9 2021.

[4] P. Incardona, A. Leo, and Y. Zaluzhnyi, “Openfpm: A scalable open framework for particle and particle-mesh codes on parallel computers,” Computer Physics Communications, vol. 241, pp. 155–177, 2019.

[5] Abhinav Singh, Philipp H. Suhrcke, Pietro Incardona, Ivo F. Sbalzarini; A numerical solver for active hydrodynamics in three dimensions and its application to active turbulence. Physics of Fluids 1 October 2023; 35 (10): 105155. https://doi.org/10.1063/5.0169546

[6] Singh, A., Foggia, A., Incardona, P. et al. A Meshfree Collocation Scheme for Surface Differential Operators on Point Clouds. J Sci Comput 96, 89 (2023). https://doi.org/10.1007/s10915-023-02313-3

[7] A. Singh, Q. Vagne, F. Jülicher, and I. F. Sbalzarini, “Spontaneous fow instabilities of active polar fuids in three dimensions,” Phys. Rev. Res., vol. 5, p. L022061, Jun 2023.

[8] Singh, Abhinav: Efficient and Scalable Simulations of Active Hydrodynamics in Three Dimensions. Dissertation, TU Dresden, 2024.

[9] Guillaume Duclos et al., Topological structure and dynamics of three-dimensional active nematics. *Science *367,1120-1124(2020).DOI:10.1126/science.aaz4547

[10] S. Alam, B. Najma, A. Singh, J. Laprade, G. Gajeshwar, H. G. Yevick, A. Baskaran, P. J. Foster, and G. Duclos, Active Fréedericksz transition in active nematic droplets, Phys. Rev. X 14, 041002 (2024).

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