Flicker in erythrocytes. II. Results of experimental studies

The phenomenon of stochastic low-frequency oscillations of erythrocyte cell membrane, termed usually the flicker of erythrocytes, is reviewed. The first part [Biol. Membrany (Rus.), 2009, vol. 26, no. 5, pp. 352–369] describes theoretical models of erythrocyte flickering and the registration techniques. In the second part presented below the main experimental results are reviewed, the problem of identification of acting mechanisms of flicker excitation is analyzed, and flicker interrelations are considered with the membrane functioning as well as with the dynamics of proteins embedded in the membrane. The possibilities and the prospects of medical diagnostics applications of flicker of erythrocytes are discussed briefly.     

Linking flickering to waves and whole-cell oscillations in a mitochondrial network model

It has been shown that transient single mitochondrial depolarizations, known as flickers, tend to occur randomly in space and time. On the other hand, many studies have shown that mitochondrial depolarization waves and whole-cell oscillations occur under oxidative stress. How single mitochondrial flickering events and whole-cell oscillations are mechanistically linked remains unclear. In this study, we developed a Markov model of the inner membrane anion channel in which reactive-oxidative-species (ROS)-induced opening of the inner membrane anion channel causes transient mitochondrial depolarizations in a single mitochondrion that occur in a nonperiodic manner, simulating flickering. We then coupled the individual mitochondria into a network, in which flickers occur randomly and sparsely when a small number of mitochondria are in the state of high superoxide production. As the number of mitochondria in the high-superoxide-production state increases, short-lived or abortive waves due to ROS-induced ROS release coexist with flickers. When the number of mitochondria in the high-superoxide-production state reaches a critical number, recurring propagating waves are observed. The origins of the waves occur randomly in space and are self-organized as a consequence of random flickering and local synchronization. We show that at this critical state, the depolarization clusters exhibit a power-law distribution, a signature of self-organized criticality. In addition, the whole-cell mitochondrial membrane potential changes from exhibiting small random fluctuations to more periodic oscillations as the superoxide production rate increases. These simulation results may provide mechanistic insight into the transition from random mitochondrial flickering to the waves and whole-cell oscillations observed in many experimental studies.     

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.     

Rapid local oscillations of the surface of the human erythrocyte

The transverse displacements of the human erythrocyte surface with amplitude 300-400 nm in the frequency range 0.2-30 Hz are recorded on the minimal area erythrocyte rim (approximately 0.5 X 0.5 microns). These local oscillations of the surface are diminished at hypoosmotic erythrocyte swelling, on addition of substances which increase the membrane rigidity (0.01% glutaraldehyde, 0.5 mM 4-hydroxymercuribenzoate, cell membrane stain--0.002% Heliogen Blue) and on discocyte--echinocyte transformation due to addition of 1-2 mM 2,4-dinitrophenol. The amplitude of transverse displacements is reduced by 1.7-2 times on erythrocytes of patients with inherent microspherocytosis. These erythrocytes have inherent defects in spectrin. It is suggested that spectrin is important for rapid local oscillations of the human erythrocyte surface.     

Spontaneous and forced oscillations of cell membrane of normal human erythrocytes: absence of resonance frequencies in a range of 0.03-500 Hz

The spectra of natural oscillations of human erythrocyte cell membranes were studied experimentally and theoretically. The measurements were carried out at room temperature for both single normal cells and erythrocyte rouleaux in a range of 0.03-500 Hz. The spectra were measured at a resolution better than 1% using two techniques: registration of spontaneous membrane oscillations induced by thermal agitation in the surrounding medium and registration of the amplitude-frequency characteristics of the forced oscillations of erythrocyte elongation induced by a high-frequency electric field with the amplitude harmonic modulation. The spectra measured by both techniques had no resonance frequencies and decreased monotonically with the frequency increase. These results are confirmed by the theory developed for the extracellular excitation mechanisms of membrane oscillations. The spectra of active oscillatory biomechanical processes were measured for comparison. These processes are ciliary beating of human bronchial epithelium and ciliary beating and artificial periodic contractions of the cytoplasm of the ciliate Spirostomum ambiguum. The quality of the resonance lines of the order of 10-20 registered may serve as estimates for the line width in search of the resonance oscillations in erythrocytes induced by active cell processes.     

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.     

Cooperative binding of primycin and gramicidin on erythrocyte membranes. A cation transport study

In this paper the authors present a comparative study of the actions of the antibiotics primycin and gramicidin on the erythrocyte membrane permeability. It has been found that both antibiotics have a nonlinear effect on the membrane permeability. Above a threshold antibiotic concentration, which is characteristic of the type of the antibiotic, the cation permeability of the erythrocyte membranes increases sharply. In the range of nonlinearity the transport-kinetic curves level off before achieving the equilibrium radioactive ion distribution between the extra- and intracellular spaces. A stochastic model of the cooperative and aspecific incorporation of antibiotic molecules into the membrane explains the experimental findings. The authors conclude that membrane permeability increases at the places where two or more antibiotic molecules form aggregates in the membrane.     

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.     

Reinhart Heinrich (1946-2006): an annotated bibliography

Reinhart Heinrich contributed to many areas of theoretical biology, most notably to metabolic control analysis, a field that he helped to create, but also different aspects of modelling and to the evolution of enzyme catalysis. His interests were initially focussed on the erythrocyte, but subsequently broadened to encompass calcium oscillations, glycolytic oscillations, membrane processes and signal transduction. His publications are arranged here according to subject area, together with some introductory notes.     

On the complex dynamics of intracellular ganglion cell light responses in the cat retina

We recorded intracellular responses from cat retinal ganglion cells to sinusoidal flickering lights, and compared the response dynamics with a theoretical model based on coupled nonlinear oscillators. Flicker responses for several different spot sizes were separated in a smooth generator (G) potential and corresponding spike trains. We have previously shown that the G-potential reveals complex, stimulus-dependent, oscillatory behavior in response to sinusoidally flickering lights. Such behavior could be simulated by a modified van der Pol oscillator. In this paper, we extend the model to account for spike generation as well, by including extended Hodgkin-Huxley equations describing local membrane properties. We quantified spike responses by several parameters describing the mean and standard deviation of spike burst duration, timing (phase shift) of bursts, and the number of spikes in a burst. The dependence of these response parameters on stimulus frequency and spot size could be reproduced in great detail by coupling the van der Pol oscillator and Hodgkin-Huxley equations. The model mimics many experimentally observed response patterns, including non-phase-locked irregular oscillations. Our findings suggest that the information in the ganglion cell spike train reflects both intraretinal processing, simulated by the van der Pol oscillator, and local membrane properties described by Hodgkin-Huxley equations. The interplay between these complex processes can be simulated by changing the coupling coefficients between the two oscillators. Our simulations therefore show that irregularities in spike trains, which normally are considered to be noise, may be interpreted as complex oscillations that might carry information.To the memory of Prof. Otto-Joachim Grusser     

Variation of frequency spectrum of the erythrocyte flickering caused by aging,osmolarity, temperature and pathological changes

Frequency spectra of the surface undulations (flickering) of erythrocyte plasma membranes are measured by direct spectral analysis of the intensity fluctuations of the light passing the cells in a phase contrast microscope. Spectra are taken as a function (1) of the temperature (2) of the viscosity and osmolarity of the outer medium (3) of the aging of cells and (4) of pathological transformations. The spectra are approximately superpositions of two Lorentzian lines. At large frequencies,f, the spectra follow f^?2. This behaviour can be interpreted in terms of cell thickness fluctuations caused by thermally excited membrane undulations provided the range of wavelengths is small. The undulations are determined by the membrane curvature elasticity while the lateral tension is negligibly small for cells of discoid shape. The technique presented allows accurate measurements of relative curvature (bending) elastic constants. The spectra of freshly drawn cells are remarkably reproducible. Aging of the cells in the medium leads to an increase in the curvature elastic constant. A decrease in osmolarity causes a reduction in the intensity and line width of the spectra and the flickering vanishes if the cell approaches a spherical shape. The effect of temperature between 10 and 40°C is astonishingly small with the exception of a sudden increase in the amplitude with increasing temperature at 35°C. The flicker spectra of a large fraction of the cells from patients suffering from cronical alcoholism exhibit a reduced line width or an increase in the curvature elastic constant.     

The suppression of rapid local surface oscillations in human erythrocytes slows and weakens their adhesion to glass

Rapid local oscillations of the erythrocyte surface with amplitude 200-300 nm are decreased by 10 times following addition of wheat germ agglutinin (10(-77) M). In this case the rate of erythrocyte adhesion to the cover glass is delayed approximately by 3-9 times. The total suppression of erythrocyte surface oscillations occurs in hypo-osmic solution or in a 0.01% solution of glutaraldehyde. It coincides with a two-fold decrease of erythrocyte adhesivity to the glass. It is suggested that the rapid erythrocyte surface oscillations may control the rate of cell adhesion to the substrate.     

Protein translocation across the endoplasmic reticulum. I. Detection in the microsomal membrane of a receptor for the signal recognition particle

Thin-section and critical-point-dried fracture-labeled preparations are used to determine the distribution and partition of glycophorin- associated wheat germ agglutinin (WGA) binding sites over protoplasmic and exoplasmic faces of freeze-fractured human erythrocyte membranes. Most wheat germ agglutinin binding sites are found over exoplasmic faces. Label is sparse over the protoplasmic faces. These results contrast with previous observations of the partition of band 3 component where biochemical analysis and fracture-label of concanavalin A (Con A) binding sites show preferential partition of this transmembrane protein with the protoplasmic face. Presence of characteristic proportions of WGA and Con A binding sites over each fracture face is interpreted to indicate the operation of a stochastic process during freeze-fracture. This process appears modulated by the relative expression of each transmembrane protein at either surface as well as by their association to components of the erythrocyte membrane skeleton.     

Rapid fluctuations in transmitter release from single vesicles in bovine adrenal chromaffin cells.

Single-vesicle release of catecholamines from chromaffin cells can be detected in real time as current spikes by the electrochemical method of amperometry. About 70% of spikes are preceded by a small "foot," the trickle of transmitter out of the early fusion pore. In addition, 20-50% of foot signals exhibit rapid fluctuations that we interpret as flickering of the fusion pore. There are also "stand-alone" foot signals, which may reflect transient fusions, in which the vesicles do not collapse completely into the plasma membrane. The number and frequency of the foot flickering are affected by intracellular Ca2+ concentration.     

Different channel-gating properties of two classes of cyclic GMP-activated channel in vertebrate photoreceptors.

We report that two types of cGMP-activated channel coexist in the photoreceptor plasma membrane, with the most commonly encountered class appearing broadly similar to the channel reported in previous patch-pipette experiments. However, we find that flickering of this channel between the open and closed states is so rapid that a discrete single-channel conductance cannot unequivocally be resolved; the occurrence of flickering is largely independent of membrane voltage and of the presence of cytoplasmic Ca2+ or Mg2+. In recordings from the inner segment we occasionally find a second class of cGMP-gated channel, with activity resembling that reported for cloned channels. This channel does not flicker, but instead exhibits distinct open-close transitions. Our results suggest that the predominant form of channel in vivo differs significantly from cloned channels, and that its gating properties are not as simple as reported previously.     

Normal band 3-cytoskeletal interactions are maintained on tanktreading erythrocytes.

Normal nonnucleated erythrocytes subjected to continuous hydrodynamic shear exhibit membrane deformation or "tanktreading," a process important for reduction of the bulk viscosity of circulating blood. To characterize the effect of this unique process on the erythrocyte membrane we have measured the lateral diffusion of band 3 during tanktreading. Band 3 is normally constrained through interactions with the spectrin-actin cytoskeleton, therefore, any significant disruption of these interactions would result in alterations in band 3 dynamics. Band 3 of human erythrocytes was labeled with dichlorotriazinyl amino fluorescein. After laser photobleaching of an equatorial stripe, fluorescence images were recorded from cells in the presence or absence of shear. The amplitude of induced nonuniformity in the surface distribution of fluorescence was calculated directly from images of unsheared cells. In shear the bleached line rotated with the tanktreading motion of the cells. The surface integral of fluorescence oscillated with this motion. For this case, the amplitude of photobleaching-induced nonuniformity was defined as the amplitude at the fundamental frequency of fast Fourier transforms in time of the oscillations. Shear stress-induced membrane flow did not interrupt the linkage of band 3 with the erythrocyte cytoskeleton. Diffusion coefficient and mobile fraction (1.5 +/- 0.5 x 10(-10) cm2/s and 54 +/- 11%, respectively) were unaffected by shear. The rate of fluorescence recovery of cells in shear was also similar at the centers and at the edges, where in-plane shear forces are maximal.     

Scanning tunneling microscopy of human erythrocyte membranes.

Images of surfaces of human erythrocyte ghosts, lecithin liposomes, spectrin, erythrocyte membrane skeleton, concanavalin A and concanavalin A--decorated erythrocyte ghosts were obtained by scanning tunneling microscopy. The dimensions and surface topography of some membrane structures are described and discussed.     

A membrane model for cytosolic calcium oscillations. A study using Xenopus oocytes.

Cytosolic calcium oscillations occur in a wide variety of cells and are involved in different cellular functions. We describe these calcium oscillations by a mathematical model based on the putative electrophysiological properties of the endoplasmic reticulum (ER) membrane. The salient features of our membrane model are calcium-dependent calcium channels and calcium pumps in the ER membrane, constant entry of calcium into the cytosol, calcium dependent removal from the cytosol, and buffering by cytoplasmic calcium binding proteins. Numerical integration of the model allows us to study the fluctuations in the cytosolic calcium concentration, the ER membrane potential, and the concentration of free calcium binding sites on a calcium binding protein. The model demonstrates the physiological features necessary for calcium oscillations and suggests that the level of calcium flux into the cytosol controls the frequency and amplitude of oscillations. The model also suggests that the level of buffering affects the frequency and amplitude of the oscillations. The model is supported by experiments indirectly measuring cytosolic calcium by calcium-induced chloride currents in Xenopus oocytes as well as cytosolic calcium oscillations observed in other preparations.     

Stochastic models for circadian rhythms: effect of molecular noise on periodic and chaotic behaviour

Circadian rhythms are endogenous oscillations that occur with a period close to 24 h in nearly all living organisms. These rhythms originate from the negative autoregulation of gene expression. Deterministic models based on such genetic regulatory processes account for the occurrence of circadian rhythms in constant environmental conditions (e.g., constant darkness), for entrainment of these rhythms by light-dark cycles, and for their phase-shifting by light pulses. When the numbers of protein and mRNA molecules involved in the oscillations are small, as may occur in cellular conditions, it becomes necessary to resort to stochastic simulations to assess the influence of molecular noise on circadian oscillations. We address the effect of molecular noise by considering the stochastic version of a deterministic model previously proposed for circadian oscillations of the PER and TIM proteins and their mRNAs in Drosophila. The model is based on repression of the per and tim genes by a complex between the PER and TIM proteins. Numerical simulations of the stochastic version of the model are performed by means of the Gillespie method. The predictions of the stochastic approach compare well with those of the deterministic model with respect both to sustained oscillations of the limit cycle type and to the influence of the proximity from a bifurcation point beyond which the system evolves to stable steady state. Stochastic simulations indicate that robust circadian oscillations can emerge at the cellular level even when the maximum numbers of mRNA and protein molecules involved in the oscillations are of the order of only a few tens or hundreds. The stochastic model also reproduces the evolution to a strange attractor in conditions where the deterministic PER-TIM model admits chaotic behaviour. The difference between periodic oscillations of the limit cycle type and aperiodic oscillations (i.e. chaos) persists in the presence of molecular noise, as shown by means of Poincaré sections. The progressive obliteration of periodicity observed as the number of molecules decreases can thus be distinguished from the aperiodicity originating from chaotic dynamics. As long as the numbers of molecules involved in the oscillations remain sufficiently large (of the order of a few tens or hundreds, or more), stochastic models therefore provide good agreement with the predictions of the deterministic model for circadian rhythms.