Complex dynamics of human red blood cell flickering: alterations with in vivo aging

Red blood cell flickering activity locally controlled by holographic optical tweezers

Red blood cells possess a singular mechanobiology, enabling efficient navigation through capillaries smaller than their own size. Their plasma membrane exhibits non-equilibrium shape fluctuation, often reported as enhanced flickering activity. Such active membrane motion is propelled by motor proteins that mediate interactions between the spectrin skeleton and the lipid bilayer. However, modulating the flickering in living red blood cells without permanently altering their mechanical properties represents a significant challenge. In this study, we developed holographic optical tweezers to generate a force field distributed along the equatorial membrane contour of individual red blood cells. In free-standing red blood cells, we observed heterogeneous flickering activity, attributed to localized membrane kickers. By employing holographic optical forces, these active kickers can be selectively halted under minimal invasion. Our findings shed light on the dynamics of membrane flickering and established a manipulation tool that could open new avenues for investigating mechanotransduction processes in living cells.

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.

Impact of prolonged chronic social isolation stress on behavior and multifractal complexity of metabolic rate in Octodon degus

Social interaction can improve animal performance through the prevention of stress-related events, the provision of security, and the enhancement of reproductive output and survival. We investigated the effects of prolonged chronic social isolation stress on behavioral, cognitive, and physiological performance in the social, long-lived rodent Octodon degus. Degu pups were separated into two social stress treatments: control (CTRL) and chronically isolated (CI) individuals from post-natal and post-weaning until adulthood. We quantified anxiety-like behavior and cognitive performance with a battery of behavioral tests. Additionally, we measured their basal metabolic rate (BMR) and analyzed the multifractal properties of the oxygen consumption time series using Multifractal Detrended Fluctuation Analysis, a well-known method for assessing the fractal characteristics of biological signals. Our results showed that CI induced a significant increase in anxiety-like behaviors and led to a reduction in social and working memory in male degus. In addition, CI-treated degus reduced the multifractal complexity of BMR compared to CTRL, which implies a decrease in the ability to respond to environmental stressors and, as a result, an unhealthy state. In contrast, we did not observe significant effects of social stress on BMR. Multivariate analyses showed a clear separation of behavior and physiological variables into two clusters, corresponding to CI and CTRL degus. This study provides novel insights into the effects of prolonged chronic social isolation stress on behavior, cognitive performance, and metabolic complexity in this rodent animal model. To the best of our knowledge, it is the first study to integrate cognitive-behavioral performance and multifractal dynamics of a physiological signal in response to prolonged social isolation. These findings highlight the importance of social interactions for the well-being and overall performance of social animals.

Complexity and Entropy in Physiological Signals (CEPS): Resonance Breathing Rate Assessed Using Measures of Fractal Dimension, Heart Rate Asymmetry and Permutation Entropy

BACKGROUND

As technology becomes more sophisticated, more accessible methods of interpretating Big Data become essential. We have continued to develop Complexity and Entropy in Physiological Signals (CEPS) as an open access MATLAB® GUI (graphical user interface) providing multiple methods for the modification and analysis of physiological data.

METHODS

To demonstrate the functionality of the software, data were collected from 44 healthy adults for a study investigating the effects on vagal tone of breathing paced at five different rates, as well as self-paced and un-paced. Five-minute 15-s recordings were used. Results were also compared with those from shorter segments of the data. Electrocardiogram (ECG), electrodermal activity (EDA) and Respiration (RSP) data were recorded. Particular attention was paid to COVID risk mitigation, and to parameter tuning for the CEPS measures. For comparison, data were processed using Kubios HRV, RR-APET and DynamicalSystems.jl software. We also compared findings for ECG RR interval (RRi) data resampled at 4 Hz (4R) or 10 Hz (10R), and non-resampled (noR). In total, we used around 190-220 measures from CEPS at various scales, depending on the analysis undertaken, with our investigation focused on three families of measures: 22 fractal dimension (FD) measures, 40 heart rate asymmetries or measures derived from Poincaré plots (HRA), and 8 measures based on permutation entropy (PE).

RESULTS

FDs for the RRi data differentiated strongly between breathing rates, whether data were resampled or not, increasing between 5 and 7 breaths per minute (BrPM). Largest effect sizes for RRi (4R and noR) differentiation between breathing rates were found for the PE-based measures. Measures that both differentiated well between breathing rates and were consistent across different RRi data lengths (1-5 min) included five PE-based (noR) and three FDs (4R). Of the top 12 measures with short-data values consistently within ± 5% of their values for the 5-min data, five were FDs, one was PE-based, and none were HRAs. Effect sizes were usually greater for CEPS measures than for those implemented in DynamicalSystems.jl.

CONCLUSION

The updated CEPS software enables visualisation and analysis of multichannel physiological data using a variety of established and recently introduced complexity entropy measures. Although equal resampling is theoretically important for FD estimation, it appears that FD measures may also be usefully applied to non-resampled data.

Multiscale Entropy Analysis of Heart Rate Variability in Neonatal Patients with and without Seizures

The complex physiological dynamics of neonatal seizures make their detection challenging. A timely diagnosis and treatment, especially in intensive care units, are essential for a better prognosis and the mitigation of possible adverse effects on the newborn's neurodevelopment. In the literature, several electroencephalographic (EEG) studies have been proposed for a parametric characterization of seizures or their detection by artificial intelligence techniques. At the same time, other sources than EEG, such as electrocardiography, have been investigated to evaluate the possible impact of neonatal seizures on the cardio-regulatory system. Heart rate variability (HRV) analysis is attracting great interest as a valuable tool in newborns applications, especially where EEG technologies are not easily available. This study investigated whether multiscale HRV entropy indexes could detect abnormal heart rate dynamics in newborns with seizures, especially during ictal events. Furthermore, entropy measures were analyzed to discriminate between newborns with seizures and seizure-free ones. A cohort of 52 patients (33 with seizures) from the Helsinki University Hospital public dataset has been evaluated. Multiscale sample and fuzzy entropy showed significant differences between the two groups (p-value < 0.05, Bonferroni multiple-comparison post hoc correction). Moreover, interictal activity showed significant differences between seizure and seizure-free patients (Mann-Whitney Test: p-value < 0.05). Therefore, our findings suggest that HRV multiscale entropy analysis could be a valuable pre-screening tool for the timely detection of seizure events in newborns.

Attenuation of thermoacoustic combustion oscillations in a swirl-stabilized turbulent combustor

We experimentally study the attenuation behavior of thermoacoustic combustion oscillations using causality analysis, multiscale randomness analysis, and a complex network. We supply a steady air jet from the injector rim to suppress combustion oscillations. The directional coupling between pressure and heat release rate fluctuations is significantly weakened during the suppression of combustion oscillations. The loss of the primary hub in the turbulence network plays an important role in the degeneration of combustion oscillations.

Brain Entropy During Aging Through a Free Energy Principle Approach

Neural complexity and brain entropy (BEN) have gained greater interest in recent years. The dynamics of neural signals and their relations with information processing continue to be investigated through different measures in a variety of noteworthy studies. The BEN of spontaneous neural activity decreases during states of reduced consciousness. This evidence has been showed in primary consciousness states, such as psychedelic states, under the name of "the entropic brain hypothesis." In this manuscript we propose an extension of this hypothesis to physiological and pathological aging. We review this particular facet of the complexity of the brain, mentioning studies that have investigated BEN in primary consciousness states, and extending this view to the field of neuroaging with a focus on resting-state functional Magnetic Resonance Imaging. We first introduce historic and conceptual ideas about entropy and neural complexity, treating the mindbrain as a complex nonlinear dynamic adaptive system, in light of the free energy principle. Then, we review the studies in this field, analyzing the idea that the aim of the neurocognitive system is to maintain a dynamic state of balance between order and chaos, both in terms of dynamics of neural signals and functional connectivity. In our exploration we will review studies both on acute psychedelic states and more chronic psychotic states and traits, such as those in schizophrenia, in order to show the increase of entropy in those states. Then we extend our exploration to physiological and pathological aging, where BEN is reduced. Finally, we propose an interpretation of these results, defining a general trend of BEN in primary states and cognitive aging.

CEPS: An Open Access MATLAB Graphical User Interface (GUI) for the Analysis of Complexity and Entropy in Physiological Signals

BACKGROUND

We developed CEPS as an open access MATLAB^® GUI (graphical user interface) for the analysis of Complexity and Entropy in Physiological Signals (CEPS), and demonstrate its use with an example data set that shows the effects of paced breathing (PB) on variability of heart, pulse and respiration rates. CEPS is also sufficiently adaptable to be used for other time series physiological data such as EEG (electroencephalography), postural sway or temperature measurements.

METHODS

Data were collected from a convenience sample of nine healthy adults in a pilot for a larger study investigating the effects on vagal tone of breathing paced at various different rates, part of a development programme for a home training stress reduction system.

RESULTS

The current version of CEPS focuses on those complexity and entropy measures that appear most frequently in the literature, together with some recently introduced entropy measures which may have advantages over those that are more established. Ten methods of estimating data complexity are currently included, and some 28 entropy measures. The GUI also includes a section for data pre-processing and standard ancillary methods to enable parameter estimation of embedding dimension m and time delay τ ('tau') where required. The software is freely available under version 3 of the GNU Lesser General Public License (LGPLv3) for non-commercial users. CEPS can be downloaded from Bitbucket. In our illustration on PB, most complexity and entropy measures decreased significantly in response to breathing at 7 breaths per minute, differentiating more clearly than conventional linear, time- and frequency-domain measures between breathing states. In contrast, Higuchi fractal dimension increased during paced breathing.

CONCLUSIONS

We have developed CEPS software as a physiological data visualiser able to integrate state of the art techniques. The interface is designed for clinical research and has a structure designed for integrating new tools. The aim is to strengthen collaboration between clinicians and the biomedical community, as demonstrated here by using CEPS to analyse various physiological responses to paced breathing.

The dynamics of plant nutation

In this article we advance a cutting-edge methodology for the study of the dynamics of plant movements of nutation. Our approach, unlike customary kinematic analyses of shape, period, or amplitude, is based on three typical signatures of adaptively controlled processes and motions, as reported in the biological and behavioral dynamics literature: harmonicity, predictability, and complexity. We illustrate the application of a dynamical methodology to the bending movements of shoots of common beans (Phaseolus vulgaris L.) in two conditions: with and without a support to climb onto. The results herewith reported support the hypothesis that patterns of nutation are influenced by the presence of a support to climb in their vicinity. The methodology is in principle applicable to a whole range of plant movements.

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.

MYH9-related disease mutations cause abnormal red blood cell morphology through increased myosin-actin binding at the membrane

MYH9-related disease (MYH9-RD) is a rare, autosomal dominant disorder caused by mutations in MYH9, the gene encoding the actin-activated motor protein non-muscle myosin IIA (NMIIA). MYH9-RD patients suffer from bleeding syndromes, progressive kidney disease, deafness, and/or cataracts, but the impact of MYH9 mutations on other NMIIA-expressing tissues remains unknown. In human red blood cells (RBCs), NMIIA assembles into bipolar filaments and binds to actin filaments (F-actin) in the spectrin-F-actin membrane skeleton to control RBC biconcave disk shape and deformability. Here, we tested the effects of MYH9 mutations in different NMIIA domains (motor, coiled-coil rod, or non-helical tail) on RBC NMIIA function. We found that MYH9-RD does not cause clinically significant anemia and that patient RBCs have normal osmotic deformability as well as normal membrane skeleton composition and micron-scale distribution. However, analysis of complete blood count data and peripheral blood smears revealed reduced hemoglobin content and elongated shapes, respectively, of MYH9-RD RBCs. Patients with mutations in the NMIIA motor domain had the highest numbers of elongated RBCs. Patients with mutations in the motor domain also had elevated association of NMIIA with F-actin at the RBC membrane. Our findings support a central role for motor domain activity in NMIIA regulation of RBC shape and define a new sub-clinical phenotype of MYH9-RD.

Myosin IIA interacts with the spectrin-actin membrane skeleton to control red blood cell membrane curvature and deformability

The biconcave disk shape and deformability of mammalian RBCs rely on the membrane skeleton, a viscoelastic network of short, membrane-associated actin filaments (F-actin) cross-linked by long, flexible spectrin tetramers. Nonmuscle myosin II (NMII) motors exert force on diverse F-actin networks to control cell shapes, but a function for NMII contractility in the 2D spectrin-F-actin network of RBCs has not been tested. Here, we show that RBCs contain membrane skeleton-associated NMIIA puncta, identified as bipolar filaments by superresolution fluorescence microscopy. MgATP disrupts NMIIA association with the membrane skeleton, consistent with NMIIA motor domains binding to membrane skeleton F-actin and contributing to membrane mechanical properties. In addition, the phosphorylation of the RBC NMIIA heavy and light chains in vivo indicates active regulation of NMIIA motor activity and filament assembly, while reduced heavy chain phosphorylation of membrane skeleton-associated NMIIA indicates assembly of stable filaments at the membrane. Treatment of RBCs with blebbistatin, an inhibitor of NMII motor activity, decreases the number of NMIIA filaments associated with the membrane and enhances local, nanoscale membrane oscillations, suggesting decreased membrane tension. Blebbistatin-treated RBCs also exhibit elongated shapes, loss of membrane curvature, and enhanced deformability, indicating a role for NMIIA contractility in promoting membrane stiffness and maintaining RBC biconcave disk cell shape. As structures similar to the RBC membrane skeleton exist in many metazoan cell types, these data demonstrate a general function for NMII in controlling specialized membrane morphology and mechanical properties through contractile interactions with short F-actin in spectrin-F-actin networks.

Complexity of preoperative blood pressure dynamics: possible utility in cardiac surgical risk assessment

Complexity measures are intended to assess the cardiovascular system's capacity to respond to stressors. We sought to determine if decreased BP complexity is associated with increased estimated risk as obtained from two standard instruments: the Society of Thoracic Surgeons' (STS) Risk of Mortality and Morbidity Index and the European System for Cardiac Operative Risk Evaluation Score (EuroSCORE II). In this observational cohort study, preoperative systolic, diastolic, mean (MAP) and pulse pressure (PP) time series were derived in 147 patients undergoing cardiac surgery. The complexity of the fluctuations of these four variables was quantified using multiscale entropy (MSE) analysis. In addition, the traditional time series measures, mean and standard deviation (SD) were also computed. The relationships between time series measures and the risk indices (after logarithmic transformation) were then assessed using nonparametric (Spearman correlation, r_s) and linear regression methods. A one standard deviation change in the complexity of systolic, diastolic and MAP time series was negatively associated (p < 0.05) with the STS and EuroSCORE indices in both unadjusted (21-34%) and models adjusted for age, gender and SD of the BP time series (15-31%). The mean and SD of BP time series were not significantly associated with the risk index except for a positive association with the SD of the diastolic BP. Lower preoperative BP complexity was associated with a higher estimated risk of adverse cardiovascular outcomes and may provide a novel approach to assessing cardiovascular risk. Future studies are needed to determine whether dynamical risk indices can improve current risk prediction tools.

A Novel Multivariate Sample Entropy Algorithm for Modeling Time Series Synchronization

Approximate and sample entropy (AE and SE) provide robust measures of the deterministic or stochastic content of a time series (regularity), as well as the degree of structural richness (complexity), through operations at multiple data scales. Despite the success of the univariate algorithms, multivariate sample entropy (mSE) algorithms are still in their infancy and have considerable shortcomings. Not only are existing mSE algorithms unable to analyse within- and cross-channel dynamics, they can counter-intuitively interpret increased correlation between variates as decreased regularity. To this end, we first revisit the embedding of multivariate delay vectors (DVs), critical to ensuring physically meaningful and accurate analysis. We next propose a novel mSE algorithm and demonstrate its improved performance over existing work, for synthetic data and for classifying wake and sleep states from real-world physiological data. It is furthermore revealed that, unlike other tools, such as the correlation of phase synchrony, synchronized regularity dynamics are uniquely identified via mSE analysis. In addition, a model for the operation of this novel algorithm in the presence of white Gaussian noise is presented, which, in contrast to the existing algorithms, reveals for the first time that increasing correlation between different variates reduces entropy.

Theory and algorithms to compute Helfrich bending forces: a review

Cell membranes are vital to shield a cell's interior from the environment. At the same time they determine to a large extent the cell's mechanical resistance to external forces. In recent years there has been considerable interest in the accurate computational modeling of such membranes, driven mainly by the amazing variety of shapes that red blood cells and model systems such as vesicles can assume in external flows. Given that the typical height of a membrane is only a few nanometers while the surface of the cell extends over many micrometers, physical modeling approaches mostly consider the interface as a two-dimensional elastic continuum. Here we review recent modeling efforts focusing on one of the computationally most intricate components, namely the membrane's bending resistance. We start with a short background on the most widely used bending model due to Helfrich. While the Helfrich bending energy by itself is an extremely simple model equation, the computation of the resulting forces is far from trivial. At the heart of these difficulties lies the fact that the forces involve second order derivatives of the local surface curvature which by itself is the second derivative of the membrane geometry. We systematically derive and compare the different routes to obtain bending forces from the Helfrich energy, namely the variational approach and the thin-shell theory. While both routes lead to mathematically identical expressions, so-called linear bending models are shown to reproduce only the leading order term while higher orders differ. The main part of the review contains a description of various computational strategies which we classify into three categories: the force, the strong and the weak formulation. We finally give some examples for the application of these strategies in actual simulations.

Plasmodium falciparum erythrocyte-binding antigen 175 triggers a biophysical change in the red blood cell that facilitates invasion

Invasion of the red blood cell (RBC) by the Plasmodium parasite defines the start of malaria disease pathogenesis. To date, experimental investigations into invasion have focused predominantly on the role of parasite adhesins or signaling pathways and the identity of binding receptors on the red cell surface. A potential role for signaling pathways within the erythrocyte, which might alter red cell biophysical properties to facilitate invasion, has largely been ignored. The parasite erythrocyte-binding antigen 175 (EBA175), a protein required for entry in most parasite strains, plays a key role by binding to glycophorin A (GPA) on the red cell surface, although the function of this binding interaction is unknown. Here, using real-time deformability cytometry and flicker spectroscopy to define biophysical properties of the erythrocyte, we show that EBA175 binding to GPA leads to an increase in the cytoskeletal tension of the red cell and a reduction in the bending modulus of the cell's membrane. We isolate the changes in the cytoskeleton and membrane and show that reduction in the bending modulus is directly correlated with parasite invasion efficiency. These data strongly imply that the malaria parasite primes the erythrocyte surface through its binding antigens, altering the biophysical nature of the target cell and thus reducing a critical energy barrier to invasion. This finding would constitute a major change in our concept of malaria parasite invasion, suggesting it is, in fact, a balance between parasite and host cell physical forces working together to facilitate entry.

Aging effect on microcirculation: A multiscale entropy approach on laser speckle contrast images

PURPOSE

It has long been known that age plays a crucial role in the deterioration of microvessels. The assessment of such deteriorations can be achieved by monitoring microvascular blood flow. Laser speckle contrast imaging (LSCI) is a powerful optical imaging tool that provides two-dimensional information on microvascular blood flow. The technique has recently been commercialized, and hence, few works discuss the postacquisition processing of laser speckle contrast images recorded in vivo. By applying entropy-based complexity measures to LSCI time series, we present herein the first attempt to study the effect of aging on microcirculation by measuring the complexity of microvascular signals over multiple time scales.

METHODS

Forearm skin microvascular blood flow was studied with LSCI in 18 healthy subjects. The subjects were subdivided into two age groups: younger (20-30 years old, n = 9) and older (50-68 years old, n = 9). To estimate age-dependent changes in microvascular blood flow, we applied three entropy-based complexity algorithms to LSCI time series.

RESULTS

The application of entropy-based complexity algorithms to LSCI time series can differentiate younger from older groups: the data fluctuations in the younger group have a significantly higher complexity than those obtained from the older group.

CONCLUSIONS

The effect of aging on microcirculation can be estimated by using entropy-based complexity algorithms to LSCI time series.

Nonlinear temperature effects on multifractal complexity of metabolic rate of mice

Complex physiological dynamics have been argued to be a signature of healthy physiological function. Here we test whether the complexity of metabolic rate fluctuations in small endotherms decreases with lower environmental temperatures. To do so, we examine the multifractal temporal scaling properties of the rate of change in oxygen consumption r(VO₂), in the laboratory mouse Mus musculus, assessing their long range correlation properties across seven different environmental temperatures, ranging from 0 °C to 30 °C. To do so, we applied multifractal detrended fluctuation analysis (MF-DFA), finding that r(VO₂) fluctuations show two scaling regimes. For small time scales below the crossover time (approximately 10² s), either monofractal or weak multifractal dynamics are observed depending on whether T_a < 15 °C or T_a > 15 °C respectively. For larger time scales, r(VO₂) fluctuations are characterized by an asymptotic scaling exponent that indicates multifractal anti-persistent or uncorrelated dynamics. For both scaling regimes, a generalization of the multiplicative cascade model provides very good fits for the Renyi exponents τ(q), showing that the infinite number of exponents h(q) can be described by only two independent parameters, a and b. We also show that the long-range correlation structure of r(VO₂) time series differs from randomly shuffled series, and may not be explained as an artifact of stochastic sampling of a linear frequency spectrum. These results show that metabolic rate dynamics in a well studied micro-endotherm are consistent with a highly non-linear feedback control system.

Differential Changes with Age in Multiscale Entropy of Electromyography Signals from Leg Muscles during Treadmill Walking

Age-related gait changes may be due to the loss of complexity in the neuromuscular system. This theory is disputed due to inconsistent results from single-scale analyses. Also, behavioral adaptations may confound these changes. We examined whether EMG dynamics during gait is less complex in older adults over a range of timescales using the multiscale entropy method, and whether slower walking attenuates this effect. Surface EMG was measured from the left vastus lateralis (VL), biceps femoris (BF), gastrocnemius (GA), and tibialis anterior (TA) in 17 young and 18 older adults as they walked on a treadmill for 5 minutes at 0.8x-1.2x of preferred speed. Sample entropy (SE) and the complexity index (CI) of the EMG signals were calculated after successive coarse-graining to extract dynamics at timescales of 27 to 270 Hz, with m = 2 and r = 0.15 SD. SE and CI were lower across the timescales in older adults in VL and BF, but higher in GA (all p<0.001); these results held for VL and GA even after accounting for longer EMG burst durations in older adults. CI was higher during slower walking speed in VL and BF (p<0.001). Results were mostly similar for m = 3 and r = 0.01-0.35. Smaller r was more sensitive to age-related differences. The decrease in complexity with aging in the timescales studied was limited to proximal muscles, particularly VL. The increase in GA may be driven by other factors. Walking slower may reflect a behavioral adaptation that allows the nervous system to function with greater complexity.

Acute and delayed response to resistance exercise leading or not leading to muscle failure

This study compared the time course of recovery following two resistance exercise protocols differing in the number of repetitions per set with regard to the maximum possible (to failure) number. Ten men performed three sets of 6 versus 12 repetitions with their 70% 1RM (3 × 6 [12] versus 3 × 12 [12]) in the bench press (BP) and squat (SQ) exercises. Mechanical [CMJ height, velocity against the 1 m s^-1 load (V₁ -load)], biochemical [testosterone, cortisol, growth hormone, prolactin, insulin-like growth factor-1, creatine kinase (CK)] and heart rate variability (HRV) and complexity (HRC) were assessed pre-, postexercise (Post) and at 6, 24 and 48 h-Post. Compared with 3 × 6 [12], the 3 × 12 [12] protocol resulted in significantly: higher repetition velocity loss within each set (BP: 65% versus 26%; SQ: 44% versus 20%); reduced V₁ -load until 24 h-Post (BP) and 6 h-Post (SQ); decreased CMJ height up to 48 h-Post; greater increases in cortisol (Post), prolactin (Post, 48 h-Post) and CK (48 h-Post); and reductions in HRV and HRC at Post. This study shows that the mechanical, neuroendocrine and autonomic cardiovascular response is markedly different when manipulating the number of repetitions per set. Halving the number of repetitions in relation to the maximum number that can be completed serves to minimize fatigue and speed up recovery following resistance training.

Levitational Image Cytometry with Temporal Resolution

A simple, yet powerful magnetic-levitation-based device is reported for real-time, label-free separation, as well as high-resolution monitoring of cell populations based on their unique magnetic and density signatures. This method allows a wide variety of cellular processes to be studied, accompanied by transient or permanent changes in cells' fundamental characteristics as a biological material.

Generalized Multiscale Entropy Analysis: Application to Quantifying the Complex Volatility of Human Heartbeat Time Series

We introduce a generalization of multiscale entropy (MSE) analysis. The method is termed MSE_n, where the subscript denotes the moment used to coarse-grain a time series. MSE_μ, described previously, uses the mean value (first moment). Here, we focus on MSEσ2, which uses the second moment, i.e., the variance. MSEσ2 quantifies the dynamics of the volatility (variance) of a signal over multiple time scales. We use the method to analyze the structure of heartbeat time series. We find that the dynamics of the volatility of heartbeat time series obtained from healthy young subjects is highly complex. Furthermore, we find that the multiscale complexity of the volatility, not only the multiscale complexity of the mean heart rate, degrades with aging and pathology. The “bursty” behavior of the dynamics may be related to intermittency in energy and information flows, as part of multiscale cycles of activation and recovery. Generalized MSE may also be useful in quantifying the dynamical properties of other physiologic and of non-physiologic time series.

Dynamic actin filaments control the mechanical behavior of the human red blood cell membrane

The short actin filaments in the spectrin-actin membrane skeleton of human red blood cells (RBCs) are capable of dynamic subunit exchange and mobility. Actin dynamics in RBCs regulates the biomechanical properties of the RBC membrane.

Short, uniform-length actin filaments function as structural nodes in the spectrin-actin membrane skeleton to optimize the biomechanical properties of red blood cells (RBCs). Despite the widespread assumption that RBC actin filaments are not dynamic (i.e., do not exchange subunits with G-actin in the cytosol), this assumption has never been rigorously tested. Here we show that a subpopulation of human RBC actin filaments is indeed dynamic, based on rhodamine-actin incorporation into filaments in resealed ghosts and fluorescence recovery after photobleaching (FRAP) analysis of actin filament mobility in intact RBCs (∼25–30% of total filaments). Cytochalasin-D inhibition of barbed-end exchange reduces rhodamine-actin incorporation and partially attenuates FRAP recovery, indicating functional interaction between actin subunit turnover at the single-filament level and mobility at the membrane-skeleton level. Moreover, perturbation of RBC actin filament assembly/disassembly with latrunculin-A or jasplakinolide induces an approximately twofold increase or ∼60% decrease, respectively, in soluble actin, resulting in altered membrane deformability, as determined by alterations in RBC transit time in a microfluidic channel assay, as well as by abnormalities in spontaneous membrane oscillations (flickering). These experiments identify a heretofore-unrecognized but functionally important subpopulation of RBC actin filaments, whose properties and architecture directly control the biomechanical properties of the RBC membrane.

Resistance training exercise program for intervention to enhance gait function in elderly chronically ill patients: multivariate multiscale entropy for center of pressure signal analysis

Falls are unpredictable accidents, and the resulting injuries can be serious in the elderly, particularly those with chronic diseases. Regular exercise is recommended to prevent and treat hypertension and other chronic diseases by reducing clinical blood pressure. The "complexity index" (CI), based on multiscale entropy (MSE) algorithm, has been applied in recent studies to show a person's adaptability to intrinsic and external perturbations and widely used measure of postural sway or stability. The multivariate multiscale entropy (MMSE) was advanced algorithm used to calculate the complexity index (CI) values of the center of pressure (COP) data. In this study, we applied the MSE & MMSE to analyze gait function of 24 elderly, chronically ill patients (44% female; 56% male; mean age, 67.56 ± 10.70 years) with either cardiovascular disease, diabetes mellitus, or osteoporosis. After a 12-week training program, postural stability measurements showed significant improvements. Our results showed beneficial effects of resistance training, which can be used to improve postural stability in the elderly and indicated that MMSE algorithms to calculate CI of the COP data were superior to the multiscale entropy (MSE) algorithm to identify the sense of balance in the elderly.

Bio-inspired cryo-ink preserves red blood cell phenotype and function during nanoliter vitrification

Current red-blood-cell cryopreservation methods utilize bulk volumes, causing cryo-injury of cells, which results in irreversible disruption of cell morphology, mechanics, and function. An innovative approach to preserve human red-blood-cell morphology, mechanics, and function following vitrification in nanoliter volumes is developed using a novel cryo-ink integrated with a bioprinting approach.

Dynamical glucometry: use of multiscale entropy analysis in diabetes

Diabetes mellitus (DM) is one of the world's most prevalent medical conditions. Contemporary management focuses on lowering mean blood glucose values toward a normal range, but largely ignores the dynamics of glucose fluctuations. We probed analyte time series obtained from continuous glucose monitor (CGM) sensors. We show that the fluctuations in CGM values sampled every 5 min are not uncorrelated noise. Next, using multiscale entropy analysis, we quantified the complexity of the temporal structure of the CGM time series from a group of elderly subjects with type 2 DM and age-matched controls. We further probed the structure of these CGM time series using detrended fluctuation analysis. Our findings indicate that the dynamics of glucose fluctuations from control subjects are more complex than those of subjects with type 2 DM over time scales ranging from about 5 min to 5 h. These findings support consideration of a new framework, dynamical glucometry, to guide mechanistic research and to help assess and compare therapeutic interventions, which should enhance complexity of glucose fluctuations and not just lower mean and variance of blood glucose levels.

A Review of Theoretical Perspectives in Cognitive Science on the Presence of 1/f Scaling in Coordinated Physiological and Cognitive Processes

Time series of human performances present fluctuations around a mean value. These fluctuations are typically considered as insignificant, and attributable to random noise. Over recent decades, it became clear that temporal fluctuations possess interesting properties, however, one of which the property of fractal 1/f scaling. 1/f scaling indicates that a measured process extends over a wide range of timescales, suggesting an assembly over multiple scales simultaneously. This paper reviews neurological, physiological, and cognitive studies that corroborate the claim that 1/f scaling is most clearly present in healthy, well-coordinated activities. Prominent hypotheses about the origins of 1/f scaling are confronted with these reviewed studies. It is concluded that 1/f scaling in living systems appears to reflect their genuine complex nature, rather than constituting a coincidental side-effect. The consequences of fractal dynamics extending from the small spatial and temporal scales (e.g., neurons) to the larger scales of human behavior and cognition, are vast, and impact the way in which relevant research questions may be approached. Rather than focusing on specialized isolable subsystems, using additive linear methodologies, nonlinear dynamics, more elegantly so, imply a complex systems methodology, thereby exploiting, rather than rejecting, mathematical concepts that enable describing large sets of natural phenomena.

Complexity-loss in fetal heart rate dynamics during labor as a potential biomarker of acidemia

BACKGROUND

Continuous fetal heart rate (FHR) monitoring remains central to intrapartum care. However, advances in signal analysis are needed to increase its accuracy in diagnosis of fetal hypoxia.

AIMS

To determine whether FHR complexity, an index of multiscale variability, is lower among fetuses born with low (≤7.05) versus higher pH values, and whether this measure can potentially be used to help discriminate the two groups.

STUDY DESIGN

Evaluation of a pre-existing database of sequentially acquired intrapartum FHR signals.

SUBJECTS

FHR tracings, obtained from a continuous scalp electrocardiogram during labor, were analyzed using the multiscale entropy (MSE) method in 148 singletons divided in two groups according to umbilical artery pH at birth: 141 fetuses with pH>7.05 and 7 with pH≤7.05. A complexity index derived from MSE analysis was calculated for each recording.

RESULTS

The complexity of FHR signals for the last two hours before delivery was significantly (p<0.004) higher for non-acidemic than for acidemic fetuses. The difference between the two groups remained significant (p<0.003) when FHR data from the last 30min before delivery were excluded.

CONCLUSION

Complexity of FHR signals, as measured by the MSE method, was significantly lower for acidemic than non-acidemic fetuses. These results are consistent with previous studies showing that decreased nonlinear complexity is a dynamical signature of disrupted physiologic control systems. This analytic approach may have discriminative value in FHR analysis.

Combat casualties undergoing lifesaving interventions have decreased heart rate complexity at multiple time scales

PURPOSE

We found that heart rate (HR) complexity metrics such as sample entropy (SampEn) identified patients with trauma receiving lifesaving interventions (LSIs). We now aimed (1) to test a multiscale entropy (MSE) index, (2) to compare it to single-scale measures including SampEn, and (3) to assess different parameter values for calculation of SampEn and MSE.

METHODS

This was a study of combat casualties in an emergency department in Iraq. Electrocardiograms of 70 acutely injured adults were recorded. Twelve underwent LSIs and 58 did not. Lifesaving interventions included endotracheal intubation (9), tube thoracostomy (9), and emergency transfusion (4). From each electrocardiogram, a segment of 800 consecutive beats was selected. Offline, R waves were detected and R-to-R interval time series were generated. Sample entropy, MSE, and time-domain measures of HR variability (mean HR, SD, the proportion of pairs of consecutive NN intervals that differ by more than 20 and 50 milliseconds, square root of the mean of the squares of differences between adjacent NN intervals) were computed.

RESULTS

Differences in mean HR (LSI: 111 ± 33, non-LSI: 90 ± 17 beats/min) were not significant. Systolic arterial pressure was statistically but not clinically different (LSI: 123 ± 19, non-LSI: 135 ± 19 mm Hg). Sample entropy (LSI: 0.90 ± 0.42, non-LSI: 1.19 ± 0.35; P < .05) and MSE index (LSI: 2.58 ± 2.55, non-LSI: 5.67 ± 2.48; P < .001) differed significantly.

CONCLUSIONS

Complexity of HR dynamics over a range of time scales was lower in high-risk than in low-risk combat casualties and outperformed traditional vital signs.

Measuring center of pressure signals to quantify human balance using multivariate multiscale entropy by designing a force platform

To assess the improvement of human body balance, a low cost and portable measuring device of center of pressure (COP), known as center of pressure and complexity monitoring system (CPCMS), has been developed for data logging and analysis. In order to prove that the system can estimate the different magnitude of different sways in comparison with the commercial Advanced Mechanical Technology Incorporation (AMTI) system, four sway tests have been developed (i.e., eyes open, eyes closed, eyes open with water pad, and eyes closed with water pad) to produce different sway displacements. Firstly, static and dynamic tests were conducted to investigate the feasibility of the system. Then, correlation tests of the CPCMS and AMTI systems have been compared with four sway tests. The results are within the acceptable range. Furthermore, multivariate empirical mode decomposition (MEMD) and enhanced multivariate multiscale entropy (MMSE) analysis methods have been used to analyze COP data reported by the CPCMS and compare it with the AMTI system. The improvements of the CPCMS are 35% to 70% (open eyes test) and 60% to 70% (eyes closed test) with and without water pad. The AMTI system has shown an improvement of 40% to 80% (open eyes test) and 65% to 75% (closed eyes test). The results indicate that the CPCMS system can achieve similar results to the commercial product so it can determine the balance.

Physiologic complexity and aging: implications for physical function and rehabilitation

The dynamics of most healthy physiological processes are complex, in that they are comprised of fluctuations with information-rich structure correlated over multiple temporospatial scales. Lipsitz and Goldberger (1992) first proposed that the aging process may be characterized by a progressive loss of physiologic complexity. We contend that this loss of complexity results in functional decline of the organism by diminishing the range of available, adaptive responses to the innumerable stressors of everyday life. From this relationship, it follows that rehabilitative interventions may be optimized by targeting the complex dynamics of human physiology, and by quantifying their effects using tools derived from complex systems theory. Here, we first discuss several caveats that one must consider when examining the functional and rehabilitative implications of physiologic complexity. We then review available evidence regarding the relationship between physiologic complexity and system functionality, as well as the potential for interventions to restore the complex dynamics that characterize healthy physiological function.

Distinguishing chaotic and stochastic dynamics from time series by using a multiscale symbolic approach

In this paper we introduce a multiscale symbolic information-theory approach for discriminating nonlinear deterministic and stochastic dynamics from time series associated with complex systems. More precisely, we show that the multiscale complexity-entropy causality plane is a useful representation space to identify the range of scales at which deterministic or noisy behaviors dominate the system's dynamics. Numerical simulations obtained from the well-known and widely used Mackey-Glass oscillator operating in a high-dimensional chaotic regime were used as test beds. The effect of an increased amount of observational white noise was carefully examined. The results obtained were contrasted with those derived from correlated stochastic processes and continuous stochastic limit cycles. Finally, several experimental and natural time series were analyzed in order to show the applicability of this scale-dependent symbolic approach in practical situations.

Age-dependent acoustic and microelastic properties of red blood cells determined by vector contrast acoustic microscopy

Variations of the mechanical properties of red blood cells that occur during their life span have long been an intriguing task for investigations. The research presented is based on noninvasive monitoring of red blood cells of different ages performed by scanning acoustic microscopy with magnitude and phase contrast. The characteristic signature of fixed cells from groups of three different ages fractionated according to mass density is obtained from the acoustic microscope images, with the data represented in polar graphs. The analysis of these data enables the determination of averaged values for the velocities of ultrasound propagating in the cells from the different groups ranging from (1,681 ± 16) m s(-1) in the youngest to (1,986 ± 20) m s(-1) in the oldest group. The determined bulk modulus varies with age from (3.04 ± 0.05) GPa to (4.34 ± 0.08) GPa. An approach to determine for an age-mixed population of red blood cells, collected from a healthy person, the age of the individual cells and the age dependence of the cell parameters including density, velocity, and attenuation of longitudinal polarized ultrasonic waves traveling in the cells is demonstrated.

Multivariate multiscale entropy: a tool for complexity analysis of multichannel data

This work generalizes the recently introduced univariate multiscale entropy (MSE) analysis to the multivariate case. This is achieved by introducing multivariate sample entropy (MSampEn) in a rigorous way, in order to account for both within- and cross-channel dependencies in multiple data channels, and by evaluating it over multiple temporal scales. The multivariate MSE (MMSE) method is shown to provide an assessment of the underlying dynamical richness of multichannel observations, and more degrees of freedom in the analysis than standard MSE. The benefits of the proposed approach are illustrated by simulations on complexity analysis of multivariate stochastic processes and on real-world multichannel physiological and environmental data.

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.

Systemic lupus erythematosus serum deposits C4d on red blood cells, decreases red blood cell membrane deformability, and promotes nitric oxide production

OBJECTIVE

Systemic lupus erythematosus (SLE) is characterized by intravascular activation of the complement system and deposition of complement fragments (C3 and C4) on plasma membranes of circulating cells, including red blood cells (RBCs). The aim of this study was to address whether this process affects the biophysical properties of RBCs.

METHODS

Serum and RBCs were isolated from patients with SLE and healthy controls. RBCs from healthy universal donors (type O, Rh negative) were incubated with SLE or control serum. We used flow cytometry to assess complement fragment deposition on RBCs. RBC membrane deformability was measured using 2-dimensional microchannel arrays. Protein phosphorylation levels were quantified by Western blotting.

RESULTS

Incubation of healthy universal donor RBCs with sera from patients with SLE, but not with control sera, led to deposition of C4d fragments on the RBCs. Complement-decorated RBCs exhibited significant decreases in both membrane deformability and flickering. Sera from SLE patients triggered a transitory Ca(++) influx in RBCs that was associated with decreased phosphorylation of β-spectrin and with increased phosphorylation of band 3, two key proteins of RBC cytoskeleton. Finally, incubation with SLE sera led to the production of nitric oxide by RBCs, whereas this did not occur with control sera.

CONCLUSION

Our data suggest that complement activation in patients with SLE leads to calcium-dependent cytosketeletal changes in RBCs that render them less deformable, probably impairing their flow through capillaries. This phenomenon may negatively affect the delivery of oxygen to the tissues.

Multivariate multiscale entropy for brain consciousness analysis

The recently introduced multiscale entropy (MSE) method accounts for long range correlations over multiple time scales and can therefore reveal the complexity of biological signals. The existing MSE algorithm deals with scalar time series whereas multivariate time series are common in experimental and biological systems. To that cause, in this paper the MSE method is extended to the multivariate case. This allows us to gain a greater insight into the complexity of the underlying signal generating system, producing multifaceted and more robust estimates than standard single channel MSE. Simulations on both synthetic data and brain consciousness analysis support the approach.

Light scattering of human red blood cells during metabolic remodeling of the membrane

We present the light scattering properties of individual human red blood cells (RBCs). We show that both the RBC static and dynamic scattering signals are altered by adenosine 5'-triphosphate (ATP)-driven membrane metabolic remodeling. To measure the light scattering signal from individual RBCs, we use diffraction phase microscopy together with a Fourier transform light scattering technique. RBC cytosolic ATPs are both chemically and metabolically depleted, and the corresponding scattering signals are compared with the light scattering signal of normal RBCs having physiologic levels of ATP.

Temperature- and hydration-dependent internal dynamics of stripped human erythrocyte vesicles studied by incoherent neutron scattering

BACKGROUND

We focus on temperature- and hydration-dependence of internal molecular motions in stripped human red blood cell (RBC) vesicles, widely used as a model system for more complex biomembranes.

METHODS

We singled out picosecond local motions of the non-exchangeable hydrogen atoms of RBC vesicles by performing elastic and quasielastic incoherent neutron scattering measurements in dry and heavy water (D₂O)-hydrated RBC powders.

RESULTS

In dry stripped RBCs, hydrogen motions remained harmonic all along the measured temperature range (100-310K) and mean-square displacements (MSDs) exhibited no temperature transition up to 310K. In contrast, MSDs of hydrated stripped RBCs (h ≈ 0.38g D₂O/g dry powder) exhibited a pronounced transition near 260K, with the sharp rise of anharmonic diffusive motions of hydrogen atoms. This transition at ~260K was correlated with both the onset of nonvibrational (harmonic and nonharmonic) motions and the melting of crystallized hydration water.

GENERAL SIGNIFICANCE

In conclusion, we have shown that MSDs in human RBC vesicles are temperature-and hydration-dependent. These results provide insight into biomembrane internal dynamics at picosecond timescale and nanometer length scale. Such motions have been shown to act as the "lubricant" of larger conformational changes on a slower, millisecond timescale that are necessary for important biological processes.

Exploring measures of whole person wellness: integrative well-being and psychological flourishing

OBJECTIVES

Whole systems of complementary and alternative medicine (WSCAM) emphasize positive emergent outcomes for the patient, for example, a sense of well-being. This paper presents a questionnaire-based study in healthy young adults for the purpose of exploring individual differences that contribute to the sense of well-being and to identify characteristics of flourishing versus nonflourishing individuals in terms of nonlinear dynamical systems concepts.

METHODS

Young adult college students (N = 856) completed questionnaires assessing global well-being (Arizona Integrative Outcomes Scale [AIOS]), global physical health, positive and negative mood (Positive and Negative Affect Schedule [PANAS]), resilience (Connor- Davidson Resilience Scale), and repressive defensiveness. Next, subjects were divided into flourisher/languisher groups by a previously determined ratio of positive/negative scores established by a study using complex systems methods.

RESULTS

Positive-to-negative affect (P:N) ratio accounted for more variance in AIOS (R(2) = 0.19; P < .001) than did separate positive or negative PANAS scores or physical health. Flourishers (14.5% of the sample) were significantly higher than languishers in defensiveness and resilience.

CONCLUSIONS

Positive-to-negative affect explains a substantial portion of the variance in well-being of healthy young adults. The low percentage of flourishers in this nonclinical sample is consistent with previous population-based studies and suggests that flourishers are a minority, even in nonclinical settings. Positive-to-negative affect may be a useful variable for subsequent prospective studies of applied WSCAM treatments and in well and clinical populations. The well-being measure used in this study is easy to complete, sensitive, and may be a useful clinical measure to track change with treatment over time.

Physiological complexity and system adaptability: evidence from postural control dynamics of older adults

The degree of multiscale complexity in human behavioral regulation, such as that required for postural control, appears to decrease with advanced aging or disease. To help delineate causes and functional consequences of complexity loss, we examined the effects of visual and somatosensory impairment on the complexity of postural sway during quiet standing and its relationship to postural adaptation to cognitive dual tasking. Participants of the MOBILIZE Boston Study were classified into mutually exclusive groups: controls [intact vision and foot somatosensation, n = 299, 76 ± 5 (SD) yr old], visual impairment only (<20/40 vision, n = 81, 77 ± 4 yr old), somatosensory impairment only (inability to perceive 5.07 monofilament on plantar halluxes, n = 48, 80 ± 5 yr old), and combined impairments (n = 25, 80 ± 4 yr old). Postural sway (i.e., center-of-pressure) dynamics were assessed during quiet standing and cognitive dual tasking, and a complexity index was quantified using multiscale entropy analysis. Postural sway speed and area, which did not correlate with complexity, were also computed. During quiet standing, the complexity index (mean ± SD) was highest in controls (9.5 ± 1.2) and successively lower in the visual (9.1 ± 1.1), somatosensory (8.6 ± 1.6), and combined (7.8 ± 1.3) impairment groups (P = 0.001). Dual tasking resulted in increased sway speed and area but reduced complexity (P < 0.01). Lower complexity during quiet standing correlated with greater absolute (R = -0.34, P = 0.002) and percent (R = -0.45, P < 0.001) increases in postural sway speed from quiet standing to dual-tasking conditions. Sensory impairments contributed to decreased postural sway complexity, which reflected reduced adaptive capacity of the postural control system. Relatively low baseline complexity may, therefore, indicate control systems that are more vulnerable to cognitive and other stressors.

Human erythrocyte flickering: temperature, ATP concentration, water transport, and cell aging, plus a computer simulation

Images of human erythrocytes from a healthy donor were recorded under differential interference contrast (DIC) microscopy; they were acquired rapidly (approximately 336 Hz) and the intensity of the centermost pixel of each cell was recorded for approximately 60 s (20,000 values). Various techniques were used to analyze the data, including detrended fluctuation analysis (DFA) and multiscale entropy (MSE); however, power spectrum analysis was deemed the most appropriate for metrifying and comparing results. This analysis was used to compare cells from young and old populations, and after perturbing normal conditions, with changes in temperature, adenosine triphosphate (ATP) concentration (using NaF, an inhibitor of glycolysis, and alpha-toxin, a pore-forming molecule used to permeabilize red cells to ATP), and water transport rates [using glycerol, and p-chloromercuriphenylsulfonic acid (pCMBS) to inhibit aquaporins, AQPs]. There were measurable differences in the membrane fluctuation characteristics in populations of young and old cells, but there was no significant change in the flickering time series on changing the temperature of an individual cell, by depleting it of ATP, or by competing with the minor water exchange pathway via AQP3 using glycerol. However, pCMBS, which inhibits AQP1, the major water exchange pathway, inhibited flickering in all cells, and yet it was restored by the membrane intercalating species dibutyl phthalate (DBP). We developed a computer model to simulate acquired displacement spectral time courses and to evaluate various methods of data analysis, and showed how the flexibility of the membrane, as defined in the model, affects the flickering time course.