Membrane viscoelasticity

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.

Dynamic photodamage of red blood cell induced by CisDiMPyP porphyrin

It is well-known that oxidative damage in red blood cell (RBC) usually causes morphological changes and increased membrane rigidity. Although many studies have focused on investigating how RBC responds to a photodynamic stimulus, the intermediate steps between membrane damage and hemolysis are not reported. To give a comprehensive insight into changes of RBC membrane property under different oxidative damage levels, we employed the photoactivation of CisDiMPyP porphyrin that primarily generates singlet oxygen ¹O₂ as oxidant species. We found that there were distinguishable characteristic damages depending on the ¹O₂ flux over the membrane, in a way that each impact of photooxidative damage was categorized under three damage levels: mild (maintaining the membrane morphology and elasticity), moderate (membrane elongation and increased membrane elasticity) and severe (wrinkle-like deformation and hemolysis). When sodium azide (NaN₃) was used as a singlet oxygen quencher, delayed cell membrane alterations and hemolysis were detected. The delay times showed that ¹O₂ indeed plays a key role that causes RBC photooxidation by CisDiMPyP. We suggest that the sequence of morphological changes (RBC discoid area expansion, wrinkle-like patterns, and hemolysis) under photooxidative damage occurs due to damage to the lipid membrane and cytoskeletal network proteins.

Compressible viscoelasticity of cell membranes determined by gigahertz-frequency acoustic vibrations

Membrane viscosity is an important property of cell biology, which determines cellular function, development and disease progression. Various experimental and computational methods have been developed to investigate the mechanics of cells. However, there have been no experimental measurements of the membrane viscosity at high-frequencies in live cells. High frequency measurements are important because they can probe viscoelastic effects. Here, we investigate the membrane viscosity at gigahertz-frequencies through the damping of the acoustic vibrations of gold nanoplates. The experiments are modeled using a continuum mechanics theory which reveals that the membranes display viscoelasticity, with an estimated relaxation time of ca. 5.7 + 2.4 / - 2.7 ps. We further demonstrate that membrane viscoelasticity can be used to differentiate a cancerous cell line (the human glioblastoma cells LN-18) from a normal cell line (the mouse brain microvascular endothelial cells bEnd.3). The viscosity of cancerous cells LN-18 is lower than that of healthy cells bEnd.3 by a factor of three. The results indicate promising applications of characterizing membrane viscoelasticity at gigahertz-frequency in cell diagnosis.

A computational model for the transit of a cancer cell through a constricted microchannel

We propose a three-dimensional computational model to simulate the transient deformation of suspended cancer cells flowing through a constricted microchannel. We model the cell as a liquid droplet enclosed by a viscoelastic membrane, and its nucleus as a smaller stiffer capsule. The cell deformation and its interaction with the suspending fluid are solved through a well-tested immersed boundary lattice Boltzmann method. To identify a minimal mechanical model that can quantitatively predict the transient cell deformation in a constricted channel, we conduct extensive parametric studies of the effects of the rheology of the cell membrane, cytoplasm and nucleus and compare the results with a recent experiment conducted on human leukaemia cells. We find that excellent agreement with the experiment can be achieved by employing a viscoelastic cell membrane model with the membrane viscosity depending on its mode of deformation (shear versus elongation). The cell nucleus limits the overall deformation of the whole cell, and its effect increases with the nucleus size. The present computational model may be used to guide the design of microfluidic devices to sort cancer cells, or to inversely infer cell mechanical properties from their flow-induced deformation.

Quantifying Shear-induced Margination and Adhesion of Platelets in Microvascular Blood Flow

Platelet margination and adhesion are two critical and closely related steps in thrombus formation. Using dissipative particle dynamics (DPD) method that seamlessly models blood cells, blood plasma, and vessel walls with functionalized surfaces, we quantify the shear-induced margination and adhesion of platelets in microvascular blood flow. The results show that the occurrence of shear-induced RBC-platelet collisions has a remarkable influence on the degree of platelet margination. We characterize the lateral motion of individual platelets by a mean square displacement analysis of platelet trajectories, and find that the wall-induced lift force and the shear-induced displacement in wall-bounded flow cause the variation in near-wall platelet distribution. We then investigate the platelet adhesive dynamics under different flow conditions, by conducting DPD simulations of blood flow in a microtube with fibrinogen-coated wall surfaces. We find that the platelet adhesion is enhanced with the increase of fibrinogen concentration level but decreased with the increase of shear rate. These results are consistent with available experimental results. In addition, we demonstrate that the adherent platelets have a negative impact on the margination dynamics of the circulating platelets, which is mainly due to the climbing effect induced by the adherent ones. Taken together, these findings provide useful insights into the platelet margination and adhesion dynamics, which may facilitate the understanding of the predominant processes governing the initial stage of thrombus formation.

Effects of membrane viscoelasticity on the red blood cell dynamics in a microcapillary

The mechanical properties of red blood cells (RBCs) play key roles in their biological functions in microcirculation. In particular, RBCs must deform significantly to travel through microcapillaries with sizes comparable with or even smaller than their own. Although the dynamics of RBCs in microcapillaries have received considerable attention, the effect of membrane viscoelasticity has been largely overlooked. In this work, we present a computational study based on the boundary integral method and thin-shell mechanics to examine how membrane viscoelasticity influences the dynamics of RBCs flowing through straight and constricted microcapillaries. Our results reveal that the cell with a viscoelastic membrane undergoes substantially different motion and deformation compared with results based on a purely elastic membrane model. Comparisons with experimental data also suggest the importance of accounting for membrane viscoelasticity to properly capture the transient dynamics of an RBC flowing through a microcapillary. Taken together, these findings demonstrate the significant effects of membrane viscoelasticity on RBC dynamics in different microcapillary environments. The computational framework also lays the groundwork for more accurate quantitative modeling of the mechanical response of RBCs in their mechanotransduction process in subsequent investigations.

Energy Dissipation in the Human Red Cell Membrane

The membrane of the human red cell consists of a lipid bilayer and a so-called membrane skeleton attached on the cytoplasmic side of the bilayer. Upon the deformation of red cells, energy is dissipated in their cytoplasm and their membrane. As to the membrane, three contributions can be distinguished: (i) A two-dimensional shear deformation with the membrane viscosity as the frictional parameter; (ii) A motion of the membrane skeleton relative to the bilayer; (iii) A relative motion of the two monolayers of the bilayer. The frictional parameter in contributions (ii) and (iii) is a frictional coefficient specific for the respective contribution. This perspective describes the history up to recent advances in the knowledge of these contributions. It reviews the mechanisms of energy dissipation on a molecular scale and suggests new ones, particularly for the first contribution. It proposes a parametric fitting expected to shed light on the discrepant values found for the membrane viscosity by different experimental approaches. It proposes strategies that could allow the determination of the frictional coefficients pertaining to the second and the third contribution. It highlights the consequences characteristic times have on the state of the red cell membrane in circulation as well as on the adaptation of computer models to the red cell history in an in vitro experiment.

Red blood cell rheology during a complete blood count: A proof of concept

Counting and sizing blood cells in hematological analyzers is achieved using the Coulter principle. The cells flow in a micro-aperture in which a strong electrical field is imposed, so that an electrical perturbation, called pulse, is measured each time a cell crosses the orifice. The pulses are expected to contain information on the shape and deformability of Red Blood Cells (RBCs), since recent studies state that RBCs rotate and deform in the micro-orifice. By implementing a dedicated numerical model, the present study sheds light on a variety of cells dynamics, which leads to different associated pulse signatures. Furthermore, simulations provide new insights on how RBCs shapes and mechanical properties affect the measured signals. Those numerical observations are confirmed by experimental assays. Finally, specific features are introduced for assessing the most relevant characteristics from the various pulse signatures and shown to highlight RBCs alterations induced by drugs. In summary, this study paves the way to a characterization of RBC rheology by routine hematological instruments.

On the significance of membrane unfolding in mechanosensitive cell spreading: Its individual and synergistic effects

Mechanosensitivity of cell spread area to substrate stiffness has been established both through experiments and different types of mathematical models of varying complexity including both the mechanics and biochemical reactions in the cell. What has not been addressed in previous mathematical models is the role of cell membrane dynamics on cell spreading, and an investigation of this issue is the goal of this work. We start with a simple mechanical model of cell spreading on a deformable substrate and progressively layer mechanisms to account for the traction dependent growth of focal adhesions, focal adhesion induced actin polymerization, membrane unfolding/exocytosis and contractility. This layering approach is intended to progressively help in understanding the role each mechanism plays in reproducing experimentally observed cell spread areas. To model membrane unfolding we introduce a novel approach based on defining an active rate of membrane deformation that is dependent on membrane tension. Our modeling approach allows us to show that tension-dependent membrane unfolding plays a critical role in achieving the large cell spread areas experimentally observed on stiff substrates. We also demonstrate that coupling between membrane unfolding and focal adhesion induced polymerization works synergistically to further enhance cell spread area sensitivity to substrate stiffness. This enhancement has to do with the fact that the peripheral velocity of spreading cells is associated with contributions from the different mechanisms by either enhancing the polymerization velocity at the leading edge or slowing down of the retrograde flow of actin within the cell. The temporal evolution of this balance in the model corresponds to the three-phase behavior observed experimentally during spreading. In the initial phase membrane unfolding is found to be particularly important.

Tank-treading dynamics of red blood cells in shear flow: On the membrane viscosity rheology

In this article, extensive three-dimensional simulations are conducted for tank-treading (TT) red blood cells (RBCs) in shear flow with different cell viscous properties and flow conditions. Apart from recent numerical studies on TT RBCs, this research considers the uncertainty in cytoplasm viscosity, covers a more complete range of shear flow situations of available experiments, and examines the TT behaviors in more details. Key TT characteristics, including the rotation frequency, deformation index, and inclination angle, are compared with available experimental results of similar shear flow conditions. Fairly good simulation-experiment agreements for these parameters can be obtained by adjusting the membrane viscosity values; however, different rheological relationships between the membrane viscosity and the flow shear rate are noted for these comparisons: shear thinning from the TT frequency, Newtonian from the inclination angle, and shear thickening from the cell deformation. Previous studies claimed a shear-thinning membrane viscosity model based on the TT frequency results; however, such a conclusion seems premature from our results and more carefully designed and better controlled investigations are required for the RBC membrane rheology. In addition, our simulation results reveal complicate RBC TT features and such information could be helpful for a better understanding of in vivo and in vitro RBC dynamics.

Automated measurement of cell mechanical properties using an integrated dielectrophoretic microfluidic device

Cell mechanics is closely related to and interacts with cellular functions, which has the potential to be an effective biomarker to indicate disease onset and progression. Although several techniques have been developed for measuring cell mechanical properties, the issues of limited measurement data and biological significance because of complex and labor-intensive manipulation remain to be addressed, especially for the dielectrophoresis-based approach that is difficult to utilize flow measurement techniques. In this work, a dielectrophoresis-based solution is proposed to automatically obtain mass cellular mechanical data by combining a designed microfluidic device integrated the functions of cell capture, dielectrophoretic stretching, and cell release and an automatic control scheme. Experiments using human umbilical vein endothelial cells and breast cells revealed the automation capability of this device. The proposed method provides an effective way to address the low-throughput problem of dielectrophoresis-based cell mechanical property measurements, which enhance the biostatistical significance for cellular mechanism studies.

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Cell capture, dielectrophoretic stretching, and release in one microfluidic chip

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Automatic measurement scheme to realize circularly measurement

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Automatic acquisition of large amounts of cell mechanical properties data

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Significant advances in dielectrophoretic measurement of cell mechanical properties

On the effects of diabetes mellitus on the mechanical properties of DRG sensory neurons and their possible relation with diabetic neuropathy

Diabetic neuropathy (DN) is one of the principal complications of diabetes mellitus (DM). Dorsal root ganglion (DRG) neurons are the primary sensory neurons that transduce mechanical, chemical, thermal, and pain stimuli. Diabetes-caused sensitivity alterations and presence of pain are due to cellular damage originated by persistent hyperglycemia, microvascular insufficiency, and oxidative and nitrosative stress. However, the underlying mechanisms have not been fully clarified. The present work addresses this problem by hypothesizing that sensitivity changes in DN result from mechanotransduction-system alterations in sensory neurons; especially, plasma membrane affectations. This hypothesis is tackled by means of elastic-deformation experiments performed on DGR neurons from a murine model for type-1 DM, as well a mathematical model of the cell mechanical structure. The obtained results suggest that the plasma-membrane fluidity of DRG sensory neurons is modified by the induction of DM, and that this alteration may correlate with changes in the cell calcium transient that results from mechanical stimuli.

Non-invasive oocyte quality assessment

Oocyte quality is perhaps the most important limiting factor in female fertility; however, the current methods of determining oocyte competence are only marginally capable of predicting a successful pregnancy. We aim to review the predictive value of non-invasive techniques for the assessment of human oocytes and their related cells and biofluids that pertain to their developmental competence. Investigation of the proteome, transcriptome, and hormonal makeup of follicular fluid, as well as cumulus-oocyte complexes are currently underway; however, prospective randomized non-selection-controlled trials of the future are needed before determining their prognostic value. The biological significance of polar body morphology and genetics are still unknown and the subject of debate. The predictive utility of zygotic viscoelasticity for embryo development has been demonstrated, but similar studies performed on oocytes have yet to be conducted. Metabolic profiling of culture media using human oocytes are also limited and may require integration of automated, high-throughput targeted metabolomic assessments in real time with microfluidic platforms. Light exposure to oocytes can be detrimental to subsequent development and utilization of time-lapse imaging and morphometrics of oocytes is wanting. Polarized light, Raman microspectroscopy, and coherent anti-Stokes Raman scattering are a few novel imaging tools that may play a more important role in future oocyte assessment. Ultimately, the integration of chemistry, genomics, microfluidics, microscopy, physics, and other biomedical engineering technologies into the basic studies of oocyte biology, and in testing and perfecting practical solutions of oocyte evaluation, are the future for non-invasive assessment of oocytes.

Loading and relaxation dynamics of a red blood cell

We use mesoscale numerical simulations to investigate the unsteady dynamics of a single red blood cell (RBC) subjected to an external mechanical load. We carry out a detailed comparison between the loading (L) dynamics, following the imposition of the mechanical load on the RBC at rest, and the relaxation (R) dynamics, allowing the RBC to relax to its original shape after the sudden arrest of the mechanical load. Such a comparison is carried out by analyzing the characteristic times of the two corresponding dynamics, i.e., t_L and t_R. When the intensity of the mechanical load is small enough, the two kinds of dynamics are symmetrical (t_L≈t_R) and independent of the typology of mechanical load (intrinsic dynamics); otherwise, in marked contrast, an asymmetry is found, wherein the loading dynamics is typically faster than the relaxation one. This asymmetry manifests itself with non-universal characteristics, e.g., dependency on the applied load and/or on the viscoelastic properties of the RBC membrane. To deepen such a non-universal behaviour, we consider the viscosity of the erythrocyte membrane as a variable parameter and focus on three different typologies of mechanical load (mechanical stretching, shear flow, elongational flow): this allows to clarify how non-universality builds up in terms of the deformation and rotational contributions induced by the mechanical load on the membrane. Finally, we also investigate the effect of the elastic shear modulus on the characteristic times t_L and t_R. Our results provide crucial and quantitative information on the unsteady dynamics of RBC and its membrane response to the imposition/cessation of external mechanical loads.

Similar but Distinct Roles of Membrane and Interior Fluid Viscosities in Capsule Dynamics in Shear Flows

PURPOSE

The dynamics of biological capsules and red blood cells in shear flows has been studied extensively with experimental, analytical, and numerical methods. In particular, the effects of various parameters, including the shear rate or shear stress, membrane elasticity, capsule shape, and interior fluid viscosity, have been investigated carefully. The role of the membrane viscosity for capsule deformation dynamics has not been examined adequately. In previous studies, the so-called energy dissipation ratio has been used to account for the membrane viscosity effect by increasing the interior viscosity; however, the applicability and accuracy of this treatment have not been evaluated carefully.

METHODS

In this study, using the recently developed finite-difference scheme for immersed boundary simulations of viscoelastic membranes, we conduct comprehensive numerical simulations of the deformation processes of an originally spherical capsule in shear flows with various combinations of membrane and interior fluid viscosities.

RESULTS

Our results show that the membrane and interior fluid viscosity have similar however different effects on the capsule deformation dynamics. While the capsule deformation decreases with both membrane and interior fluid viscosities, a typical decrease-then-increase variation is observed for the inclination angle as the membrane viscosity increases, instead of the monotonic decrease in the inclination angle with the interior fluid viscosity increase. Also, although both large membrane and interior fluid viscosity values can introduce oscillations in the capsule deformation and inclination, larger aptitudes and slow decay processes are noticed at larger membrane viscosities. The variations of other dynamic parameters of the capsule, including the circumference, average membrane velocity, and rotation frequency, are also analyzed, and an intuitive mechanism is proposed to relate the membrane velocity and rotation frequency to the capsule deformation and inclination angle. The simple mechanism is then applied to explain the spoon-like variation patterns for membrane velocity and rotation frequency observed in our results. Furthermore, we examine the validity of the energy dissipation ratio approach based on the mathematical functional dependence.

CONCLUSIONS

Our results and analysis show that the dissipation ratio is a system and process dependent variable and it cannot be treated as a constant even for the same capsule. This research is valuable for a better understanding of the complex capsule dynamics in flows and also suggests that the membrane viscosity needs to be considered explicitly for accurate and reliable results in future studies.

Modeling of the Aorta: Complexities and Inadequacies

The aorta is a very complex organ comprising three layers, consisting of four kinds of tissues. It is an anisotropic, inhomogeneous, multiconstituent, and living organ that presents both a formidable challenge and a tremendous opportunity to a modeler to mathematically characterize its structure. Unfortunately, even the most sophisticated models in vogue do not faithfully take into consideration its various complexities, falling very short of putting into place a reasonable model, as they ignore many of the quintessential features that need to be taken into account. In this article, we address the various features that need to be taken into account to develop a meaningful model of the aorta.

Rapid formation of human immunodeficiency virus-like particles

Understanding the molecular mechanisms involved in the assembly of viruses is essential for discerning how viruses transmit from cell to cell and host to host. Although molecular aspects of assembly have been studied for many viruses, we still have little information about these events in real time. Enveloped viruses such as HIV that assemble at, and bud from, the plasma membrane have been studied in some detail using live cell fluorescence imaging techniques; however, these approaches provide little information about the real-time morphological changes that take place as viral components come together to form individual virus particles. Here we used correlative scanning ion conductance microscopy and fluorescence confocal microscopy to measure the topological changes, together with the recruitment of fluorescently labeled viral proteins such as Gag and Vpr, during the assembly and release of individual HIV virus-like particles (VLPs) from the top, nonadherent surfaces of living cells. We show that 1) labeling of viral proteins with green fluorescent protein affects particle formation, 2) the kinetics of particle assembly on different plasma membrane domains can vary, possibly as a consequence of differences in membrane biophysical properties, and 3) VLPs budding from the top, unimpeded surface of cells can reach full size in 20 s and disappear from the budding site in 0.5 to 3 min from the moment curvature is initially detected, significantly faster than has been previously reported.

A system for the high-throughput measurement of the shear modulus distribution of human red blood cells

Reduced deformability of red blood cells (RBCs) can affect the hemodynamics of the microcirculation and reduce oxygen transport efficiency. It is also well known that reduced RBC deformability is a signature of various physical disorders, including sepsis, and that the primary determinant of RBC deformability is the membrane shear modulus. To measure the distribution of an individual's RBC shear modulus with high throughput, we a) developed a high-fidelity computational model of RBCs in confined microchannels to inform design decisions; b) created a novel experimental system combining microfluidic flow, imaging, and image analysis; and c) performed automated comparisons between measured quantities and numerical predictions to extract quantitative measures of the RBC shear modulus for each of thousands of cells. We applied our computational simulation platform to construct the appropriate deformability figure(s) of merit to quantify RBC stiffness based on an experimentally measured, steady-state cell shape in flow through a microchannel. In particular, we determined a shape parameter based on the second moment of the cell shape that is sensitive to the changes in the membrane stiffness and cell size. We then conducted microfluidic experiments and developed custom automated image processing codes to identify and track the position and shape of individual RBCs within micro-constrictions. The fabricated microchannels include a square cross-section imaging region (7 by 7 μm) and we applied order 10 kPa pressure differences to induce order 10 mm s^-1 cell velocities. The combination of modeling, microfluidics, and imaging enables, for the first time, quantitative measurement of the shear moduli of thousands of RBCs in human blood samples. We demonstrate the high-throughput features by sensitive quantification of the changes in the distribution of RBC stiffness with aging. This combined measurement and computational platform is ultimately intended to diagnose blood cell disorders in patients.

On the effects of membrane viscosity on transient red blood cell dynamics

Computational Fluid Dynamics (CFD) is currently used to design and improve the hydraulic properties of biomedical devices, wherein the large scale blood circulation needs to be simulated by accounting for the mechanical response of red blood cells (RBCs) at the mesoscale. In many practical instances, biomedical devices work on time-scales comparable to the intrinsic relaxation time of RBCs: thus, a systematic understanding of the time-dependent response of erythrocyte membranes is crucial for the effective design of such devices. So far, this information has been deduced from experimental data, which do not necessarily adapt to the broad variety of fluid dynamic conditions that can be encountered in practice. This work explores the novel possibility of studying the time-dependent response of an erythrocyte membrane to external mechanical loads via mesoscale numerical simulations, with a primary focus on the detailed characterisation of the RBC relaxation time tc following the arrest of the external mechanical load. The adopted mesoscale model exploits a hybrid Immersed Boundary-Lattice Boltzmann Method (IB-LBM), coupled with the Standard Linear Solid (SLS) model to account for the RBC membrane viscosity. We underscore the key importance of the 2D membrane viscosity μm to correctly reproduce the relaxation time of the RBC membrane. A detailed assessment of the dependencies on the typology and strength of the applied mechanical loads is also provided. Overall, our findings open interesting future perspectives for the study of the non-linear response of RBCs immersed in time-dependent strain fields.

Dual shape recovery of red blood cells flowing out of a microfluidic constriction

Micropipette aspiration, optical tweezers, rheometry, or ecktacytometry have been used to study the shape recovery of healthy human Red Blood Cells (RBCs) and measure associated relaxation times of the order of 100-300 ms. These measurements are in good agreement with the Kelvin-Voigt model, which describes the cell as a visco-elastic material, predicting that its relaxation time only depends on cell intrinsic properties. However, such mechanical solicitation techniques are far from being relevant regarding RBC solicitation in vivo. In this paper, we report for the first time the existence of two different behaviors of the RBC shape recovery while flowing out of a microfluidic constricted channel. The calculation of the viscous stress corresponding to the frontier between the two recovery modes confirms that the RBC resistance to shear μ is the elastic property dominating the transition between the two recovery behaviors. We also quantified associated recovery times τ r and report values as low as 4 ms-which is almost two decades smaller than the typical RBC relaxation time-at high viscosity and flow velocity of the carrier fluid. Although we cannot talk about relaxation time because the cell is never at rest, we believe that the measured shape recovery time arises from the coupling of the cell intrinsic deformability and the hydrodynamic stress. Depending on the flow conditions, the cell mechanics becomes dominant and drives the shape recovery process, allowing the measurement of recovery times of the same order of magnitude than relaxation times previously published. Finally, we demonstrated that the measurement of the shape recovery time can be used to distinguish Plasmodium falciparum (causing malaria) infected RBCs from healthy RBCs.

Structure, mechanical properties, and modeling of cyclically compressed pulmonary emboli

Pulmonary embolism occurs when blood flow to a part of the lungs is blocked by a venous thrombus that has traveled from the lower limbs. Little is known about the mechanical behavior of emboli under compressive forces from the surrounding musculature and blood pressure. We measured the stress-strain responses of human pulmonary emboli under cyclic compression, and showed that emboli exhibit a hysteretic stress-strain curve. The fibrin fibers and red blood cells (RBCs) are damaged during the compression process, causing irreversible changes in the structure of the emboli. We showed using electron and confocal microscopy that bundling of fibrin fibers occurs due to compression, and damage is accumulated as more cycles are applied. The stress-strain curves depend on embolus structure, such that variations in composition give quantitatively different responses. Emboli with a high fibrin component demonstrate higher normal stress compared to emboli that have a high RBC component. We compared the compression response of emboli to that of whole blood clots containing various volume fractions of RBCs, and found that RBCs rupture at a certain critical stress. We describe the hysteretic response characteristic of foams, using a model of phase transitions in which the compressed foam is segregated into coexisting rarefied and densified phases whose fractions change during compression. Our model takes account of the rupture of RBCs in the compressed emboli and stresses due to fluid flow through their small pores. Our results can help in classifying emboli as rich in fibrin or rich in red blood cells, and can help in understanding what responses to expect when stresses are applied to thrombi in vivo.

Experimental study of the difference in deformation between normal and pathological, renal and bladder, cells induced by acoustic radiation force

Previous studies have shown that alterations in the mechanical properties of cells may be associated with the onset and progression of some forms of pathology. In this paper, an experimental study of two types of cells, renal (cancer) and bladder (cancer) cells, is described which used acoustic radiation force (ARF) generated by a high-frequency ultrasound focusing transducer and performed on the operating platform of an inverted light microscope. Comparing images of cancer cells with those of normal cells of the same kind, we find that the cancer cells are more prone to deform than normal cells of the same kind under the same ARF. In addition, cancer cells with higher malignancy are more deformable than those with lower malignancy. This means that the deformability of cells may be used to distinguish diseased cells from normal ones, and more aggressive cells from less aggressive ones, which may provide a more rapid and accurate method for clinical diagnosis of urological disease in the future.

Surface Shear Viscosity and Interleaflet Friction from Nonequilibrium Simulations of Lipid Bilayers

Nonequilibrium simulation protocols based on shear deformations are applied to determine the surface viscosity and interleaflet friction of lipid bilayers. At high shear rates, a non-Newtonian shear thinning regime is observed, but lower shear rates yield a Newtonian plateau and results that are consistent with equilibrium measurements based on fluctuation-dissipation theorems. Application to all-atom bilayers modeled with the CHARMM36 parameter set yields values for the surface viscosity that are consistent with microscopic measurements based on membrane protein diffusion but are approximately 10 times lower than more macroscopic experimental measurements. The interleaflet friction is about 10 times lower than experimental measurements. Trends across different lipids, temperatures, and ternary liquid-disordered phase mixtures produce results that are consistent with experimental diffusion constants. Application of the protocol to the liquid-ordered phase fails to yield a Newtonian plateau, suggesting more complex rheology.

Interplay of elastic instabilities and viscoelasticity in the finite deformation of thin membranes

Pneumatic structures and actuators are found in a variety of natural and engineered systems such as dielectric actuators, soft robots, plants and fungi cells, or even the vocal sac of frogs. These structures are often subjected to mechanical instabilities arising from the thinning of their cross section and that may be harvested to perform mechanical work at a low energetic cost. While most of our understanding of this unstable behavior is for purely elastic membranes, real materials including lipid bilayers, elastomers, and connective tissues typically display a time-dependent viscoelastic response. This paper thus explores the role of viscous effects on the nature of this elastic instability when such membranes are dynamically inflated. For this, we first introduce an extension of the transient network theory to describe the finite strain viscoelastic response of membranes, enabling an elegant formulation while keeping a close connection with the dynamics of the underlying polymer network. We then combine experiments and simulations to analyze the viscoelastic behavior of an inflated blister made of a commercial adhesive tape (VHB 4905). Our results show that the viscous component induces a rich spectrum of behaviors bounded by two well-known elastic solutions corresponding to very high and very low inflation rates. We also show that membrane relaxation may induce unwanted buckling when it is subjected to cyclic inflations at certain frequencies. These results have clear implications for the inflation and mechanical work performed by time-dependent pneumatic structures and instability-based actuators.

Mechanics and Dynamics of Bacterial Cell Lysis

Membrane lysis, or rupture, is a cell death pathway in bacteria frequently caused by cell wall-targeting antibiotics. Although previous studies have clarified the biochemical mechanisms of antibiotic action, a physical understanding of the processes leading to lysis remains lacking. Here, we analyze the dynamics of membrane bulging and lysis in Escherichia coli, in which the formation of an initial, partially subtended spherical bulge ("bulging") after cell wall digestion occurs on a characteristic timescale of 1 s and the growth of the bulge ("swelling") occurs on a slower characteristic timescale of 100 s. We show that bulging can be energetically favorable due to the relaxation of the entropic and stretching energies of the inner membrane, cell wall, and outer membrane and that the experimentally observed timescales are consistent with model predictions. We then show that swelling is mediated by the enlargement of wall defects, after which cell lysis is consistent with both the inner and outer membranes exceeding characteristic estimates of the yield areal strains of biological membranes. These results contrast biological membrane physics and the physics of thin, rigid shells. They also have implications for cellular morphogenesis and antibiotic discovery across different species of bacteria.

Entry and passage behavior of biological cells in a constricted compliant microchannel

We report an experimental and theoretical investigation of the entry and passage behaviour of biological cells (HeLa and MDA-MB-231) in a constricted compliant microchannel. Entry of a cell into a micro-constriction takes place in three successive regimes: protrusion and contact (cell protrudes its leading edge and makes a contact with the channel wall), squeeze (cell deforms to enter into the constriction) and release (cell starts moving forward). While the protrusion and contact regime is insensitive to the flexibility of the channel, the squeeze zone is significantly smaller in the case of a more compliant channel. Similarly, in the release zone, the acceleration of the cells into the microconstriction is higher in the case of a more compliant channel. The results showed that for a fixed size ratio ρ and E c, the extension ratio λ decreases and transit velocity U c increases with increase in the compliance parameter f p. The variation in the cell velocity is governed by force due to the cell stiffness F s as well as that due to the viscous dampening F d, explained using the Kelvin-Voigt viscoelastic model. The entry time t e = m(ρ) k 1 (1 + f p) k 2 (E c) k 3 and induced hydrodynamic resistance of a cell ΔR c/R = k(ρ) a (1 + k f f p) b (k E E c) c were correlated with cell size ratio ρ, Young's modulus E c and compliance parameter f p, which showed that both entry time t e and the induced hydrodynamic resistance ΔR c are most sensitive to the change in the compliance parameter f p. This study provides understanding of the passage of cells in compliant micro-confinements that can have significant impact on mechanophenotyping of single cells.

A combined experimental and theoretical approach towards mechanophenotyping of biological cells using a constricted microchannel

We report a combined experimental and theoretical technique that enables the characterization of various mechanical properties of biological cells. The cells were infused into a microfluidic device that comprises multiple parallel micro-constrictions to eliminate device clogging and facilitate characterization of cells of different sizes and types on a single device. The extension ratio λ and transit velocity U_c of the cells were measured using high-speed and high-resolution imaging which were then used in a theoretical model to predict the Young's modulus E_c = f(λ, U_c) of the cells. The predicted Young's modulus E_c values for three different cell lines (182 ± 34.74 Pa for MDA MB 231, 360 ± 75 Pa for MCF 10A and, 763 ± 93 Pa for HeLa) compare well with those reported in the literature from micropipette measurements and atomic force microscopy measurement within 10% and 15%, respectively. Also, the Young's modulus of MDA-MB-231 cells treated with 50 μM 4-hyrdroxyacetophenone (for localization of myosin II) for 30 min was found out to be 260 ± 52 Pa. The entry time t_e of cells into the micro-constrictions was predicted using the model and validated using experimentally measured data. The entry and transit behaviors of cells in the micro-constriction including cell deformation (extension ratio λ) and velocity U_c were experimentally measured and used to predict various cell properties such as the Young's modulus, cytoplasmic viscosity and induced hydrodynamic resistance of different types of cells. The proposed combined experimental and theoretical approach leads to a new paradigm for mechanophenotyping of biological cells.

Phase transitions during compression and decompression of clots from platelet-poor plasma, platelet-rich plasma and whole blood

Blood clots are required to stem bleeding and are subject to a variety of stresses, but they can also block blood vessels and cause heart attacks and ischemic strokes. We measured the compressive response of human platelet-poor plasma (PPP) clots, platelet-rich plasma (PRP) clots and whole blood clots and correlated these measurements with confocal and scanning electron microscopy to track changes in clot structure. Stress-strain curves revealed four characteristic regions, for compression-decompression: (1) linear elastic region; (2) upper plateau or softening region; (3) non-linear elastic region or re-stretching of the network; (4) lower plateau in which dissociation of some newly made connections occurs. Our experiments revealed that compression proceeds by the passage of a phase boundary through the clot separating rarefied and densified phases. This observation motivates a model of fibrin mechanics based on the continuum theory of phase transitions, which accounts for the pre-stress caused by platelets, the adhesion of fibrin fibers in the densified phase, the compression of red blood cells (RBCs), and the pumping of liquids through the clot during compression/decompression. Our experiments and theory provide insights into the mechanical behavior of blood clots that could have implications clinically and in the design of fibrin-based biomaterials.

STATEMENT OF SIGNIFICANCE

The objective of this paper is to measure and mathematically model the compression behavior of various human blood clots. We show by a combination of confocal and scanning electron microscopy that compression proceeds by the passage of a front through the sample that separates a densified region of the clot from a rarefied region, and that the compression/decompression response is reversible with hysteresis. These observations form the basis of a model for the compression response of clots based on the continuum theory of phase transitions. Our studies may reveal how clot rheology under large compression in vivo due to muscle contraction, platelet retraction and hydrodynamic flow varies under various pathophysiological conditions and could inform the design of fibrin based biomaterials.

Interfacing 3D magnetic twisting cytometry with confocal fluorescence microscopy to image force responses in living cells

Cells and tissues can undergo a variety of biological and structural changes in response to mechanical forces. Only a few existing techniques are available for quantification of structural changes at high resolution in response to forces applied along different directions. 3D-magnetic twisting cytometry (3D-MTC) is a technique for applying local mechanical stresses to living cells. Here we describe a protocol for interfacing 3D-MTC with confocal fluorescence microscopy. In 3D-MTC, ferromagnetic beads are bound to the cell surface via surface receptors, followed by their magnetization in any desired direction. A magnetic twisting field in a different direction is then applied to generate rotational shear stresses in any desired direction. This protocol describes how to combine magnetic-field-induced mechanical stimulation with confocal fluorescence microscopy and provides an optional extension for super-resolution imaging using stimulated emission depletion (STED) nanoscopy. This technology allows for rapid real-time acquisition of a living cell's mechanical responses to forces via specific receptors and for quantifying structural and biochemical changes in the same cell using confocal fluorescence microscopy or STED. The integrated 3D-MTC-microscopy platform takes ∼20 d to construct, and the experimental procedures require ∼4 d when carried out by a life sciences graduate student.

Mechanical diagnosis of human erythrocytes by ultra-high speed manipulation unraveled critical time window for global cytoskeletal remodeling

Large deformability of erythrocytes in microvasculature is a prerequisite to realize smooth circulation. We develop a novel tool for the three-step “Catch-Load-Launch” manipulation of a human erythrocyte based on an ultra-high speed position control by a microfluidic “robotic pump”. Quantification of the erythrocyte shape recovery as a function of loading time uncovered the critical time window for the transition between fast and slow recoveries. The comparison with erythrocytes under depletion of adenosine triphosphate revealed that the cytoskeletal remodeling over a whole cell occurs in 3 orders of magnitude longer timescale than the local dissociation-reassociation of a single spectrin node. Finally, we modeled septic conditions by incubating erythrocytes with endotoxin, and found that the exposure to endotoxin results in a significant delay in the characteristic transition time for cytoskeletal remodeling. The high speed manipulation of erythrocytes with a robotic pump technique allows for high throughput mechanical diagnosis of blood-related diseases.

Mechanics of Biomimetic Liposomes Encapsulating an Actin Shell

Cell-shape changes are insured by a thin, dynamic, cortical layer of cytoskeleton underneath the plasma membrane. How this thin cortical structure impacts the mechanical properties of the whole cell is not fully understood. Here, we study the mechanics of liposomes or giant unilamellar vesicles, when a biomimetic actin cortex is grown at the inner layer of the lipid membrane via actin-nucleation-promoting factors. Using a hydrodynamic tube-pulling technique, we show that tube dynamics is clearly affected by the presence of an actin shell anchored to the lipid bilayer. The same force pulls much shorter tubes in the presence of the actin shell compared to bare membranes. However, in both cases, we observe that the dynamics of tube extrusion has two distinct features characteristic of viscoelastic materials: rapid elastic elongation, followed by a slower elongation phase at a constant rate. We interpret the initial elastic regime by an increase of membrane tension due to the loss of lipids into the tube. Tube length is considerably shorter for cortex liposomes at comparable pulling forces, resulting in a higher spring constant. The presence of the actin shell seems to restrict lipid mobility, as is observed in the corral effect in cells. The viscous regime for bare liposomes corresponds to a leakout of the internal liquid at constant membrane tension. The presence of the actin shell leads to a larger friction coefficient. As the tube is pulled from a patchy surface, membrane tension increases locally, leading to a Marangoni flow of lipids. As a conclusion, the presence of an actin shell is revealed by its action that alters membrane mechanics.

Hemodynamics in stenotic vessels of small diameter under steady state conditions: Effect of viscoelasticity and migration of red blood cells

BACKGROUND

In microcirculation, the non-Newtonian behavior of blood and the complexity of the microvessel network are responsible for the high flow resistance and the large reduction of the blood pressure. Red blood cell aggregation along with inward radial migration are two significant mechanisms determining the former. Yet, their impact on hemodynamics in non-straight vessels is not well understood.

OBJECTIVE

In this study, the steady state blood flow in stenotic rigid vessels is examined, employing a sophisticated non-homogeneous constitutive law. The effect of red blood cells migration on the hydrodynamics is quantified and the constitutive model's accuracy is evaluated.

METHODS

A numerical algorithm based on the two-dimensional mixed finite element method and the EVSS/SUPG technique for a stable discretization of the mass and momentum conservation equations in addition to the constitutive model is employed.

RESULTS

The numerical simulations show that a cell-depleted layer develops along the vessel wall with an almost constant thickness for slow flow conditions. This causes the reduction of the drag force and the increase of the pressure gradient as the constriction ratio decreases.

CONCLUSIONS

Viscoelastic effects in blood flow were found to be responsible for steeper decreases of tube and discharge hematocrits as decreasing function of constriction ratio.

Elastic deformations of bolalipid membranes

Archaeal membranes have unique mechanical properties that enable these organisms to survive under extremely aggressive environmental conditions. The so-called bolalipids contribute to this exceptional stability. They have two polar heads joined by two hydrocarbon chains. The two headgroups can face different sides of the membrane (O-shape conformation) or the same side (U-shape conformation). We have developed an elasticity theory for bolalipid membranes and show that the energetic contributions of (i) tilt deformations, (ii) area compression/stretching deformations, (iii) as well as those of Gaussian splay from the two membrane surfaces are additive, while splay deformations yield a cross-term. The presence of a small fraction of U-shaped molecules resulted in spontaneous membrane curvature. We estimated the tilt modulus to be approximately equal to that of membranes in eukaryotic cells. In contrast to conventional lipids, the bolalipid membrane possesses two splay moduli, one of which is estimated to be an order of magnitude larger than that of conventional lipids. The projected values of elastic moduli act to hamper pore formation and to decelerate membrane fusion and fission.

Continuum modeling of deformation and aggregation of red blood cells

In order to gain better understanding for rheology of an isolated red blood cell (RBC) and a group of multiple RBCs, new continuum models for describing mechanical properties of cellular structures of an RBC and inter-cellular interactions among multiple RBCs are developed. The viscous property of an RBC membrane, which characterizes dynamic behaviors of an RBC under stress loading and unloading processes, is determined using a generalized Maxwell model. The present model is capable of predicting stress relaxation and stress-strain hysteresis, of which prediction is not possible using the commonly used Kelvin-Voigt model. Nonlinear elasticity of an RBC is determined using the Yeoh hyperelastic material model in a framework of continuum mechanics using finite-element approximation. A novel method to model inter-cellular interactions among multiple adjacent RBCs is also developed. Unlike the previous modeling approaches for aggregation of RBCs, where interaction energy for aggregation is curve-fitted using a Morse-type potential function, the interaction energy is analytically determined. The present aggregation model, therefore, allows us to predict various effects of physical parameters such as the osmotic pressure, the thickness of a glycocalyx layer, the penetration depth, and the permittivity, on the depletion and electrostatic energy among RBCs. Simulations for elongation and recovery deformation of an RBC and for aggregation of multiple RBCs are conducted to evaluate the efficacy of the present continuum modeling methods.

Dynamics of a single red blood cell in simple shear flow

This work describes simulations of a red blood cell (RBC) in simple shear flow, focusing on the dependence of the cell dynamics on the spontaneous curvature of the membrane. The results show that an oblate spheroidal spontaneous curvature maintains the dimple of the RBC during tank-treading dynamics as well as exhibits off-shear-plane tumbling consistent with the experimental observations of Dupire et al. [J. Dupire, M. Socol, and A. Viallat, Proc. Natl. Acad. Sci. USA 109, 20808 (2012)] and their hypothesis of an inhomogeneous spontaneous shape. As the flow strength (capillary number Ca) is increased at a particular viscosity ratio between inner and outer fluid, the dynamics undergo transitions in the following sequence: tumbling, kayaking or rolling, tilted tank-treading, oscillating-swinging, swinging, and tank-treading. The tilted tank-treading (or spinning frisbee) regime has been previously observed in experiments but not in simulations. Two distinct classes of regime are identified: a membrane reorientation regime, where the part of membrane that is at the dimple at rest moves to the rim and vice versa, is observed in motions at high Ca such as tilted tank-treading, oscillating-swinging, swinging, and tank-treading, and a nonreorientation regime, where the part of the membrane starting from the dimple stays at the dimple, is observed in motions at low Ca such as rolling, tumbling, kayaking, and flip-flopping.

Reprint of: Connections between single-cell biomechanics and human disease states: gastrointestinal cancer and malaria

We investigate connections between single-cell mechanical properties and subcellular structural reorganization from biochemical factors in the context of two distinctly different human diseases: gastrointestinal tumor and malaria. Although the cell lineages and the biochemical links to pathogenesis are vastly different in these two cases, we compare and contrast chemomechanical pathways whereby intracellular structural rearrangements lead to global changes in mechanical deformability of the cell. This single-cell biomechanical response, in turn, seems to mediate cell mobility and thereby facilitates disease progression in situations where the elastic modulus increases or decreases due to membrane or cytoskeleton reorganization. We first present new experiments on elastic response and energy dissipation under repeated tensile loading of epithelial pancreatic cancer cells in force- or displacement-control. Energy dissipation from repeated stretching significantly increases and the cell's elastic modulus decreases after treatment of Panc-1 pancreatic cancer cells with sphingosylphosphorylcholine (SPC), a bioactive lipid that influences cancer metastasis. When the cell is treated instead with lysophosphatidic acid, which facilitates actin stress fiber formation, neither energy dissipation nor modulus is noticeably affected. Integrating recent studies with our new observations, we ascribe these trends to possible SPC-induced reorganization primarily of keratin network to perinuclear region of cell; the intermediate filament fraction of the cytoskeleton thus appears to dominate deformability of the epithelial cell. Possible consequences of these results to cell mobility and cancer metastasis are postulated. We then turn attention to progressive changes in mechanical properties of the human red blood cell (RBC) infected with the malaria parasite Plasmodium falciparum. We present, for the first time, continuous force-displacement curves obtained from in-vitro deformation of RBC with optical tweezers for different intracellular developmental stages of parasite. The shear modulus of RBC is found to increase up to 10-fold during parasite development, which is a noticeably greater effect than that from prior estimates. By integrating our new experimental results with published literature on deformability of Plasmodium-harbouring RBC, we examine the biochemical conditions mediating increases or decreases in modulus, and their implications for disease progression. Some general perspectives on connections among structure, single-cell mechanical properties and biological responses associated with pathogenic processes are also provided in the context of the two diseases considered in this work.

Theoretical study of microbubble dynamics in sonoporation

Sonoporation is a promising technology for promoting the transfer of drug or gene into cells using ultrasound-mediated microbubbles that transiently break up the cell membrane. In this article, a model is established to analyze the dynamics of ultrasound-mediated microbubble near the cell membrane, which may be especially useful for understanding the mechanisms of sonoporation. In the model, the velocity potential of fluid on the microbubble surface and on the cell membrane is obtained by the unsteady Bernoulli equations, and it is solved by using the boundary integral equations. By numerically analyzing the model, the typical microbubble dynamics near the cell membrane are enumerated, which may be mainly governed by mechanical index. The model also established the connections among the parameters of ultrasound exposure, microbubble characteristics, and cell membrane properties in sonoporation.

Viscoelastic transient of confined red blood cells

The unique ability of a red blood cell to flow through extremely small microcapillaries depends on the viscoelastic properties of its membrane. Here, we study in vitro the response time upon flow startup exhibited by red blood cells confined into microchannels. We show that the characteristic transient time depends on the imposed flow strength, and that such a dependence gives access to both the effective viscosity and the elastic modulus controlling the temporal response of red cells. A simple theoretical analysis of our experimental data, validated by numerical simulations, further allows us to compute an estimate for the two-dimensional membrane viscosity of red blood cells, η(mem)(2D) ∼ 10(-7) N ⋅ s ⋅ m(-1). By comparing our results with those from previous studies, we discuss and clarify the origin of the discrepancies found in the literature regarding the determination of η(mem)(2D), and reconcile seemingly conflicting conclusions from previous works.

Nonlinear viscoelastic contact mechanics of long rectangular membranes

A theoretical and numerical analysis of a long rectangular nonlinear viscoelastic membrane in adhesionless contact with a rigid substrate is presented. Computations are carried out for the case where material behaviour is given by Christensen's large deformation viscoelastic law. The effect of friction, loading and unloading rates, hold time and material viscosity on the deformation, energy dissipation and detachment load is investigated in detail. Wrinkling of the membrane is found for a subset of the parameter space. Our results show that energy dissipation and detachment load depend on the contact length achieved at peak pressure, in addition to the rate of loading and unloading. Our numerical results also reveal that there can be situations where maximum dissipation does not correspond to maximum detachment load.