Determination of red blood cell membrane viscosity from rheoscopic observations of tank-treading motion

Tran‐Son‐Tay, Roger; Sutera, Salvatore P.; Rao, P. Raghupathi

doi:10.1016/s0006-3495(84)83999-5

Cited by 181 publications

(182 citation statements)

References 8 publications

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“…Although many experimental studies have been devoted to the measurement of TT frequency, considerable uncertainty exists with respect to the dependence of TT frequency (f) of RBCs on shear rate ð_ γÞ. For example, Fischer et al (35) and Tran-Son-Tay et al (36) found that f increases linearly with _ γ. By contrast, Fischer (17) found that f ∼ _ γ β with the scaling exponent β between 0.85 and 0.95.…”

Section: Resultsmentioning

confidence: 99%

Lipid bilayer and cytoskeletal interactions in a red blood cell

Peng

Pivkin

et al. 2013

Proc. Natl. Acad. Sci. U.S.A.

161

150

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We study the biomechanical interactions between the lipid bilayer and the cytoskeleton in a red blood cell (RBC) by developing a general framework for mesoscopic simulations. We treated the lipid bilayer and the cytoskeleton as two distinct components and developed a unique whole-cell model of the RBC, using dissipative particle dynamics (DPD). The model is validated by comparing the predicted results with measurements from four different and independent experiments. First, we simulated the micropipette aspiration and quantified the cytoskeletal deformation. Second, we studied the membrane fluctuations of healthy RBCs and RBCs parasitized to different intraerythrocytic stages by the malaria-inducing parasite Plasmodium falciparum. Third, we subjected the RBC to shear flow and investigated the dependence of its tank-treading frequency on shear rate. Finally, we simulated the bilayer-cytoskeletal detachment in channel flow to quantify the strength of such interactions when the corresponding bonds break. Taken together, these experiments and corresponding systematic DPD simulations probe the governing constitutive response of the cytoskeleton, elastic stiffness, viscous friction, and strength of bilayer-cytoskeletal interactions as well as membrane viscosities. Hence, the DPD simulations and comparisons with available independent experiments serve as validation of the unique two-component model and lead to useful insights into the biomechanical interactions between the lipid bilayer and the cytoskeleton of the RBC. Furthermore, they provide a basis for further studies to probe cell mechanistic processes in health and disease in a manner that guides the design and interpretation of experiments and to develop simulations of phenomena that cannot be studied systematically by experiments alone.coarse graining | worm-like chain | multiscale modeling | adhesion energy | erythrocyte T he red blood cell (RBC) membrane consists of two components: a lipid bilayer and an attached 2D spectrin network that acts as the cytoskeleton. The resistance of the lipid bilayer to bending is controlled by the bending rigidity, k c , whereas the spectrin network's resistance to shear strain is characterized by the in-plane shear modulus, μ s . Under normal conditions, the cytoskeleton is tightly attached to the lipid bilayer from the cytoplasmic side. However, under certain pathological conditions, e.g., in sickle cell disease, the cytoskeleton may become dissociated from the lipid bilayer (1). Although the biomechanics of the two-component erythrocyte membrane have been studied extensively for decades (2), the mechanical properties of the interactions between the lipid bilayer and the cytoskeleton (such as elastic stiffness, viscous friction, and strength) via the pinning connections of transmembrane proteins are still largely unknown. This is at least in part ascribed to the fact that it is difficult to measure these interactions directly from experiments, because the length scale of these connections is too small compared with the chara...

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Section: Resultsmentioning

confidence: 99%

Lipid bilayer and cytoskeletal interactions in a red blood cell

Peng

Pivkin

et al. 2013

Proc. Natl. Acad. Sci. U.S.A.

161

150

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“…The other model is in contradiction to our results because dependence on s is equivalent to s 0 5 1. Even when the membrane viscosity is neglected, accounting for the cytoplasmic viscosity alone should result in s 0 [ 1 as it was shown that the energy dissipation in the cytoplasm constitutes an appreciable portion of the total dissipation in the tank-treading red cell (5,(13)(14)(15).…”

Section: Comparison To Red Cell Modelsmentioning

confidence: 99%

Effects of shear rate and suspending medium viscosity on elongation of red cells tank‐treading in shear flow

Fischer

Korzeniewski

2011

Cytometry Pt A

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Elongation measurements of red cells subjected to simple shear flow are usually performed using a single suspending medium (viscosity g 0 ) and varying the mean shear rate ð _ cÞ. Such data are often plotted versus the shear stress ðs ¼ g 0 _ cÞ suggesting that the elongation scales with s. In this work, normal blood samples were tested in a rheoscope varying both g 0 and _ c. The ranges of _ c were chosen to restrict the elongation of the red cells to low values where the behavior is dominated by their intrinsic properties. It was found that the elongation scales with g s 0 _ c with s decreasing from two at g 0 5 20 mPas to unity at g 0 5 70 mPas. Above g 0 5 70 mPas, the elongation is therefore essentially determined by the membrane elasticity alone. A side observation was a large variation of the elongation both intraindividually and interindividually. ' International Society for Advancement of CytometryKey terms rheoscope; image processing; computer modeling; scaling behavior; shape distributions; share of cell viscosities A standard method to measure the mechanical properties of red cells is to suspend the cells in solutions much more viscous than blood plasma and to measure their elongation when the suspension is subjected to simple shear flow (1,2). In addition to being elongated, the membrane moves around the elongated shape thus inducing an eddy flow within the cytoplasm. The membrane motion has been termed tanktread motion (1). The elongation is usually quantified by an elongation index EI ¼ LÀB LþB , where L and B denote the length and the width of the elongated cell. Measurements of EI of different blood samples are usually performed using a constant viscosity of the suspending medium (g 0 ) under variation of the mean shear rate ð _ cÞ. Such data are often plotted versus the shear stress of the undisturbed shear flow ðs ¼ g 0 _ cÞ suggesting that EI scales with s. If, on the other hand, the same blood sample was tested varying both g 0 and _ c, it was shown that EI does not scale with s. Using four viscosities between 12 and 51 mPas, EI was found to scale with g 1:5 0 _ c (3). An exponent greater unity can also be inferred from other experimental results (4,5).To explain this finding, the following hypothesis is put forward. (i) Besides elastic stresses, viscous stresses resist an elongation of tank-treading red cells. (ii) A variable contribution of the viscous stresses being three dimensional in the cytoplasm and two dimensional in the membrane is responsible for an exponent greater unity.To rationalize the hypothesis, we consider the following experiment. We first measure EI with a certain set of _ c and g 0 . Then we decrease _ c by a certain amount and increase g 0 to such an extent that EI remains constant. The elastic stresses and bending moments in the membrane remain essentially constant as EI did not change.

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“…Moreover, the actual state of deformation of the elastic skeleton either in the flowing or in the resting RBC is still conjectural ("shape memory" problem) [7]. Most models [6,8] derive from the analytical framework of Keller and Skalak (KS) [9], which treats the RBC as a fluid ellipsoidal membrane enclosing a viscous liquid. Although this model qualitatively retrieves the two modes of motion, it does not capture the observed shear-rate dependency of the tumblingtanktreading transition.…”

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confidence: 99%

Swinging of Red Blood Cells under Shear Flow

2007

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We reveal that under moderate shear stress (ηγ ≈ 0.1 Pa) red blood cells present an oscillation of their inclination (swinging) superimposed to the long-observed steady tanktreading (TT) motion. A model based on a fluid ellipsoid surrounded by a visco-elastic membrane initially unstrained (shape memory) predicts all observed features of the motion: an increase of both swinging amplitude and period (1/2 the TT period) upon decreasing ηγ, a ηγ-triggered transition towards a narrow ηγ-range intermittent regime of successive swinging and tumbling, and a pure tumbling motion at lower ηγ-values. A human red blood cell (RBC) is a biconcave flattened disk, essentially made of a Newtonian hemoglobin solution encapsulated by a fluid and incompressible lipid bilayer, underlined by a thin elastic cytoskeleton (spectrin network) [1]. The complex structure of RBCs and their response to a viscous shear flow have a great influence on flow and mass transport in the microcirculation in both health and disease [2]. The full understanding of this response requires a direct comprehensive observation of cell motion and deformation, and a model for deducing the cell intrinsic properties from its behavior in shear flow. It is generally admitted that the two possible RBC movements are the unsteady tumbling solid-like motion [3], and the drop-like 'tanktreading' motion for higher shear stresses, where the cell maintains a steady orientation, while the membrane rotates about the internal fluid, as reported respectively for RBCs suspended in plasma or in high-viscosity media and submitted to high shear stresses [3,4,5,6]. However, the RBC movement at smaller shear rate and close to the tumbling-tanktreading transition, has not been fully explored. Moreover, the actual state of deformation of the elastic skeleton either in the flowing or in the resting RBC is still conjectural ("shape memory" problem) [7]. Most models [6,8] derive from the analytical framework of Keller and Skalak (KS) [9], which treats the RBC as a fluid ellipsoidal membrane enclosing a viscous liquid. Although this model qualitatively retrieves the two modes of motion, it does not capture the observed shear-rate dependency of the tumblingtanktreading transition. In particular, the model does not account for the possible elastic energy storage induced by the local deformations of the cytoskeleton during tanktreading. Approaches including membrane elasticity are either restricted to spherical resting shapes because of analytical complexities [10], or propose encouraging but still limited numerical analysis on tanktreading elastic biconcave capsules [11].Here, we reveal a new regime of motion for RBCs under small shear flow, characterized by an elastic capsule-like oscillation of the cell inclination superimposed to tanktreading that we name swinging. We develop a model, which predicts both swinging and the shear-stress dependency of the tumbling-tanktreading transition. It demonstrates the existence of the elastic shape memory in the membrane.Direct measurements of cell ori...

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Determination of red blood cell membrane viscosity from rheoscopic observations of tank-treading motion

Cited by 181 publications

References 8 publications

Lipid bilayer and cytoskeletal interactions in a red blood cell

Lipid bilayer and cytoskeletal interactions in a red blood cell

Effects of shear rate and suspending medium viscosity on elongation of red cells tank‐treading in shear flow

Swinging of Red Blood Cells under Shear Flow

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