“It’s hard to imagine that nothing at all could be so exciting, could be so much fun.” So sang the Talking Heads, who could have been describing a thermodynamicist’s heaven, where “nothing” is in fact something called equilibrium. Right next door to this heaven is a region called nonequilibrium thermodynamics that is even more fun. It is where life resides and motion is not merely thermal. In recent years, scientists have been probing this region, distinguishing the random motions of particles in nonliving molecular systems from the motility of active living matter. The probing, however, has been a little heavy handed.

A gentler approach has been worked out by scientists based at Ludwig-Maximilians-Universitaet (LMU). They have developed a method that can differentiate between the active motions characteristic of living cells and those driven by the random molecular movements that give rise to passive diffusion. The technique also provides deeper insights into fundamental processes that are specific to biological systems.

Details of the method appeared April 29 in Science, in an article entitled, “Broken Detailed Balance at Mesoscopic Scales in Active Biological Systems.” The article describes how video microscopy together with statistical thermodynamics can be used to identify unambiguously which random fluctuations at the cellular scale are out of equilibrium

As the article’s title suggests, the method developed by the LMU scientists makes use of the principle of detailed balance, which states that, in systems that have attained equilibrium, the average rate of every elementary process is equal to that of its reverse—forward and backward reactions effectively cancel out. If this principle does not hold, the system is by definition in a nonequilibrium state and must be driven by the input of energy from an external source.

“Living systems function out of equilibrium and are characterized by directed fluxes through chemical states, which violate detailed balance at the molecular scale,” wrote the authors of the Science article. “Here we introduce a method to probe for broken detailed balance and demonstrate how such nonequilibrium dynamics are manifest at the mesoscopic scale.”

The LMU team analyzed the motions of two types of hair-like cell protrusions made up of proteinaceous filaments—the so-called flagella found on the unicellular green alga Chlamydomonas reinhardtii and the primary cilium found on many epithelial tissues in multicellular organisms. Flagella and primary cilia are quite similar in their basic structure, but their biological functions and modes of action differ. Flagella are used by microorganisms to swim through liquid media, whereas primary cilia act primarily as motile sensors on epithelial surfaces.

“The periodic beating of an isolated flagellum from Chlamydomonas reinhardtii exhibits probability flux in the phase space of shapes,” the authors explained. “With a model, we show how the breaking of detailed balance can also be quantified in stationary, nonequilibrium stochastic systems in the absence of periodic motion. We further demonstrate such broken detailed balance in the nonperiodic fluctuations of primary cilia of epithelial cells.”

“With the help of our imaging data,” said LMU physicist Professor Chase Broedersz, “we were able to demonstrate that, instead of simply waving back and forth, both flagella and cilia on average carry out cycles of actively driven and distinct movements—and in so doing they violate the principle of detailed balance.”

Moreover, the two organelles differ with respect to the precise nature of the movements they exhibit. Flagella beat periodically, and their motions display relatively little random variability. Ciliary motions, on the other hand, are characterized by a much higher level of irregularity. In spite of these differences, however, the analyses showed that both systems contravene the principle of detailed balance.

“These findings are of interest not only in the context of biology, although they provide a means of recognizing nonequilibrium situations in biological systems and afford new insights into the complex processes that make life possible,” asserted Prof. Broedersz. “They are also of great significance for the fields of statistical mechanics and biophysics, because they raise fundamental issues relating to the question of how active molecular processes drive large-scale nonequilibrium dynamics.”

The article contributed by the LMU team was accompanied by a perspective (“A fresh eye on nonequilibrium systems”) authored by scientists based at the National University of Singapore and the Institut Curie. In this perspective, the LMU method was contrasted with earlier methods: “[The new method] requires neither the invasive injection of probes nor external perturbations of the system under study. Instead, it relies only on the observation of spontaneous fluctuations of the system itself using simple time-resolved imaging.”

“The method is not limited to mechanical degrees of freedoms such as flagellar position, but can be extended to chemical or electrical variables, such as electron currents or calcium concentration,” the perspective’s authors continued. “[It] has the potential to become a standard tool not only in biological physics, but also more generally in the study of fluctuating systems.”