Living matter breaks classical physical symmetry rules in collective motion, study finds

Key facts

In physical science, passive materials such as water, simple polymers, and non-living liquid crystals follow well-documented symmetry principles grounded in thermodynamics and statistical mechanics. When passive liquid crystals transition between structured and disordered states, their constituent molecules align according to energy minimization principles, maintaining spatial parity and reversible trajectories under time inversion.

However, the Ben-Gurion University of the Negev (BGU) research team observed that living cells behave fundamentally differently when organizing into collective flows. Living entities consume chemical energy—typically stored as adenosine triphosphate (ATP) in eukaryotic cells or generated via metabolic processes in bacteria—to self-propel and exert forces on neighboring cells and their surrounding extracellular matrix. This continuous internal energy dissipation places living matter far from thermodynamic equilibrium.

The BGU researchers tracked the emergence and decay of collective cellular motion across multiple experimental configurations, analyzing both high-density swarms of motile bacteria and confluent layers of epithelial tissue cells. In classical liquid crystal models, topological defects—points where directional order breaks down—form and annihilate in symmetric, predictable pairs. The study revealed that in living active matter, the formation and breakdown of these collective flow patterns do not obey these traditional rules.

Instead, the creation and annihilation of topological defects in living tissues and bacterial swarms exhibit strong directional biases and irreversible dynamics. As cellular flows spontaneously generate turbulence or collapse into ordered streams, the spatial patterns observed during pattern formation do not mirror those seen during pattern breakdown. This structural asymmetry violates classical Onsager reciprocity relations and time-reversal symmetry, proving that passive physical models cannot adequately describe the phase transitions and flow dynamics of living cellular collectives.

Why it matters

Understanding the physical laws that govern living matter has direct implications across biophysics, developmental biology, materials science, and oncology. For decades, biophysicists have relied on modified versions of passive liquid crystal theory—known as active nematic models—to describe cellular tissues. However, using passive models to represent active biological systems often leads to incorrect predictions regarding force distribution, tissue deformation, and collective transport. By precisely defining how living systems break physical symmetries, the BGU study offers an improved mathematical framework for modeling biological motion.

In medical research, collective cell migration is a foundational process in embryonic tissue development, wound healing, and cancer metastasis. During organogenesis, cells must migrate in coordinated sheets to form complex three-dimensional structures. When skin or vascular walls suffer injury, neighboring cells migrate collectively to close the wound. Conversely, during malignant tumor invasion, cancerous cells frequently break away from primary tumors and invade surrounding tissues as collective clusters rather than isolated units.

Accurate physical models of these collective behaviors allow biomedical researchers to better simulate how tissue structures respond to mechanical strain, biochemical signaling, and pharmacological interventions. Furthermore, in materials science, understanding how biological systems harness localized energy to achieve self-assembly without thermodynamic symmetry constraints could enable the design of novel synthetic materials. Such active biological materials could self-repair, generate continuous microfluidic pumping without external mechanical parts, or autonomously reconfigure their structural properties in response to environmental cues.

The study of active matter emerged as a distinct subfield of soft condensed matter physics in the late 1990s and early 2000s. A seminal landmark occurred in 1995 when theoretical physicist Tamas Vicsek and colleagues introduced a simple mathematical model describing the collective motion of self-propelled particles, such as flocking birds or swarming fish. Shortly thereafter, soft matter theorists adapted the mathematical tools of liquid crystal physics—pioneered in part by Nobel laureate Pierre-Gilles de Gennes in the late 20th century—to describe biological systems whose constituent elements align like rod-like molecules.

Liquid crystals are states of matter that possess properties between those of conventional liquids and solid crystals. In passive liquid crystals, such as those used in electronic displays, elongated molecules align along a common directional vector, known as the director field. The physics of passive liquid crystals is governed by minimum energy principles: when external forces are removed, the system returns to a low-energy, symmetric configuration governed by thermodynamic equilibrium.

In contrast, active matter consists of individual units that convert internal chemical energy into mechanical work. Examples range from molecular motors moving along cytoskeletal filaments within a single cell to swarming bacteria, epithelial cell sheets, schools of fish, and human crowds. Because energy is continuously injected at the individual particle scale, active matter operates permanently out of equilibrium.

Over the past two decades, physicists introduced "active nematic" continuum theories by adding active stress terms to traditional liquid crystal equations. These active stresses reflect the pushing or pulling forces exerted by self-propelled entities. While active nematic models successfully captured phenomena like active turbulence and spontaneous flow generation, they frequently retained underlying mathematical symmetries inherited from passive liquid crystal theories. The BGU study directly targets this theoretical limitation, demonstrating that the biological mechanisms driving cellular movement actively break these passive symmetries during dynamic pattern formation and decay.

Reaction

The publication of the research in Nature Physics has drawn attention from both the physics and biological research communities, highlighting an ongoing shift toward treating living matter as an entirely separate class of physical material rather than a modified derivative of passive soft matter.

Theoretical physicists specializing in non-equilibrium statistical mechanics are expected to re-evaluate current active nematic equations to incorporate the explicit symmetry-breaking terms identified by the BGU team. Researchers in biological physics will likely focus on linking these macroscopic symmetry violations to specific microscopic biomechanical structures, such as actin-myosin contractility, cell-cell adhesion complexes like cadherins, and flagellar propulsion mechanisms.

While the study presents a fundamental physical framework, developmental biologists and medical researchers are expected to examine whether specific tissue types or disease states exhibit distinct degrees of symmetry breaking. Academic forums and upcoming physics conferences, such as the American Physical Society March Meeting, are anticipated to feature discussions on how to integrate these non-equilibrium physical laws into computational simulations of organoid growth and tumor expansion.

What we don't know yet

Despite establishing that cellular flows violate classical symmetry models, several critical questions remain unresolved regarding the exact biological drivers behind these physical phenomena. First, the precise biochemical pathways that control the magnitude of physical symmetry breaking across different tissue types are not fully mapped. It remains unclear how specific intracellular signaling cascades—such as Rho-GTPase pathways that regulate cellular contractility—directly map onto the mathematical symmetry-breaking parameters identified in the study.

Second, the current findings primarily address two-dimensional and quasi-two-dimensional experimental setups, such as cell monolayers on glass slides or thin bacterial suspensions. How these physical symmetry violations translate into fully three-dimensional environments, such as developing embryos or solid tumors embedded within dense extracellular matrices, remains an open area of investigation.

Finally, researchers have yet to determine whether malignant cells exhibit different physical symmetry-breaking signatures compared to healthy, non-cancerous cells. If cancerous tissue displays distinct non-equilibrium flow symmetries during collective invasion, this physical property could potentially serve as a novel diagnostic biomarker or therapeutic target, though experimental proof of this concept is currently lacking.

What to watch

In the coming months and years, several key developments will indicate how this theoretical advance shapes biological physics and biomedical applications. Researchers will closely watch for follow-up studies that attempt to formulate unified mathematical equations that explicitly account for the broken symmetries observed in living flows.

A critical milestone will be the implementation of these new physical parameters into biophysical modeling software, which researchers use to simulate morphogenesis, wound healing, and vascular network formation. If updated models demonstrate significantly higher predictive accuracy when compared against experimental tissue growth data, the theoretical framework proposed by the BGU team will likely become standard in computational biology.

Additionally, experimental groups are expected to test these principles in complex 3D organoid cultures and animal models. Observational studies tracking whether cellular symmetry breaking varies during specific developmental stages or disease progressions will provide critical validation. In the field of engineering, materials scientists will monitor attempts to construct bio-hybrid active systems that utilize non-equilibrium symmetry breaking to create self-driven fluidic pumps and self-healing bio-materials.

This report is based on original research published in Nature Physics and reported by phys.org on September 22, 2026.