Cell membrane fluctuations are regulated by medium macroviscosity: evidence for a metabolic driving force

Viscoelastic phenotyping of red blood cells

Red blood cells (RBCs) are the simplest cell types with complex dynamical and viscoelastic phenomenology. While the mechanical rigidity and the flickering noise of RBCs have been extensively investigated, an accurate determination of the constitutive equations of the relaxational kinetics is lacking. Here we measure the force relaxation of RBCs under different types of tensional and compressive extension-jump protocols by attaching an optically trapped bead to the RBC membrane. Relaxational kinetics follows linear response from 60 pN (tensional) to -20 pN (compressive) applied forces, exhibiting a triple exponential function with three well-separated timescales over four decades (0.01-100 s). While the fast timescale (τF∼0.02(1)s) corresponds to the relaxation of the membrane, the intermediate and slow timescales (τI=4(1)s; τS=70(8)s) likely arise from the cortex dynamics and the cytosol viscosity. Relaxation is highly heterogeneous across the RBC population, yet the three relaxation times are correlated, showing dynamical scaling. Finally, we find that glucose depletion and laser illumination of RBCs lead to faster triple exponential kinetics and RBC rigidification. Viscoelastic phenotyping is a promising dynamical biomarker applicable to other cell types and active systems.

Measuring sub-nanometer undulations at microsecond temporal resolution with metal- and graphene-induced energy transfer spectroscopy

Out-of-plane fluctuations, also known as stochastic displacements, of biological membranes play a crucial role in regulating many essential life processes within cells and organelles. Despite the availability of various methods for quantifying membrane dynamics, accurately quantifying complex membrane systems with rapid and tiny fluctuations, such as mitochondria, remains a challenge. In this work, we present a methodology that combines metal/graphene-induced energy transfer (MIET/GIET) with fluorescence correlation spectroscopy (FCS) to quantify out-of-plane fluctuations of membranes with simultaneous spatiotemporal resolution of approximately one nanometer and one microsecond. To validate the technique and spatiotemporal resolution, we measure bending undulations of model membranes. Furthermore, we demonstrate the versatility and applicability of MIET/GIET-FCS for studying diverse membrane systems, including the widely studied fluctuating membrane system of human red blood cells, as well as two unexplored membrane systems with tiny fluctuations, a pore-spanning membrane, and mitochondrial inner/outer membranes.

Non-Markovian Modeling of Nonequilibrium Fluctuations and Dissipation in Active Viscoelastic Biomatter

Based on a Hamiltonian that incorporates the elastic coupling between a tracer particle and the embedding active viscoelastic biomatter, we derive a generalized non-Markovian Langevin model for the nonequilibrium mechanical tracer response. Our analytical expressions for the frequency-dependent tracer response function and the tracer positional autocorrelation function agree quantitatively with experimental data for red blood cells and actomyosin networks with and without adenosine triphosphate over the entire frequency range and in particular reproduce the low-frequency violation of the fluctuation-dissipation theorem. The viscoelastic power laws, the elastic constants and effective friction coefficients extracted from the experimental data allow straightforward physical interpretation.

3D culture of bovine articular chondrocytes in viscous medium encapsulated in agarose hydrogels for investigation of viscosity influence on cell functions

The mechanical properties of an extracellular microenvironment can affect cell functions. The effects of elasticity and viscoelasticity on cell functions have been extensively studied with hydrogels of tunable mechanical properties. However, investigation of the viscosity effect on cell functions is still very limited and it can be tricky to explore how viscosity affects cells in three-dimensional (3D) culture due to the lack of appropriate tools. In this study, agarose hydrogel containers were prepared and used to encapsulate viscous media for 3D cell culture to investigate the viscosity effect on the functions of bovine articular chondrocytes (BACs). Polyethylene glycol of different molecular weights was used to adjust culture medium viscosity in a large range (72.8-679.2 mPa s). The viscosity affected gene expression and secretion of cartilagenious matrices, while it did not affect BAC proliferation. The BACs cultured in the lower viscosity medium (72.8 mPa s) showed a higher level of cartilaginous gene expression and matrix secretion.

A particle-based computational model to analyse remodelling of the red blood cell cytoskeleton during malaria infections

Red blood cells can withstand the harsh mechanical conditions in the vasculature only because the bending rigidity of their plasma membrane is complemented by the shear elasticity of the underlying spectrin-actin network. During an infection by the malaria parasite Plasmodium falciparum, the parasite mines host actin from the junctional complexes and establishes a system of adhesive knobs, whose main structural component is the knob-associated histidine rich protein (KAHRP) secreted by the parasite. Here we aim at a mechanistic understanding of this dramatic transformation process. We have developed a particle-based computational model for the cytoskeleton of red blood cells and simulated it with Brownian dynamics to predict the mechanical changes resulting from actin mining and KAHRP-clustering. Our simulations include the three-dimensional conformations of the semi-flexible spectrin chains, the capping of the actin protofilaments and several established binding sites for KAHRP. For the healthy red blood cell, we find that incorporation of actin protofilaments leads to two regimes in the shear response. Actin mining decreases the shear modulus, but knob formation increases it. We show that dynamical changes in KAHRP binding affinities can explain the experimentally observed relocalization of KAHRP from ankyrin to actin complexes and demonstrate good qualitative agreement with experiments by measuring pair cross-correlations both in the computer simulations and in super-resolution imaging experiments.

Malaria is one of the deadliest infectious diseases and its symptoms are related to the blood stage, when the parasite multiplies within red blood cells. In order to avoid clearance by the spleen, the parasite produces specific factors like the adhesion receptor PfEMP1 and the multifunctional protein KAHRP that lead to the formation of adhesive knobs on the surface of the red blood cells and thus increase residence time in the vasculature. We have developed a computational model for the parasite-induced remodelling of the actin-spectrin network to quantitatively predict the dynamical changes in the mechanical properties of the infected red blood cells and the spatial distribution of the different protein components of the membrane skeleton. Our simulations show that KAHRP can relocate to actin junctions due to dynamical changes in binding affinities, in good qualitative agreement with super-resolution imaging experiments. In the future, our simulation framework can be used to gain further mechanistic insight into the way malaria parasites attack the red blood cell cytoskeleton.

Quantitative absorption imaging of red blood cells to determine physical and mechanical properties

Red blood cells or erythrocytes, constituting 40 to 45 percent of the total volume of human blood are vesicles filled with hemoglobin with a fluid-like lipid bilayer membrane connected to a 2D spectrin network. The shape, volume, hemoglobin mass, and membrane stiffness of RBCs are important characteristics that influence their ability to circulate through the body and transport oxygen to tissues. In this study, we show that a simple two-LED set up in conjunction with standard microscope imaging can accurately determine the physical and mechanical properties of single RBCs. The Beer-Lambert law and undulatory motion dynamics of the membrane have been used to measure the total volume, hemoglobin mass, membrane tension coefficient, and bending modulus of RBCs. We also show that this method is sensitive enough to distinguish between the mechanical properties of RBCs during morphological changes from a typical discocyte to echinocytes and spherocytes. Measured values of the tension coefficient and bending modulus are 1.27 × 10-6 J m-2 and 7.09 × 10-2 J for discocytes, 4.80 × 10-6 J m-2 and 7.70 × 10-20 J for echinocytes, and 9.85 × 10-6 J m-2 and 9.69 × 10-20 J for spherocytes, respectively. This quantitative light absorption imaging reduces the complexity related to the quantitative imaging of the biophysical and mechanical properties of a single RBC that may lead to enhanced yet simplified point of care devices for analyzing blood cells.

Dynamics of a membrane coupled to an active fluid

The dynamics of a membrane coupled to an active fluid on top of a substrate is considered theoretically. It is assumed that the director field of the active fluid has rotational symmetry in the membrane plane. This situation is likely to be relevant for in vitro reconstructed actomyosin-membrane system. Different from a membrane coupled to a polar active fluid, this model predicts that only when the viscosity of the fluid above the membrane is sufficiently large, a contractile active fluid is able to slow down the relaxation of the membrane for perturbations with wavelength comparable to the thickness of the active fluid. Hence, our model predicts a finite-wavelength instability in the limit of strong contractility, which is different from a membrane coupled to a polar active fluid. However, a membrane coupled to an extensile active fluid is always unstable against long-wavelength perturbations due to active extensile stress enhanced membrane undulation.

Spontaneous cellular vibratory motions of osteocytes are regulated by ATP and spectrin network

Vibration at high frequency has been demonstrated to be anabolic for bone and embedded osteocytes. The response of osteocytes to vibration is frequency-dependent, but the mechanism remains unclear. Our previous computational study using an osteocyte finite element model has predicted a resonance effect involving in the frequency-dependent response of osteocytes to vibration. However, the cellular spontaneous vibratory motion of osteocytes has not been confirmed. In the present study, the cellular vibratory motions (CVM) of osteocytes were recorded by a custom-built digital holographic microscopy and quantitatively analyzed. The roles of ATP and spectrin network in the CVM of osteocytes were studied. Results showed the MLO-Y4 osteocytes displayed dynamic vibratory motions with an amplitude of ~80 nm, which is relied both on the ATP content and spectrin network. Spectrum analysis showed several frequency peaks in CVM of MLO-Y4 osteocytes at 30 Hz, 39 Hz, 83 Hz and 89 Hz. These peak frequencies are close to the commonly used effective frequencies in animal training and in-vitro cell experiments, and show a correlation with the computational predictions of the osteocyte finite element model. These results implicate that osteocytes are dynamic and the cellular dynamic motion is involved in the cellular mechanotransduction of vibration.

Erythrocyte Aging, Protection via Vesiculation: An Analysis Methodology via Oscillatory Flow

We demonstrate that erythrocyte deformations, specifically of a type as occur in splenic flow (Zhu et al., 2017), and of the type that promote vesiculation can be caused by simple, yet tailored, oscillatory shear flow. We show that such oscillatory shear flow provides an ideal environment to explore a wide variety of metabolic and biochemical effects that promote erythrocyte vesiculation. Deformation details, typical of splenic flow, such as in-folding and implications for membrane/skeleton interaction are demonstrated and quantitatively analyzed. We introduce a theoretical, essentially analytical, vesiculation model that directly couples to our more complex numerical, multilevel, model that clearly delineates various fundamental elements, i.e., sub-processes, that are involved and mediate the vesiculation process. This analytical model highlights particulary important vesiculation precursors such as areas of membrane/skeleton disruptions that trigger the vesiculation process. We demonstrate, using flow cytometry, that the deformations we experimentally induce on cells, and numerically simulate, do not induce lethal forms of cell damage but do induce vesiculation as theoretically forecasted. This, we demonstrate, provides a direct link to cell membrane/skeletal damage such as is associated with metabolic and aging damage. An additional noteworthy feature of this approach is the avoidance of artificial devices, e.g., micro-fluidic chambers, in which deformations and their time scales are often unrepresentative of physiological processes such as splenic flow.

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

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.

Do Skeletal Dynamics Mediate Sugar Uptake and Transport in Human Erythrocytes?

We explore, herein, the hypothesis that transport of molecules or ions into erythrocytes may be affected and directly stimulated by the dynamics of the spectrin/actin skeleton. Skeleton/actin motions are driven by thermal fluctuations that may be influenced by ATP hydrolysis as well as by structural alterations of the junctional complexes that connect the skeleton to the cell's lipid membrane. Specifically, we focus on the uptake of glucose into erythrocytes via glucose transporter 1 and on the kinetics of glucose disassociation at the endofacial side of glucose transporter 1. We argue that glucose disassociation is affected by both hydrodynamic forces induced by the actin/spectrin skeleton and by probable contact of the swinging 37-nm-long F-actin protofilament with glucose, an effect we dub the "stickball effect." Our hypothesis and results are interpreted within the framework of the kinetic measurements and compartmental kinetic models of Carruthers and co-workers; these experimental results and models describe glucose disassociation as the "slow step" (i.e., rate-limiting step) in the uptake process. Our hypothesis is further supported by direct simulations of skeleton-enhanced transport using our molecular-based models for the actin/spectrin skeleton as well as by experimental measurements of glucose uptake into cells subject to shear deformations, which demonstrate the hydrodynamic effects of advection. Our simulations have, in fact, previously demonstrated enhanced skeletal dynamics in cells in shear deformations, as they occur naturally within the skeleton, which is an effect also supported by experimental observations.

Atomic force microscopy: From red blood cells to immunohaematology

Atomic force microscopy (AFM) offers complementary imaging modes that can provide morphological and structural details of red blood cells (RBCs), and characterize interactions between specific biomolecules and RBC surface antigen. This review describes the applications of AFM in determining RBC health by the observation of cell morphology, elasticity and surface roughness. Measurement of interaction forces between plasma proteins and antibodies against RBC surface antigen using the AFM also brought new information to the immunohaematology field. With constant improvisation of the AFM in resolution and imaging time, the reaction of RBC to changes in the physico-chemistry of its environment and the presence of RBC surface antigen specific-biomolecules is achievable.

Accelerating metabolism and transmembrane cation flux by distorting red blood cells

Under static conditions, mammalian red blood cells (RBCs) require a continuous supply of energy, typically via glucose, to maintain their biconcave disc shape. Mechanical distortion, in a complementary way, should lead to increased energy demand that is manifest in accelerated glycolysis. The experimental challenge in observing this phenomenon was met by reversibly and reproducibly distorting the cells and noninvasively measuring glycolytic flux. This was done with a gel-distorting device that was coupled with ¹³C nuclear magnetic resonance (NMR) spectroscopy. We measured [3-¹³C]l-lactate production from [1,6-¹³C]d-glucose in the RBCs suspended in gelatin gels, and up to 90% rate enhancements were recorded. Thus, for the first time, we present experiments that demonstrate the linkage of mechanical distortion to metabolic changes in whole mammalian cells. In seeking a mechanism for the linkage between shape and energy supply, we measured transmembrane cation flux with Cs⁺ (as a K⁺ congener) using ¹³³Cs NMR spectroscopy, and the cation flux was increased up to fivefold. The postulated mechanism for these notable (in terms of whole-body energy consumption) responses is stimulation of Ca-adenosine triphosphatase by increased transmembrane flux of Ca²⁺ via the channel protein Piezo1 and increased glycolysis because its flux is adenosine triphosphate demand-regulated.

Geometric localization of thermal fluctuations in red blood cells

Cell shapes are related to their biological function. More generally, membrane morphology plays a role in the segregation and activity of transmembrane proteins. Here we show geometric implications regarding how cellular mechanics plays a role in localizing thermal fluctuations on the membrane. We show theoretically that certain geometric features of curved shells control the spatial distribution of membrane undulations. We experimentally verify this theory using discocyte red blood cells and find that geometry alone is sufficient to account for the observed spatial distribution of fluctuations. Our results, based on statistical physics and membrane elasticity, have general implications for the use of membrane shape to control thermal undulations in a variety of nanostructured materials ranging from cell membranes to graphene sheets.

The thermal fluctuations of membranes and nanoscale shells affect their mechanical characteristics. Whereas these fluctuations are well understood for flat membranes, curved shells show anomalous behavior due to the geometric coupling between in-plane elasticity and out-of-plane bending. Using conventional shallow shell theory in combination with equilibrium statistical physics we theoretically demonstrate that thermalized shells containing regions of negative Gaussian curvature naturally develop anomalously large fluctuations. Moreover, the existence of special curves, “singular lines,” leads to a breakdown of linear membrane theory. As a result, these geometric curves effectively partition the cell into regions whose fluctuations are only weakly coupled. We validate these predictions using high-resolution microscopy of human red blood cells (RBCs) as a case study. Our observations show geometry-dependent localization of thermal fluctuations consistent with our theoretical modeling, demonstrating the efficacy in combining shell theory with equilibrium statistical physics for describing the thermalized morphology of cellular membranes.

Quantum Interference and Selectivity through Biological Ion Channels

The mechanism of selectivity in ion channels is still an open question in biology for more than half a century. Here, we suggest that quantum interference can be a solution to explain the selectivity mechanism in ion channels since interference happens between similar ions through the same size of ion channels. In this paper, we simulate two neighboring ion channels on a cell membrane with the famous double-slit experiment in physics to investigate whether there is any possibility of matter-wave interference of ions via movement through ion channels. Our obtained decoherence timescales indicate that the quantum states of ions can only survive for short times, i.e. ≈100 picoseconds in each channel and ≈17-53 picoseconds outside the channels, giving the result that the quantum interference of ions seems unlikely due to environmental decoherence. However, we discuss our results and raise few points, which increase the possibility of interference.

A self-filling microfluidic device for noninvasive and time-resolved single red blood cell experiments

Existing approaches to red blood cell (RBC) experiments on the single-cell level usually rely on chemical or physical manipulations that often cause difficulties with preserving the RBC's integrity in a controlled microenvironment. Here, we introduce a straightforward, self-filling microfluidic device that autonomously separates and isolates single RBCs directly from unprocessed human blood samples and confines them in diffusion-controlled microchambers by solely exploiting their unique intrinsic properties. We were able to study the photo-induced oxygenation cycle of single functional RBCs by Raman microscopy without the limitations typically observed in optical tweezers based methods. Using bright-field microscopy, our noninvasive approach further enabled the time-resolved analysis of RBC flickering during the reversible shape evolution from the discocyte to the echinocyte morphology. Due to its specialized geometry, our device is particularly suited for studying the temporal behavior of single RBCs under precise control of their environment that will provide important insights into the RBC's biomedical and biophysical properties.

Oscillations of Bubble Shape Cause Anomalous Surfactant Diffusion: Experiments, Theory, and Simulations

We investigate, both theoretically and experimentally, the role played by the oscillations of the cell membrane on the capture rate of substances freely diffusing around the cell. To obtain quantitative results, we propose and build up a reproducible and tunable biomimetic experimental model system to simulate the phenomenon of an oscillation-enhanced (or depressed) capture rate (chemoreception) of a diffusant. The main advantage compared to real biological systems is that the different oscillation parameters (type of deformation, frequencies, and amplitudes) can be finely tuned. The model system that we use is an anchored gas drop submitted to a diffusive flow of charged surfactants. When the surfactant meets the surface of the bubble, it is reversibly adsorbed. Bubble oscillations of the order of a few nanometers are selectively excited, and surfactant transport is accurately measured. The surfactant concentration past the oscillating bubbles was detected by conductivity measurements. The results highlight the role of surface oscillations on the diffusant capture rate. Particularly unexpected is the onset of intense overshoots during the adsorption process. The phenomenon is particularly relevant when the bubbles are exposed to intense forced oscillations near resonance.

Dynamics of a membrane interacting with an active wall

Active motions of a biological membrane can be induced by nonthermal fluctuations that occur in the outer environment of the membrane. We discuss the dynamics of a membrane interacting hydrodynamically with an active wall that exerts random velocities on the ambient fluid. Solving the hydrodynamic equations of a bound membrane, we first derive a dynamic equation for the membrane fluctuation amplitude in the presence of different types of walls. Membrane two-point correlation functions are calculated for three different cases: (i) a static wall, (ii) an active wall, and (iii) an active wall with an intrinsic time scale. We focus on the mean squared displacement (MSD) of a tagged membrane describing the Brownian motion of a membrane segment. For the static wall case, there are two asymptotic regimes of MSD (∼t^{2/3} and ∼t^{1/3}) when the hydrodynamic decay rate changes monotonically. In the case of an active wall, the MSD grows linearly in time (∼t) in the early stage, which is unusual for a membrane segment. This linear-growth region of the MSD is further extended when the active wall has a finite intrinsic time scale.

Direct Cytoskeleton Forces Cause Membrane Softening in Red Blood Cells

Erythrocytes are flexible cells specialized in the systemic transport of oxygen in vertebrates. This physiological function is connected to their outstanding ability to deform in passing through narrow capillaries. In recent years, there has been an influx of experimental evidence of enhanced cell-shape fluctuations related to metabolically driven activity of the erythroid membrane skeleton. However, no direct observation of the active cytoskeleton forces has yet been reported to our knowledge. Here, we show experimental evidence of the presence of temporally correlated forces superposed over the thermal fluctuations of the erythrocyte membrane. These forces are ATP-dependent and drive enhanced flickering motions in human erythrocytes. Theoretical analyses provide support for a direct force exerted on the membrane by the cytoskeleton nodes as pulses of well-defined average duration. In addition, such metabolically regulated active forces cause global membrane softening, a mechanical attribute related to the functional erythroid deformability.

Quantification of the Influence of Endotoxins on the Mechanics of Adult and Neonatal Red Blood Cells

In this study, we physically modeled the influence of endotoxin-induced sepsis symptoms on human red blood cells (RBCs) by quantifying the impact of endotoxins on the cell mechanics by the analysis of Fourier-transformed mean square amplitude of shape fluctuation, called flicker spectroscopy. With the aid of a microfluidic diffusion chamber, we noninvasively determined principal mechanical parameters of human RBCs in the absence and presence of endotoxins for individual RBCs for the first time. Because of the elongation of saccharide chain length of endotoxins, we found an increase in the morphological transition from discocytes to echinocytes, and monotonic changes in the mechanical parameters. Since septic shocks often cause lethal risks of neonates, we measured the mechanical parameters of neonatal RBCs, and compared them to those of adult RBCs. The quantitative comparison reveals that neonatal RBCs are more susceptible to the effect of endotoxins than adult RBCs. Furthermore, coincubation with the antiseptic peptide P19-2.5 (Aspidasept) with endotoxin results in a slight suppression of the impact of the endotoxin. The strategy proposed in our study can potentially be applied for the quantitative diagnosis of RBCs based on mechanical readouts.

Membrane flickering of the human erythrocyte: constrained random walk used with Bayesian analysis

The involvement of adenosine triphosphate (ATP) in erythrocyte (red blood cell; RBC) membrane flickering is of particular interest, because ATP turnover in the cell as a whole is not yet fully accounted for. We sought the origins of flickering by deriving a mathematical model of it, on the basis of the idea of thermally driven collisions of small molecules with the membrane, which responds like an over-damped spring. The model gave simulated responses that were similar to a constrained random walk and had the same frequency-spectral characteristics of membrane displacement as those recorded from RBCs by use of differential interference contrast light microscopy. Bayesian analysis was used as the basis for determination, from experimental results, of the values of the parameters in the model. The analysis was used in the accompanying article in which we investigated the response of membrane flickering to different effector molecules and physicochemical conditions. The results implied ATP was involved only indirectly in membrane flickering.

Membrane flickering of the human erythrocyte: physical and chemical effectors

Recent studies suggest a link between adenosine triphosphate (ATP) concentration and the amplitude of cell membrane flickering (CMF) in the human erythrocyte (red blood cell; RBC). Potentially, the origin of this phenomenon and the unique discocyte shape could be active processes that account for some of the ATP turnover in the RBC. Active flickering could depend on several factors, including pH, osmolality, enzymatic rates and metabolic fluxes. In the present work, we applied the data analysis described in the previous article to study time courses of flickering RBCs acquired using differential interference contrast light microscopy in the presence of selected effectors. We also recorded images of air bubbles in aqueous detergent solutions and oil droplets in water, both of which showed rapid fluctuations in image intensity, the former showing the same type of spectral envelope (relative frequency composition) to RBCs. We conclude that CMF is not directly an active process, but that ATP affects the elastic properties of the membrane that flickers in response to molecular bombardment in a manner that is described mathematically by a constrained random walk.

Generic instabilities in a fluid membrane coupled to a thin layer of ordered active polar fluid

We develop an effective two-dimensional coarse-grained description for the coupled system of a planar fluid membrane anchored to a thin layer of polar ordered active fluid below. The macroscopic orientation of the active fluid layer is assumed to be perpendicular to the attached membrane. We demonstrate that activity or nonequilibrium drive of the active fluid makes such a system generically linearly unstable for either signature of a model parameter [Formula: see text] [Formula: see text] that characterises the strength of activity. Depending upon boundary conditions and within a range of the model parameters, underdamped propagating waves may be present in our model. We discuss the phenomenological significance of our results.

Nonequilibrium fluctuations of mechanically stretched single red blood cells detected by optical tweezers

We study the thermal and out-of-equilibrium mechanical dynamics of single, living human red blood cells (RBCs) by combining two-probe passive and active microrheology techniques. Both experiments were performed quasisimultaneously on the same cell using two identical polystyrene probes, biochemically attached to the cell membrane. We obtained compelling evidence of nonequilibrium fluctuations in the RBCs under physiological condition and without the influence of any external chemicals. The spectral distributions of metabolically driven forces and viscoelastic response were evaluated in the relaxed and stretched states, intended to simulate the varying natural environment of the cells during blood circulation. We found that the internally generated forces are more pronounced in the stretched state, suggesting a stress-dependent RBC activity.

Instabilities and diffusion in a hydrodynamic model of a fluid membrane coupled to a thin active fluid layer

We construct a coarse-grained effective two-dimensional (2d hydrodynamic theory as a theoretical model for a coupled system of a fluid membrane and a thin layer of a polar active fluid in its ordered state that is anchored to the membrane. We show that such a system is prone to generic instabilities through the interplay of nonequilibrium drive, polar order and membrane fluctuation. We use our model equations to calculate diffusion coefficients of an inclusion in the membrane and show that their values depend strongly on the system size, in contrast to their equilibrium values. Our work extends the work of S. Sankararaman and S. Ramaswamy (Phys. Rev. Lett., 102, 118107 (2009)) to a coupled system of a fluid membrane and an ordered active fluid layer. Our model is broadly inspired by and should be useful as a starting point for theoretical descriptions of the coupled dynamics of a cell membrane and a cortical actin layer anchored to it.

Effect of hydroperoxides on red blood cell membrane mechanical properties

We investigate the effect of oxidative stress on red blood cell membrane mechanical properties in vitro using detailed analysis of the membrane thermal fluctuation spectrum. Two different oxidants, the cytosol-soluble hydrogen peroxide and the membrane-soluble cumene hydroperoxide, are used, and their effects on the membrane bending elastic modulus, surface tension, strength of confinement due to the membrane skeleton, and 2D shear elastic modulus are measured. We find that both oxidants alter significantly the membrane elastic properties, but their effects differ qualitatively and quantitatively. While hydrogen peroxide mainly affects the elasticity of the membrane protein skeleton (increasing the membrane shear modulus), cumene hydroperoxide has an impact on both membrane skeleton and lipid bilayer mechanical properties, as can be seen from the increased values of the shear and bending elastic moduli. The biologically important implication of these results is that the effects of oxidative stress on the biophysical properties, and hence the physiological functions, of the cell membrane depend on the nature of the oxidative agent. Thermal fluctuation spectroscopy provides a means of characterizing these different effects, potentially in a clinical milieu.

A modified FCCS procedure applied to Ly49A-MHC class I cis-interaction studies in cell membranes

The activity of natural killer (NK) cells is regulated by a fine-tuned balance between activating and inhibitory receptors. Dual-color fluorescence cross-correlation spectroscopy (FCCS) was used to directly demonstrate a so-called cis-interaction between a member of the inhibitory NK cell receptor family Ly49 (Ly49A), and its ligand, the major histocompatibility complex (MHC) class I, within the plasma membrane of the same cell. By a refined FCCS model, calibrated by positive and negative control experiments on cells from the same lymphoid cell line, concentrations and diffusion coefficients of free and interacting proteins could be determined on a collection of cells. Using the intrinsic intercellular variation of their expression levels for titration, it was found that the fraction of Ly49A receptors bound in cis increase with increasing amounts of MHC class I ligand. This increase shows a tendency to be more abrupt than for a diffusion limited - three dimensional bimolecular reaction, which most likely reflects the two-dimensional confinement of the reaction. For the Ly49A- MHC class I interaction it indicates that within a critical concentration range the local concentration level of MHC class I can provide a distinct regulation mechanism of the NK cell activity.

Detrended fluctuation analysis of membrane flickering in discocyte and spherocyte red blood cells using quantitative phase microscopy

Dynamic analyses of vibrational motion in cell membranes provide a lot of information on the complex dynamic motilities of a red blood cell (RBC). Here, we present the correlation properties of membrane fluctuation in discocyte and spherocyte RBCs by using quantitative phase microscopy (QPM). Since QPM can provide nanometer sensitivity in thickness measurement within a millisecond time scale, we were able to observe the membrane flicking of an RBC in nanometer resolution up to the bandwidth of 50 Hz. The correlation properties of the vibrational motion were analyzed with the detrended fluctuation analysis (DFA) method. Fractal scaling exponent α in the DFA method was calculated for the vibrational motion of a cell surface at various surface points for normal discocyte and abnormal spherocyte RBCs. Measured α values for normal RBCs are distributed between 0.7 and 1.0, whereas those for abnormal spherocyte RBCs are within a range from 0.85 to 1.2. We have also verified that the vibrational motion of background fluid outside of a cell has an α value close to 0.5, which is a typical property of an uncorrelated white noise.

Effective 3D viscoelasticity of red blood cells measured by diffraction phase microscopy

We present optical measurements of nanoscale red blood cell fluctuations obtained by highly sensitive quantitative phase imaging. These spatio-temporal fluctuations are modeled in terms of the bulk viscoelastic response of the cell. Relating the displacement distribution to the storage and loss moduli of the bulk has the advantage of incorporating all geometric and cortical effects into a single effective medium behavior. The results on normal cells indicate that the viscous modulus is much larger than the elastic one throughout the entire frequency range covered by the measurement, indicating fluid behavior.

Electromagnetic cellular interactions

Chemical and electrical interaction within and between cells is well established. Just the opposite is true about cellular interactions via other physical fields. The most probable candidate for an other form of cellular interaction is the electromagnetic field. We review theories and experiments on how cells can generate and detect electromagnetic fields generally, and if the cell-generated electromagnetic field can mediate cellular interactions. We do not limit here ourselves to specialized electro-excitable cells. Rather we describe physical processes that are of a more general nature and probably present in almost every type of living cell. The spectral range included is broad; from kHz to the visible part of the electromagnetic spectrum. We show that there is a rather large number of theories on how cells can generate and detect electromagnetic fields and discuss experimental evidence on electromagnetic cellular interactions in the modern scientific literature. Although small, it is continuously accumulating.

Biophysics of magnetic orientation: strengthening the interface between theory and experimental design

The first demonstrations of magnetic effects on the behaviour of migratory birds and homing pigeons in laboratory and field experiments, respectively, provided evidence for the longstanding hypothesis that animals such as birds that migrate and home over long distances would benefit from possession of a magnetic sense. Subsequent identification of at least two plausible biophysical mechanisms for magnetoreception in animals, one based on biogenic magnetite and another on radical-pair biochemical reactions, led to major efforts over recent decades to test predictions of the two models, as well as efforts to understand the ultrastructure and function of the possible magnetoreceptor cells. Unfortunately, progress in understanding the magnetic sense has been challenged by: (i) the availability of a relatively small number of techniques for analysing behavioural responses to magnetic fields by animals; (ii) difficulty in achieving reproducible results using the techniques; and (iii) difficulty in development and implementation of new techniques that might bring greater experimental power. As a consequence, laboratory and field techniques used to study the magnetic sense today remain substantially unchanged, despite the huge developments in technology and instrumentation since the techniques were developed in the 1950s. New methods developed for behavioural study of the magnetic sense over the last 30 years include the use of laboratory conditioning techniques and tracking devices based on transmission of radio signals to and from satellites. Here we consider methodological developments in the study of the magnetic sense and present suggestions for increasing the reproducibility and ease of interpretation of experimental studies. We recommend that future experiments invest more effort in automating control of experiments and data capture, control of stimulation and full blinding of experiments in the rare cases where automation is impossible. We also propose new experiments to confirm whether or not animals can detect magnetic fields using the radical-pair effect together with an alternate hypothesis that may explain the dependence on light of responses by animals to magnetic field stimuli.

Metabolic remodeling of the human red blood cell membrane

The remarkable deformability of the human red blood cell (RBC) results from the coupled dynamic response of the phospholipid bilayer and the spectrin molecular network. Here we present quantitative connections between spectrin morphology and membrane fluctuations of human RBCs by using dynamic full-field laser interferometry techniques. We present conclusive evidence that the presence of adenosine 5'-triphosphate (ATP) facilitates non-equilibrium dynamic fluctuations in the RBC membrane that are highly correlated with the biconcave shape of RBCs. Spatial analysis of the fluctuations reveals that these non-equilibrium membrane vibrations are enhanced at the scale of spectrin mesh size. Our results indicate that the dynamic remodeling of the coupled membranes powered by ATP results in non-equilibrium membrane fluctuations manifesting from both metabolic and thermal energies and also maintains the biconcave shape of RBCs.

Flickering analysis of erythrocyte mechanical properties: dependence on oxygenation level, cell shape, and hydration level

Erythrocytes (red blood cells) play an essential role in the respiratory functions of vertebrates, carrying oxygen from lungs to tissues and CO(2) from tissues to lungs. They are mechanically very soft, enabling circulation through small capillaries. The small thermally induced displacements of the membrane provide an important tool in the investigation of the mechanics of the cell membrane. However, despite numerous studies, uncertainties in the interpretation of the data, and in the values derived for the main parameters of cell mechanics, have rendered past conclusions from the fluctuation approach somewhat controversial. Here we revisit the experimental method and theoretical analysis of fluctuations, to adapt them to the case of cell contour fluctuations, which are readily observable experimentally. This enables direct measurements of membrane tension, of bending modulus, and of the viscosity of the cell cytoplasm. Of the various factors that influence the mechanical properties of the cell, we focus here on: 1), the level of oxygenation, as monitored by Raman spectrometry; 2), cell shape; and 3), the concentration of hemoglobin. The results show that, contrary to previous reports, there is no significant difference in cell tension and bending modulus between oxygenated and deoxygenated states, in line with the softness requirement for optimal circulatory flow in both states. On the other hand, tension and bending moduli of discocyte- and spherocyte-shaped cells differ markedly, in both the oxygenated and deoxygenated states. The tension in spherocytes is much higher, consistent with recent theoretical models that describe the transitions between red blood cell shapes as a function of membrane tension. Cell cytoplasmic viscosity is strongly influenced by the hydration state. The implications of these results to circulatory flow dynamics in physiological and pathological conditions are discussed.

ATP-dependent mechanics of red blood cells

Red blood cells are amazingly deformable structures able to recover their initial shape even after large deformations as when passing through tight blood capillaries. The reason for this exceptional property is found in the composition of the membrane and the membrane-cytoskeleton interaction. We investigate the mechanics and the dynamics of RBCs by a unique noninvasive technique, using weak optical tweezers to measure membrane fluctuation amplitudes with mus temporal and sub nm spatial resolution. This enhanced edge detection method allows to span over >4 orders of magnitude in frequency. Hence, we can simultaneously measure red blood cell membrane mechanical properties such as bending modulus kappa = 2.8 +/- 0.3 x 10(-19)J = 67.6 +/- 7.2 k(B)T, tension sigma = 6.5 +/- 2.1 x 10(-7)N/m, and an effective viscosity eta(eff) = 81 +/- 3.7 x 10(-3) Pa s that suggests unknown dissipative processes. We furthermore show that cell mechanics highly depends on the membrane-spectrin interaction mediated by the phosphorylation of the interconnection protein 4.1R. Inhibition and activation of this phosphorylation significantly affects tension and effective viscosity. Our results show that on short time scales (slower than 100 ms) the membrane fluctuates as in thermodynamic equilibrium. At time scales longer than 100 ms, the equilibrium description breaks down and fluctuation amplitudes are higher by 40% than predicted by the membrane equilibrium theory. Possible explanations for this discrepancy are influences of the spectrin that is not included in the membrane theory or nonequilibrium fluctuations that can be accounted for by defining a nonthermal effective energy of up to E(eff) = 1.4 +/- 0.1 k(B)T, that corresponds to an actively increased effective temperature.

Spatial analysis of erythrocyte membrane fluctuations by digital holographic microscopy

Red blood cell (RBC) membrane fluctuations provide important insights into cell states. We present a spatial analysis of red blood cell membrane fluctuations by using digital holographic microscopy (DHM). This interferometric and dye-free technique, possessing nanometric axial and microsecond temporal sensitivities enables to measure cell membrane fluctuations (CMF) on the whole cell surface. DHM acquisition is combined with a model which allows extracting the membrane fluctuation amplitude, while taking into account cell membrane topology. Uneven distribution of CMF amplitudes over the RBC surface is observed, showing maximal values in a ring corresponding to the highest points on the RBC torus as well as in some scattered areas in the inner region of the RBC. CMF amplitudes of 35.9+/-8.9 nm and 4.7+/-0.5 nm (averaged over the cell surface) were determined for normal and ethanol-fixed RBCs, respectively.

Cytoskeleton mediated effective elastic properties of model red blood cell membranes

The plasma membrane of human red blood cells consists of a lipid bilayer attached to a regular network of underlying cytoskeletal polymers. We model this system at a dynamic coarse-grained level, treating the bilayer as an elastic sheet and the cytoskeletal network as a series of phantom entropic springs. In contrast to prior simulation efforts, we explicitly account for dynamics of the cytoskeletal network, both via motion of the protein anchors that attach the cytoskeleton to the bilayer and through breaking and reconnection of individual cytoskeletal filaments. Simulation results are explained in the context of a simple mean field percolation model and comparison is made to experimental measurements of red blood cell fluctuation amplitudes.

Functional coupling of TRPV4 cationic channel and large conductance, calcium-dependent potassium channel in human bronchial epithelial cell lines

Calcium-dependent potassium channels are implicated in electrolyte transport, cell volume regulation and mechanical responses in epithelia, although the pathways for calcium entry and their coupling to the activation of potassium channels are not fully understood. We now show molecular evidence for the presence of TRPV4, a calcium permeable channel sensitive to osmotic and mechanical stress, and its functional coupling to the large conductance calcium-dependent potassium channel (BK(Ca)) in a human bronchial epithelial cell line (HBE). Reverse transcriptase polymerase chain reaction, intracellular calcium imaging and whole-cell patch-clamp experiments using HBE cells demonstrated the presence of TRPV4 messenger and Ca(2+) entry, and outwardly rectifying cationic currents elicited by the TRPV4 specific activator 4alpha-phorbol 12,13-didecanoate (4alphaPDD). Cell-attached and whole-cell patch-clamp of HBE cells exposed to 4alphaPDD, and hypotonic and high-viscosity solutions (related to mechanical stress) revealed the activation of BK(Ca) channels subsequent to extracellular Ca(2+) influx via TRPV4, an effect lost upon antisense-mediated knock-down of TRPV4. Further analysis of BK(Ca) modulation after TRPV4 activation showed that the Ca(2+) signal can be generated away from the BK(Ca) location at the plasma membrane, and it is not mediated by intracellular Ca(2+) release via ryanodine receptors. Finally, we have shown that, unlike the reported disengagement of TRPV4 and BK(Ca) in response to hypotonic solutions, cystic fibrosis bronchial epithelial cells (CFBE) preserve the functional coupling of TRPV4 and BK(Ca) in response to high-viscous solutions.

IP3 sensitizes TRPV4 channel to the mechano- and osmotransducing messenger 5'-6'-epoxyeicosatrienoic acid

Mechanical and osmotic sensitivity of the transient receptor potential vanilloid 4 (TRPV4) channel depends on phospholipase A₂ (PLA₂) activation and the subsequent production of the arachidonic acid metabolites, epoxyeicosatrienoic acid (EET). We show that both high viscous loading and hypotonicity stimuli in native ciliated epithelial cells use PLA₂–EET as the primary pathway to activate TRPV4. Under conditions of low PLA₂ activation, both also use extracellular ATP-mediated activation of phospholipase C (PLC)–inositol trisphosphate (IP₃) signaling to support TRPV4 gating. IP₃, without being an agonist itself, sensitizes TRPV4 to EET in epithelial ciliated cells and cells heterologously expressing TRPV4, an effect inhibited by the IP₃ receptor antagonist xestospongin C. Coimmunoprecipitation assays indicated a physical interaction between TRPV4 and IP₃ receptor 3. Collectively, our study suggests a functional coupling between plasma membrane TRPV4 channels and intracellular store Ca²⁺ channels required to initiate and maintain the oscillatory Ca²⁺ signal triggered by high viscosity and hypotonic stimuli that do not reach a threshold level of PLA₂ activation.

An image-processing technique for measuring the dynamic movement of cell membranes

An automated method has been developed to measure and compare the dynamic movement of cell membranes. Using the red blood cell as a common example the method locates the edge of the cell, with sub-pixel precision at multiple points on the periphery. This method is a different implementation to a technique used for giant unilamellar vesicles and addresses issues relating specifically to biological cells, in particular relating to finding a local minima, calculating equi-spaced measuring points for arbitrary shapes and using the perpendicular direction to the edge for position measurement. Parameters have been defined to characterise the cell's membrane behaviour and the analysis program allows the automatic compilation of multiple tests under varying conditions, and statistical comparison of identical populations of cells.

Fluctuations of the red blood cell membrane: relation to mechanical properties and lack of ATP dependence

We have analyzed the fluctuations of the red blood cell membrane in both the temporal ((omega(s(-1))) and spatial (q(m(-1))) frequency domains. The cells were examined over a range of osmolarities leading to cell volumes from 50% to 170% of that in the isotonic state. The fluctuations of the isotonic cell showed an approximately q(-3)-dependence, indicative of a motion dominated by bending, with an inferred bending modulus of approximately 9 x 10(-19) J. When the cells were osmotically swollen to just below the point of lysis (166% of physiological volume), a q(-1)-dependence of the fluctuations supervened, implying that the motion was now dominated by membrane tension; estimated as approximately 1.3 x 10(-4) nm(-1). When, on the other hand, the cells were osmotically dehydrated, the fluctuation amplitude progressively decreased. This was caused by a rise in internal viscosity, as shown by measurements on resealed ghosts containing a reduced hemoglobin concentration, which displayed no such effect. We examined, in addition, cells depleted of ATP, before the onset of echinocytosis, and could observe no change in fluctuation amplitude. We conclude that the membrane fluctuations of the red cell are governed by bending modulus, membrane tension, and cytosolic viscosity, with little or no dependence on the presence or absence of ATP.

Coherence properties of red blood cell membrane motions

We use a highly sensitive, noncontact, optical interferometric technique to quantify the red blood cell membrane fluctuations at the nanometer and millisecond scales. The results reveal significant properties of both temporal and spatial coherence associated with the membrane dynamics. We show that these correlations can be accounted for by the viscoelastic properties of the cell membrane. From this measurement, we extract the loss and storage moduli associated with the membrane and find a crossover frequency at which the buffer viscosity seems to become dominant.

Tether extrusion from red blood cells: integral proteins unbinding from cytoskeleton

We investigate the mechanical strength of adhesion and the dynamics of detachment of the membrane from the cytoskeleton of red blood cells (RBCs). Using hydrodynamical flows, we extract membrane tethers from RBCs locally attached to the tip of a microneedle. We monitor their extrusion and retraction dynamics versus flow velocity (i.e., extrusion force) over successive extrusion-retraction cycles. Membrane tether extrusion is carried out on healthy RBCs and ATP-depleted or -inhibited RBCs. For healthy RBCs, extrusion is slow, constant in velocity, and reproducible through several extrusion-retraction cycles. For ATP-depleted or -inhibited cells, extrusion dynamics exhibit an aging phenomenon through extrusion-retraction cycles: because the extruded membrane is not able to retract properly onto the cell body, each subsequent extrusion exhibits a loss of resistance to tether growth over the tether length extruded at the previous cycle. In contrast, the additionally extruded tether length follows healthy dynamics. The extrusion velocity L depends on the extrusion force f according to a nonlinear fashion. We interpret this result with a model that includes the dynamical feature of membrane-cytoskeleton association. Tether extrusion leads to a radial membrane flow from the cell body toward the tether. In a distal permeation regime, the flow passes through the integral proteins bound to the cytoskeleton without affecting their binding dynamics. In a proximal sliding regime, where membrane radial velocity is higher, integral proteins can be torn out, leading to the sliding of the membrane over the cytoskeleton. Extrusion dynamics are governed by the more dissipative permeation regime: this leads to an increase of the membrane tension and a narrowing of the tether, which explains the power law behavior of L(f). Our main result is that ATP is necessary for the extruded membrane to retract onto the cell body. Under ATP depletion or inhibition conditions, the aging of the RBC after extrusion is interpreted as a perturbation of membrane-cytoskeleton linkage dynamics.

Active elastic network: cytoskeleton of the red blood cell

In red blood cells there is a cortical cytoskeleton; a two-dimensional elastic network of membrane-attached proteins. We describe, using a simple model, how the metabolic activity of the cell, through the consumption of ATP, controls the stiffness of this elastic network. The unusual mechanical property of active strain softening is described and compared to experimental data. As a by-product of this activity there is also an active contribution to the amplitude of membrane fluctuations. We model this membrane as a field of independent "curvature motors," and calculate the spectrum of active fluctuations. We find that the active cytoskeleton contributes to the amplitude of the membrane height fluctuations at intermediate wavelengths, as observed experimentally.

Molecular rotors—fluorescent biosensors for viscosity and flow

Viscosity is a measure of the resistance of a fluid against gradients in flow (shear rate). Both flow and viscosity play an important role in all biological systems from the microscopic (e.g., cellular) to the systemic level. Many methods to measure viscosity and flow have drawbacks, such as the tedious and time-consuming measurement process, expensive instrumentation, or the restriction to bulk sample sizes. Fluorescent environment-sensitive dyes are known to show high sensitivity and high spatial and temporal resolution. Molecular rotors are a group of fluorescent molecules that form twisted intramolecular charge transfer (TICT) states upon photoexcitation and therefore exhibit two competing deexcitation pathways: fluorescence emission and non-radiative deexcitation from the TICT state. Since TICT formation is viscosity-dependent, the emission intensity of molecular rotors depends on the solvent's viscosity. Furthermore, shear-stress dependency of the emission intensity was recently described. Although the photophysical processes are widely explored, the practical application of molecular rotors as sensors for viscosity and the fluid flow introduce additional challenges. Intensity-based measurements are influenced by fluid optical properties and dye concentration, and solvent-dye interaction requires calibration of the measurement system to a specific solvent. Ratiometric dyes and measurement systems help solve these challenges. In addition, the combination of molecular rotors with specific recognition groups allows them to target specific sites, for example the cell membrane or cytoplasm. Molecular rotors are therefore emerging as new biosensors for both bulk and local microviscosity, and for flow and fluid shear stress on a microscopic scale and with real-time response.