Cytosol Viscosity Research Articles

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.

Effect of Cell Age and Membrane Rigidity on Red Blood Cell Shape in Capillary Flow.

Blood flow in the microcirculatory system is crucially affected by intrinsic red blood cell (RBC) properties, such as their deformability. In the smallest vessels of this network, RBCs adapt their shapes to the flow conditions. Although it is known that the age of RBCs modifies their physical properties, such as increased cytosol viscosity and altered viscoelastic membrane properties, the evolution of their shape-adapting abilities during senescence remains unclear. In this study, we investigated the effect of RBC properties on the microcapillary in vitro flow behavior and their characteristic shapes in microfluidic channels. For this, we fractioned RBCs from healthy donors according to their age. Moreover, the membranes of fresh RBCs were chemically rigidified using diamide to study the effect of isolated graded-membrane rigidity. Our results show that a fraction of stable, asymmetric, off-centered slipper-like cells at high velocities decreases with increasing age or diamide concentration. However, while old cells form an enhanced number of stable symmetric croissants at the channel centerline, this shape class is suppressed for purely rigidified cells with diamide. Our study provides further knowledge about the distinct effects of age-related changes of intrinsic cell properties on the single-cell flow behavior of RBCs in confined flows due to inter-cellular age-related cell heterogeneity.

The Mechanics of (Poro-)Elastic Contractile Actomyosin Networks As a Model System of the Cell Cytoskeleton.

Cells can actively change their shapes and become motile, a property that depends on their ability to actively reorganize their internal structure. This feature is attributed to the mechanical and dynamic properties of the cell cytoskeleton, notably, the actomyosin cytoskeleton, which is an active gel of polar actin filaments, myosin motors, and accessory proteins that exhibit intrinsic contraction properties. The usually accepted view is that the cytoskeleton behaves as a viscoelastic material. However, this model cannot always explain the experimental results, which are more consistent with a picture describing the cytoskeleton as a poroelastic active material-an elastic network embedded with cytosol. Contractility gradients generated by the myosin motors drive the flow of the cytosol across the gel pores, which infers that the mechanics of the cytoskeleton and the cytosol are tightly coupled. One main feature of poroelasticity is the diffusive relaxation of stresses in the network, characterized by an effective diffusion constant that depends on the gel elastic modulus, porosity, and cytosol (solvent) viscosity. As cells have many ways to regulate their structure and material properties, our current understanding of how cytoskeleton mechanics and cytosol flow dynamics are coupled remains poorly understood. Here, an in vitro reconstitution approach is employed to characterize the material properties of poroelastic actomyosin gels as a model system for the cell cytoskeleton. Gel contraction is driven by myosin motor contractility, which leads to the emergence of a flow of the penetrating solvent. The paper describes how to prepare these gels and run experiments. We also discuss how to measure and analyze the solvent flow and gel contraction both at the local and global scales. The various scaling relations used for data quantification are given. Finally, the experimental challenges and common pitfalls are discussed, including their relevance to cell cytoskeleton mechanics.

Intracellular Crowding by Bio-Orthogonal Hydrogel Formation Induces Reversible Molecular Stasis.

To survive extreme conditions, certain animals enter a reversible protective stasis through vitrification of the cytosol by polymeric molecules such as proteins and polysaccharides. In this work, synthetic gelation of the cytosol in living cells is used to induce reversible molecular stasis. Through the sequential lipofectamine-mediated transfection of complementary poly(ethylene glycol) macromers into mammalian cells, intracellular crosslinking occurs through bio-orthogonal strain-promoted azide-alkyne cycloaddition click reactions. This achieves efficient polymer uptake with minimal cell death (99% viable). Intracellular crosslinking decreases DNA replication and protein synthesis, and increases the quiescent population by 2.5-fold. Real-time tracking of single cells containing intracellular crosslinked polymers identifies increases in intermitotic time (15 hvs 19 h) and decreases in motility (30 µm h-1 vs 15µm h-1 ). The cytosol viscosity increases threefold after intracellular crosslinking and results in disordered cytoskeletal structure in addition to the disruption of cellular coordination in a scratch assay. By incorporating photodegradable nitrobenzyl moieties into the polymer backbone, the effects of intracellular crosslinking are reversed upon exposure to light, thereby restoring proliferation (80% phospho-Rb+ cells), protein translation, and migration. Reversible intracellular crosslinking provides a novel method for dynamic manipulation of intracellular mechanics, altering essential processes that determine cellular function.

Functional and Conformational Plasticity of an Animal Group 1 LEA Protein.

Group 1 (Dur-19, PF00477, LEA_5) Late Embryogenesis Abundant (LEA) proteins are present in organisms from all three domains of life, Archaea, Bacteria, and Eukarya. Surprisingly, Artemia is the only genus known to include animals that express group 1 LEA proteins in their desiccation-tolerant life-history stages. Bioinformatics analysis of circular dichroism data indicates that the group 1 LEA protein AfLEA1 is surprisingly ordered in the hydrated state and undergoes during desiccation one of the most pronounced disorder-to-order transitions described for LEA proteins from A. franciscana. The secondary structure in the hydrated state is dominated by random coils (42%) and β-sheets (35%) but converts to predominately α-helices (85%) when desiccated. Interestingly, AfLEA1 interacts with other proteins and nucleic acids, and RNA promotes liquid–liquid phase separation (LLPS) of the protein from the solvent during dehydration in vitro. Furthermore, AfLEA1 protects the enzyme lactate dehydrogenase (LDH) during desiccation but does not aid in restoring LDH activity after desiccation-induced inactivation. Ectopically expressed in D. melanogaster Kc167 cells, AfLEA1 localizes predominantly to the cytosol and increases the cytosolic viscosity during desiccation compared to untransfected control cells. Furthermore, the protein formed small biomolecular condensates in the cytoplasm of about 38% of Kc167 cells. These findings provide additional evidence for the hypothesis that the formation of biomolecular condensates to promote water stress tolerance during anhydrobiosis may be a shared feature across several groups of LEA proteins that display LLPS behaviors.

Multiscale computational framework for predicting viscoelasticity of red blood cells in aging and mechanical fatigue

Red blood cells (RBCs) experience significant cyclic deformation through large elastic stretching and relaxation as they circulate in the bloodstream. Such hundreds of thousands times cell deformation causes cumulative fatigue damage to the circulating RBCs, leading to alterations in cell deformability and membrane viscoelasticity. Here, we employ a two-step multiscale computational framework based on coarse-grained molecular dynamics (CGMD) and dissipative particle dynamics (DPD) to probe the viscoelastic properties of the surface-altered RBCs in aging and mechanical fatigue, using experimental information on the molecular structures of both RBC membrane and cytosolic Hb as well as Hb concentration of RBC cytosol. We perform CGMD simulations to compute the shear modulus and membrane viscosity of a small RBC patch with altered horizontal connectivity within spectrin network; meanwhile, we compute the shear viscosity of RBC cytosol under different Hb concentrations. We then use these computed parameters as inputs for a more coarse-grained DPD-based RBC model at the whole-cell level to probe cell deformation, dynamic relaxation, viscoelastic performance of the altered RBC membrane. We find that the RBC membrane rigidity increases with the enhanced horizontal connectivity within spectrin network, but by a factor less than the effective membrane viscosity, resulting in an elevated characteristic relaxation time with increasing fatigue cycles. In addition, we quantify the two-dimensional storage and loss moduli of RBC membrane under time-dependent loading, revealing that the loss modulus is much larger than the storage modulus throughout the entire frequency range covered by the simulations, especially under enhanced connectivity in the cytoskeletal network, which is analogous to the performance of typical viscoelastic materials. These quantitative findings provide unique insights into the progressive damage of circulating RBCs, and demonstrate the capability of the two-step multiscale framework in effectively predicting the altered viscoelastic properties of RBCs influenced by in vivo aging and mechanical fatigue.

Red blood cell shape transitions and dynamics in time-dependent capillary flows

The dynamics of single red blood cells (RBCs) determine microvascular blood flow by adapting their shape to the flow conditions in the narrow vessels. In this study, we explore the dynamics and shape transitions of RBCs on the cellular scale under confined and unsteady flow conditions using a combination of microfluidic experiments and numerical simulations. Tracking RBCs in a comoving frame in time-dependent flows reveals that the mean transition time from the symmetric croissant to the off-centered, nonsymmetric slipper shape is significantly faster than the opposite shape transition, which exhibits pronounced cell rotations. Complementary simulations indicate that these dynamics depend on the orientation of the RBC membrane in the channel during the time-dependent flow. Moreover, we show how the tank-treading movement of slipper-shaped RBCs in combination with the narrow channel leads to oscillations of the cell's center of mass. The frequency of these oscillations depends on the cell velocity, the viscosity of the surrounding fluid, and the cytosol viscosity. These results provide a potential framework to identify and study pathological changes in RBC properties.

Importance of Viscosity Contrast for the Motion of Erythrocytes in Microcapillaries

The dynamics and deformation of red blood cells (RBCs) in microcirculation affect the flow resistance and transport properties of whole blood. One of the key properties that can alter RBC dynamics in flow is the contrast λ (or ratio) of viscosities between RBC cytosol and blood plasma. Here, we study the dependence of RBC shape and dynamics on the viscosity contrast in tube flow, using mesoscopic hydrodynamics simulations. State diagrams of different RBC dynamical states, including tumbling cells, parachutes, and tank-treading slippers, are constructed for various viscosity contrasts and wide ranges of flow rates and tube diameters (or RBC confinements). Despite similarities in the classification of RBC behavior for different viscosity contrasts, there are notable differences in the corresponding state diagrams. In particular, the region of parachutes is significantly larger for λ = 1 in comparison to λ = 5. Furthermore, the viscosity contrast strongly affects the tumbling-to-slipper transition, thus modifying the regions of occurrence of these states as a function of flow rate and RBC confinement. Also, an increase in cytosol viscosity leads to a reduction in membrane tension induced by flow stresses. Physical mechanisms that determine these differences in RBC dynamical states as a function of λ are discussed.

Effect of cytosol viscosity on the flow behavior of red blood cell suspensions in microvessels.

The flow behavior of blood is strongly affected by red blood cell (RBC) properties, such as the viscosity ratio C between cytosol and suspending medium, which can significantly be altered in several pathologies (e.g. sickle-cell disease, malaria). The main objective of this study is to understand the effect of C on macroscopic blood flow properties such as flow resistance in microvessels, and to link it to the deformation and dynamics of single RBCs. We employ mesoscopic hydrodynamic simulations to investigate flow properties of RBC suspensions with different cytosol viscosities for various flow conditions in cylindrical microchannels. Starting from a dispersed cell configuration which approximates RBC dispersion at vessel bifurcations in the microvasculature, we find that the flow convergence and development of RBC-free layer (RBC-FL) depend only weakly on C, and require a convergence length in the range of 25D-50D, where D is channel diameter. In vessels with , the final resistance of developed flow is nearly the same for C=5 and C=1, while for , the flow resistance for C=5 is about 10% larger than for C=1. The similarities and differences in flow resistance can be explained by viscosity-dependent RBC-FL thicknesses, which are associated with the viscosity-dependent dynamics of single RBCs. The weak effect on the flow resistance and RBC-FL explains why RBCs can contain a high concentration of hemoglobin for efficient oxygen delivery, without a pronounced increase in the flow resistance. Furthermore, our results suggest that significant alterations in microvascular flow in various pathologies are likely not due to mere changes in cytosolic viscosity.

Oxygenation state of hemoglobin defines dynamics of water molecules in its vicinity.

This study focuses on assessing the possible impact of changes in hemoglobin (Hb) oxygenation on the state of water in its hydration shell as it contributes to red blood cell deformability. Microwave Dielectric Spectroscopy (MDS) was used to monitor the changes in interactions between water molecules and Hb, the number of water molecules in the protein hydration shell, and the dynamics of pre-protein water in response to the transition of Hb from the tense (T) to the relaxed (R) state, and vice versa. Measurements were performed for Hb solutions of different concentrations (5 g/dl-30 g/dl) in phosphate-buffered saline buffer. Cole-Cole parameters of the main water relaxation peak in terms of interactions of water molecules (dipole-dipole/ionic dipole) during the oxygenation-deoxygenation cycle were used to analyze the obtained data. The water mobility-represented by α as a function of ln τ-differed dramatically between the R (oxygenated) state and the T (deoxygenated) state of Hb at physiologically relevant concentrations (30 g/dl-35 g/dl or 4.5 mM-5.5 mM). At these concentrations, oxygenated hemoglobin was characterized by substantially lower mobility of water in the hydration shell, measured as an increase in relaxation time, compared to deoxyhemoglobin. This change indicated an increase in red blood cell cytosolic viscosity when cells were oxygenated and a decrease in viscosity upon deoxygenation. Information provided by MDS on the intraerythrocytic water state of intact red blood cells reflects its interaction with all of the cytosolic components, making these measurements powerful predictors of the changes in the rheological properties of red blood cells, regardless of the cause.

The effects of the surrounding viscoelastic media on the buckling behavior of single microfilament within the cell: A mechanical model

In the present study, a mechanical model is applied to account the effects of the surrounding viscoelastic media on the buckling behavior of single microfilament within the cell. The model immeasurably associates filament\'s bending rigidity, neighboring system elasticity, and cytosol viscosity with buckling wavelengths, buckling growth rates and buckling amplitudes of the filament. Cytoskeleton components in living cell bear large compressive force and are responsible in maintaining the cell shape. Actually these filaments are surrounded by viscoelastic media consisting of other filaments network and viscous cytosole within the cell. This surrounding, viscoelastic media affects the buckling behavior of these filaments when external force is applied on these filaments. The obtained results, indicate that the coupling of viscoelastic media with the viscous cytosol greatly affect the buckling behavior of microfilament. The buckling forces increased with the increase in the intensity of surrounding viscoelastic media.

Calcium dynamically alters erythrocyte mechanical response to shear

Red blood cells (RBC) are constantly exposed to varying mechanical forces while traversing the cardiovascular system. Upon exposure to mechanical stimuli (e.g., shear stress), calcium enters the cell and prompts potassium-efflux. Efflux of potassium is accompanied by a loss of intracellular fluid; thus, the volume of RBC decreases proportionately (i.e., ‘Gárdos effect’). The mechanical properties of the cell are subsequently impacted due to complex interactions between cytosolic viscosity (dependent on cell hydration), the surface-area-to-volume ratio, and other molecular processes. The dynamic effects of calcium on RBC mechanics are yet to be elucidated, although accumulating evidence suggests a vital role. The present study thus examined the effects of calcium on contemporary biomechanical properties of RBC in conjunction with high-precision geometrical analyses with exposure to shear. Mechanical stimulation of RBC was performed using a co-axial Couette shearing system to deform the cell membrane; intracellular signaling events were observed via fluorescent imaging. Calcium was introduced into RBC using ionophore A23187. Increased intracellular calcium significantly impaired RBC deformability; these impairments were mediated by a calcium-induced reduction of cell volume through the Gárdos channel. Extracellular calcium in the absence of the ionophore only had an effect under shear, not at stasis. Under low shear, the presence of extracellular calcium induced progressive lysis of a sub-population of RBC; all remaining RBC exhibited exceptional capacity to deform, implying preferential removal of potentially aged cells. Collectively, we provide evidence of the mechanism by which calcium acutely regulates RBC mechanical properties.

Methods to Investigate the Deformability of RBC During Malaria.

Despite a 30% decline in mortality since 2000, malaria still affected 219 million subjects and caused 435,000 deaths in 2017. Red blood cells (RBC) host Plasmodium parasites that cause malaria, of which Plasmodium falciparum is the most pathogenic. The deformability of RBC is markedly modified by invasion and development of P. falciparum. Surface membrane area is potentially impacted by parasite entry and development, the cytoskeleton is modified by parasite proteins and cytosol viscosity is altered by parasite metabolism. RBC hosting mature parasites (second half of the asexual erythrocytic cycle) are abnormally stiff but the main reason for their absence from the circulation is their adherence to endothelial cells, mediated by parasite proteins exposed at the infected-RBC surface. By contrast, the circulation of non-adherent rings and gametocytes, depends predominantly on deformability. Altered deformability of rings and of uninfected-RBC altered by malaria infection is an important determinant of malaria pathogenesis. It also impacts the response to antimalarial therapy. Unlike conventional antimalarials that target mature stages, currently recommended first-line artemisinin derivatives and the emerging spiroindolones act on circulating rings. Methods to investigate the deformability of RBC are therefore critical to understand the clearance of infected- and uninfected-RBC in malaria. Herein, we review the main methods to assess the deformability of P. falciparum infected-RBC, and their contribution to the understanding of how P. falciparum infection causes disease, how the parasite is transmitted and how antimalarial drugs induce parasite clearance.

Po-323 In vivo monitoring of tumour responses to chemotherapy using multiparameter fluorescence imaging

IntroductionAn increasing number of recent studies suggest that tumour response to chemotherapy cannot be fully described in terms of only interaction of the drug with the main cellular target (e.g. DNA or microtubules) but can include multiple physiological and physicochemical changes. Insight into drug-induced functional alterations in cancer cells and tissues is crucially important for understanding of mechanisms of a drug action and for development new approaches to enable monitoring of the early-treatment response.Material and methodsIn our studies, we focus on multiparameteric analysis of tumour responses to chemotherapy using advanced fluorescence imaging techniques. Previously, we developed methodologies for in vivo probing several parameters, including cytosolic pH, metabolic status, and viscosity of plasma membrane, in mouse tumour models. Mapping of cytosolic pH in tumours is performed using ratiometric genetically encoded sensor SypHer2 and fluorescence whole-body imaging [Shirmanova et al. BBA-GS 2015]. Imaging of cellular metabolism is based on the visualisation of fluorescence intensities and lifetimes of intrinsic metabolic cofactors NAD(P)H and FAD [Shirmanova et al. Sci.Rep. 2017]. Viscosity is measured using molecular BODIPY-based rotor and fluorescence lifetime imaging microscopy (FLIM) [Shimolina et al. Sci.Rep. 2017].Results and discussionsWe showed that acidification of cytosolic pH occurs after therapy with cisplatin in vivo, and this, likely, favours metabolic reorganisation of cells. Treated tumours exhibited a decreased relative contribution from free (cytosolic, protein-unbound) NAD(P)H, indicating a metabolic shift from glycolysis towards oxidative metabolism. It is interesting that optical metabolic imaging could allow early detection of tumour response to chemotherapy, before there are changes in tumour size, and metabolic changes were the same for therapeutic agents with different mechanisms of action (cisplatin, paclitaxel). Moreover, tumours treated with cisplatin displayed decreased plasma membrane viscosity. Presumably, this alteration of viscosity participates in cisplatin-induced apoptosis. Similar changes of pH, energy metabolism and viscosity were previously reported for cisplatin-treated cultured cancer cells.ConclusionThese results, therefore, suggest that all investigated parameters play a role in the cytotoxicity of the drugs and may provide a useful approach for monitoring tumour responses to chemotherapy. The study was supported by the Russian Science Foundation (#14-25-00129).

Characterization of Cytoskeletal Pore Size Using Quantum Dots

Cytoskeletal pore size is a key factor in determining the intracellular molecular transportation, yet it is technically challenging to investigate correlations between the cytoskeletal pore size and cytoplasmic diffusion. Here, we report the application of quantum dots (QD) to measure the cytoskeletal pore size. QDs are first transfected into a cell, leading to different sizes of QD-encapsulating vesicles. The distribution of QD vesicles in cells reflects the cytoskeletal pore size. Further, we can predict the cytosolic viscosity from the measured pore size using the poroelasticity scaling theory. This predicted cytosolic viscosity is verified by measuring Brownian motions of the QDs in cells and transforming the motion characteristics into cytosolic viscosity via the Stocks–Einstein relation. This strategy also provides a practical method for quantifying the cytoskeletal pore sizes. Together, this research demonstrates the efficacy of applying QDs in further studies of intracellular physical properties that play key roles in intracellular molecular transports.

Probing metabolite diffusion at ultra-short time scales in the mouse brain using optimized oscillating gradients and "short"-echo-time diffusion-weighted MRS.

Measuring diffusion at ultra-short time scales may yield information about short-range intracellular structure and cytosol viscosity. However, reaching such time scales usually requires oscillating gradients, which in turn imply long echo times TE . Here we propose a new kind of stretched oscillating gradient that allows us to increase diffusion-weighting b while preserving spectral and temporal properties of the gradient modulation. We used these optimized gradients to measure metabolite diffusion in the mouse brain down to effective diffusion times of 1ms while keeping TE relatively short (60ms). At such TE , a significant macromolecule signal could still be observed and used as an internal reference of approximately null diffusivity, which proved critical to discard datasets corrupted by some motion artifact. The methods introduced here may be useful to improve the accuracy and precision of metabolite apparent diffusion coefficient measurements with oscillating gradients.

Red cells’ dynamic morphologies govern blood shear thinning under microcirculatory flow conditions

Blood viscosity decreases with shear stress, a property essential for an efficient perfusion of the vascular tree. Shear thinning is intimately related to the dynamics and mutual interactions of RBCs, the major component of blood. Because of the lack of knowledge about the behavior of RBCs under physiological conditions, the link between RBC dynamics and blood rheology remains unsettled. We performed experiments and simulations in microcirculatory flow conditions of viscosity, shear rates, and volume fractions, and our study reveals rich RBC dynamics that govern shear thinning. In contrast to the current paradigm, which assumes that RBCs align steadily around the flow direction while their membranes and cytoplasm circulate, we show that RBCs successively tumble, roll, deform into rolling stomatocytes, and, finally, adopt highly deformed polylobed shapes for increasing shear stresses, even for semidilute volume fractions of the microcirculation. Our results suggest that any pathological change in plasma composition, RBC cytosol viscosity, or membrane mechanical properties will affect the onset of these morphological transitions and should play a central role in pathological blood rheology and flow behavior.

Brain intracellular metabolites are freely diffusing along cell fibers in grey and white matter, as measured by diffusion-weighted MR spectroscopy in the human brain at 7 T.

Due to the specific compartmentation of brain metabolites, diffusion-weighted magnetic resonance spectroscopy opens unique insight into neuronal and astrocytic microstructures. The apparent diffusion coefficient (ADC) of brain metabolites depends on various intracellular parameters including cytosol viscosity and molecular crowding. When diffusion time (t d) is long enough, the size and geometry of the compartment in which the metabolites diffuse strongly influence metabolites ADC. In a previous study, performed in the macaque brain, we measured neuronal and astrocytic metabolites ADC at long t d (from 86 to 1,011 ms) in a large voxel enclosing an equal proportion of white and grey matter. We showed that metabolites apparently diffuse freely along the axis of dendrites, axons and astrocytic processes. To assess potential differences between these two tissue types, here we measured for the first time in the Human brain the t d-dependency of metabolites trace/3 ADC at 7 teslas using a localized diffusion-weighted STEAM sequence, in parietal and occipital voxels, respectively, containing mainly white and grey matter. We show that, in both tissues and over the observed timescale (t d varying from 92 to 712 ms) metabolite ADC reaches a non-zero plateau, suggesting that metabolites are not confined inside subcellular regions such as cell bodies, or inside subcellular compartments such as organelles, but are rather free to diffuse in the whole fiber-like structure of neurons and astrocytes. Beyond the fundamental insights into intracellular compartmentation of metabolites, this work also provides a new framework for interpreting results of neuroimaging techniques based on molecular diffusion, such as diffusion-weighted magnetic resonance spectroscopy and imaging.

A higher-order mathematical modeling for dynamic behavior of protein microtubule shell structures including shear deformation and small-scale effects

Microtubules in mammalian cells are cylindrical protein polymers which structurally and dynamically organize functional activities in living cells. They are important for maintaining cell structures, providing platforms for intracellular transport, and forming the spindle during mitosis, as well as other cellular processes. Various in vitro studies have shown that microtubules react to applied mechanical loading and physical environment. To investigate the mechanisms underlying such phenomena, a mathematical model based on the orthotropic higher-order shear deformation shell formulation and Hamilton’s principle is presented in this paper for dynamic behavior of microtubules. The numerical results obtained by the proposed shell model are verified by the experimental data from the literature, showing great consistency. The nonlocal elasticity theory is also utilized to describe the nano-scale effects of the microtubule structure. The wave propagation and vibration characteristics of the microtubule are examined in the presence and absence of the cytosol employing proposed formulations. The effects of different system parameters such as length, small scale parameter, and cytosol viscosity on vibrational behavior of a microtubule are elucidated. The definitions of critical length and critical viscosity are introduced and the results obtained using the higher order shell model are compared with those obtained employing a first-order shear deformation theory. This comparison shows that the small scale effects become important for higher values of the wave vector and the proposed model gives more accurate results for both small and large values of wave vectors. Moreover, it is shown that for higher circumferential wave number, the torsional wave velocity obtained by the higher-order shell model tend to be higher than the one predicted by the first-order shell model.

The flow of red blood cells through a narrow spleen-like slit

Small slits between endothelial cells in the spleen are perhaps the smallest blood passages in the body, and red blood cells must deform significantly to pass through them. These slits have been posited to participate in the removal of senescent blood cells from the circulation, a key function of the spleen. One of the effects of red blood cell aging is an increased cytosol viscosity; relaxation time measurements suggest their interior viscosity can increase by up to a factor of 10 toward the end of their normal 120 day circulating lifetime. We employ a boundary integral model to simulate red blood cells as they deform sufficiently to flow through such a small passage, whether in the spleen or in a microfluidic device. Different flow rates and cytosol viscosities show three distinct behaviors. (1) For sufficiently slow flow, the pressure gradient is insufficient to overcome elastic resistance and the cell becomes jammed. (2) For faster flow, the cell passes the slit, though more slowly for higher cytosol viscosity. This can be hypothesized to facilitate recognition of senescent cells. (3) A surprising behavior is observed for high elastic capillary numbers, due either to high velocity or high cytosol viscosity. In this case, the cells infold within the slit, with a finger of low-viscosity plasma pushing deeply into the cell from its upstream side. Such infolding might provide an additional mechanism for jamming, and the sharpness of the resulting features would be expected to promote cell degradation. Linear analysis of a model system shows a similar instability, which is analyzed in regard to the cell flow. This linear analysis also suggests a similar instability for unphysiologically low cytosol viscosity. Simulations confirm that a similar infolding also occurs in this case, which intriguingly suggests that normal cytosol viscosities are in a range that is protective against such deformations.