Red blood cells, or erythrocytes, are seen to flicker under optical microscopy, a phenomenon initially described as thermal fluctuations of the cell membrane. But recent studies have suggested the involvement of non-equilibrium processes, without definitively ruling out equilibrium interpretations. Using active and passive microrheology to directly compare the membrane response and fluctuations on single erythrocytes, we report here a violation of the fluctuation–dissipation relation, which is a direct demonstration of the non-equilibrium nature of flickering. With an analytical model of the composite erythrocyte membrane and realistic stochastic simulations, we show that several molecular mechanisms may explain the active fluctuations, and we predict their kinetics. We demonstrate that tangential metabolic activity in the network formed by spectrin, a cytoskeletal protein, can generate curvature-mediated active membrane motions. We also show that other active membrane processes represented by direct normal force dipoles may explain the observed membrane activity. Our findings provide solid experimental and theoretical frameworks for future investigations of the origin and function of active motion in cells. The membranes of red blood cells exhibit a flickering motion that has long been ascribed a thermal origin. Microrheology experiments provide direct evidence that flickering is an active process characterized by non-equilibrium dynamics.

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Equilibrium physics breakdown reveals the active nature of red blood cell flickering

Living systems operate far from thermodynamic equilibrium. Enzymatic activity can induce broken detailed balance at the molecular scale. This molecular scale breaking of detailed balance is crucial to achieve biological functions such as high-fidelity transcription and translation, sensing, adaptation, biochemical patterning, and force generation. While biological systems such as motor enzymes violate detailed balance at the molecular scale, it remains unclear how non-equilibrium dynamics manifests at the mesoscale in systems that are driven through the collective activity of many motors. Indeed, in several cellular systems the presence of non-equilibrium dynamics is not always evident at large scales. For example, in the cytoskeleton or in chromosomes one can observe stationary stochastic processes that appear at first glance thermally driven. This raises the question how non-equilibrium fluctuations can be discerned from thermal noise. We discuss approaches that have recently been developed to address this question, including methods based on measuring the extent to which the system violates the fluctuation-dissipation theorem. We also review applications of this approach to reconstituted cytoskeletal networks, the cytoplasm of living cells, and cell membranes. Furthermore, we discuss a more recent approach to detect actively driven dynamics, which is based on inferring broken detailed balance. This constitutes a non-invasive method that uses time-lapse microscopy data, and can be applied to a broad range of systems in cells and tissue. We discuss the ideas underlying this method and its application to several examples including flagella, primary cilia, and cytoskeletal networks. Finally, we briefly discuss recent developments in stochastic thermodynamics and non-equilibrium statistical mechanics, which offer new perspectives to understand the physics of living systems.

https://iopscience.iop.org/article/10.1088/1361-6633/aab3ed/pdf

Broken detailed balance and non-equilibrium dynamics in living systems: a review

The membranes of red blood cells exhibit a flickering motion that has long been ascribed a thermal origin. Microrheology experiments provide direct evidence that flickering is an active process characterized by non-equilibrium dynamics.

Shape fluctuations of lipid membranes have intrigued cell biologists and physicists alike. In the cellular context, their origin-thermal or active-and their physiological significance are open questions. These small incessant displacements, also called membrane undulations, have mostly been studied in model membranes and membranes of simple cells like erythrocytes. Thermal fluctuations of such membranes have been very well described both theoretically and experimentally; active fluctuations are a topic of current interest. Experimentally, membrane fluctuations are not easy to measure, the main challenge being to develop techniques which are capable of measuring very small displacements at very high speed, and preferably over a large area and long time. Scattering techniques have given access to fluctuations in membrane stacks and a variety of optical microscopy based techniques have been devised to study membrane fluctuations of unilamellar vesicles, erythrocytes and other cells. Among them are flicker spectroscopy, dynamic light scattering, diffraction phase microscopy and reflection interference contrast microscopy. Each of these techniques has its advantages and limitations. Here we review the basic principles of the major experimental techniques used to measure bending or shape fluctuations of biomembranes. We report seminal results obtained with each technique and highlight how these studies furthered our understanding of physical properties of membranes and their interactions. We also discuss suggested role of membrane fluctuations in different biological processes.

https://iopscience.iop.org/article/10.1088/0022-3727/49/24/243002/pdf

Measuring shape fluctuations in biological membranes

Living systems operate far from thermodynamic equilibrium. Enzymatic activity can induce broken detailed balance at the molecular scale. This molecular scale breaking of detailed balance is crucial to achieve biological functions such as high-fidelity transcription and translation, sensing, adaptation, biochemical patterning, and force generation. While biological systems such as motor enzymes violate detailed balance at the molecular scale, it remains unclear how non-equilibrium dynamics manifests at the mesoscale in systems that are driven through the collective activity of many motors. Indeed, in several cellular systems the presence of non-equilibrium dynamics is not always evident at large scales. For example, in the cytoskeleton or in chromosomes one can observe stationary stochastic processes that appear at first glance thermally driven. This raises the question how non-equilibrium fluctuations can be discerned from thermal noise. We discuss approaches that have recently been developed to address this question, including methods based on measuring the extent to which the system violates the fluctuation-dissipation theorem. Furthermore, we discuss a more recent approach to detect actively driven dynamics, which is based on inferring broken detailed balance. This constitutes a non-invasive method that uses time-lapse microscopy data, and can be applied to a broad range of systems in cells and tissue. We discuss the ideas underlying this method and its application to several examples including flagella, primary cilia, and cytoskeletal networks. Finally, we briefly discuss recent developments in stochastic thermodynamics and non-equilibrium statistical mechanics, which offer new perspectives to understand the physics of living systems.

Broken detailed balance and non-equilibrium dynamics in living systems

Stochastic displacements or fluctuations of biological membranes are increasingly recognized as an important aspect of many physiological processes, but hitherto their precise quantification in living cells was limited due to a lack of tools to accurately record them. Here we introduce a novel technique--dynamic optical displacement spectroscopy (DODS), to measure stochastic displacements of membranes with unprecedented combined spatiotemporal resolution of 20 nm and 10 μs. The technique was validated by measuring bending fluctuations of model membranes. DODS was then used to explore the fluctuations in human red blood cells, which showed an ATP-induced enhancement of non-Gaussian behaviour. Plasma membrane fluctuations of human macrophages were quantified to this accuracy for the first time. Stimulation with a cytokine enhanced non-Gaussian contributions to these fluctuations. Simplicity of implementation, and high accuracy make DODS a promising tool for comprehensive understanding of stochastic membrane processes.

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Cornelia Monzel

Papers

Measuring fast stochastic displacements of bio-membranes with dynamic optical displacement spectroscopy