Transit Time Theory for a Droplet Passing through a Slit in Pressure-Driven Low Reynolds Number Flows.

Soft objects squeezing through small apertures are crucial for many in vivo and in vitro processes. Red blood cell transit time through splenic inter-endothelial slits (IESs) plays a crucial role in blood filtration and disease progression, while droplet velocity through constrictions in microfluidic devices is important for effective manipulation and separation processes. As these transit phenomena are not well understood, we sought to establish analytical and numerical solutions of viscous droplet transit through a rectangular slit. This study extends from our former theory of a circular pore because a rectangular slit is more realistic in many physiological and engineering applications. Here, we derived the ordinary differential equations (ODEs) of a droplet passing through a slit by combining planar Poiseuille flow, the Young-Laplace equations, and modifying them to consider the lubrication layer between the droplet and the slit wall. Compared to the pore case, we used the Roscoe solution instead of the Sampson one to account for the flow entering and exiting a rectangular slit. When the surface tension and lubrication layer were negligible, we derived the closed-form solutions of transit time. When the surface tension and lubrication layer were finite, the ODEs were solved numerically to study the impact of various parameters on the transit time. With our solutions, we identified the impact of prescribed pressure drop, slit dimensions, and droplet parameters such as surface tension, viscosity, and volume on transit time. In addition, we also considered the effect of pressure drop and surface tension near critical values. For this study, critical surface tension for a given pressure drop describes the threshold droplet surface tension that prevents transit, and critical pressure for a given surface tension describes the threshold pressure drop that prevents transit. Our solutions demonstrate that there is a linear relationship between pressure and the reciprocal of the transit time (referred to as inverse transit time), as well as a linear relationship between viscosity and transit time. Additionally, when the droplet size increases with respect to the slit dimensions, there is a corresponding increase in transit time. Most notably, we emphasize the initial antagonistic effect of surface tension which resists droplet passage but at the same time decreases the lubrication layer, thus facilitating passage. Our results provide quantitative calculations for understanding cells passing through slit-like constrictions and designing droplet microfluidic experiments.

Physical mechanisms of red blood cell splenic filtration.

The splenic interendothelial slits fulfill the essential function of continuously filtering red blood cells (RBCs) from the bloodstream to eliminate abnormal and aged cells. To date, the process by which 8 [Formula: see text]m RBCs pass through 0.3 [Formula: see text]m-wide slits remains enigmatic. Does the slit caliber increase during RBC passage as sometimes suggested? Here, we elucidated the mechanisms that govern the RBC retention or passage dynamics in slits by combining multiscale modeling, live imaging, and microfluidic experiments on an original device with submicron-wide physiologically calibrated slits. We observed that healthy RBCs pass through 0.28 [Formula: see text]m-wide rigid slits at 37 °C. To achieve this feat, they must meet two requirements. Geometrically, their surface area-to-volume ratio must be compatible with a shape in two tether-connected equal spheres. Mechanically, the cells with a low surface area-to-volume ratio (28% of RBCs in a 0.4 [Formula: see text]m-wide slit) must locally unfold their spectrin cytoskeleton inside the slit. In contrast, activation of the mechanosensitive PIEZO1 channel is not required. The RBC transit time through the slits follows a [Formula: see text]1 and [Formula: see text]3 power law with in-slit pressure drop and slip width, respectively. This law is similar to that of a Newtonian fluid in a two-dimensional Poiseuille flow, showing that the dynamics of RBCs is controlled by their cytoplasmic viscosity. Altogether, our results show that filtration through submicron-wide slits is possible without further slit opening. Furthermore, our approach addresses the critical need for in vitro evaluation of splenic clearance of diseased or engineered RBCs for transfusion and drug delivery.

Enhanced cell viscosity: A new phenotype associated with lamin A/C alterations.

Lamin A/C is a well-established key contributor to nuclear stiffness and its role in nucleus mechanical properties has been extensively studied. However, its impact on whole-cell mechanics has been poorly addressed, particularly concerning measurable physical parameters. In this study, we combined microfluidic experiments with theoretical analyses to quantitatively estimate the whole-cell mechanical properties. This allowed us to characterize the mechanical changes induced in cells by lamin A/C alterations and prelamin A accumulation resulting from atazanavir treatment or lipodystrophy-associated LMNA R482W pathogenic variant. Our results reveal a distinctive increase in long-time viscosity as a signature of cells affected by lamin A/C alterations. Furthermore, they show that the whole-cell response to mechanical stress is driven not only by the nucleus but also by the nucleo-cytoskeleton links and the microtubule network. The enhanced cell viscosity assessed with our microfluidic assay could serve as a valuable diagnosis marker for lamin-related diseases.

Classification of red cell dynamics with convolutional and recurrent neural networks: a sickle cell disease case study.

The fraction of red blood cells adopting a specific motion under low shear flow is a promising inexpensive marker for monitoring the clinical status of patients with sickle cell disease. Its high-throughput measurement relies on the video analysis of thousands of cell motions for each blood sample to eliminate a large majority of unreliable samples (out of focus or overlapping cells) and discriminate between tank-treading and flipping motion, characterizing highly and poorly deformable cells respectively. Moreover, these videos are of different durations (from 6 to more than 100 frames). We present a two-stage end-to-end machine learning pipeline able to automatically classify cell motions in videos with a high class imbalance. By extending, comparing, and combining two state-of-the-art methods, a convolutional neural network (CNN) model and a recurrent CNN, we are able to automatically discard 97% of the unreliable cell sequences (first stage) and classify highly and poorly deformable red cell sequences with 97% accuracy and an F1-score of 0.94 (second stage). Dataset and codes are publicly released for the community.

Longitudinal to Transverse Metachronal Wave Transitions in an In Vitro Model of Ciliated Bronchial Epithelium.

Myriads of cilia beat on ciliated epithelia, which are ubiquitous in life. When ciliary beats are synchronized, metachronal waves emerge, whose direction of propagation depends on the living system in an unexplained way. We show on a reconstructed human bronchial epithelium in vitro that the direction of propagation is determined by the ability of mucus to be transported at the epithelial surface. Numerical simulations show that longitudinal waves maximize the transport of mucus while transverse waves, observed when the mucus is rigid and still, minimize the energy dissipated by the cilia.

Lrrcc1 and Ccdc61 are conserved effectors of multiciliated cell function.

Ciliated epithelia perform essential functions in animals across evolution, ranging from locomotion of marine organisms to mucociliary clearance of airways in mammals. These epithelia are composed of multiciliated cells (MCCs) harboring myriads of motile cilia, which rest on modified centrioles called basal bodies (BBs), and beat coordinately to generate directed fluid flows. Thus, BB biogenesis and organization is central to MCC function. In basal eukaryotes, the coiled-coil domain proteins Lrrcc1 and Ccdc61 have previously been shown to be required for proper BB construction and function. Here, we used the Xenopus embryonic ciliated epidermis to characterize Lrrcc1 and Ccdc61 in vertebrate MCCs. We found that they both encode BB components, localized proximally at the junction with striated rootlets. Knocking down either gene caused defects in BB docking, spacing and polarization. Moreover, their depletion impaired the apical cytoskeleton and altered ciliary beating. Consequently, cilia-powered fluid flow was greatly reduced in morphant tadpoles, which displayed enhanced mortality when exposed to pathogenic bacteria. This work illustrates how integration across organizational scales make elementary BB components essential for the emergence of the physiological function of ciliated epithelia.

Dynamics of Individual Red Blood Cells Under Shear Flow: A Way to Discriminate Deformability Alterations.

In this work, we compared the dynamics of motion in a linear shear flow of individual red blood cells (RBCs) from healthy and pathological donors (Sickle Cell Disease (SCD) or Sickle Cell-ß-thalassemia) and of low and high densities, in a suspending medium of higher viscosity. In these conditions, at lower shear rates, biconcave discocyte-shaped RBCs present an unsteady flip-flopping motion, where the cell axis of symmetry rotates in the shear plane, rocking to and fro between an orbital angle ±Ï• observed when the cell is on its edge. We show that the evolution of ϕ depends solely on RBC density for healthy RBCs, with denser RBCs displaying lower ϕ values than the lighter ones. Typically, at a shear stress of 0.08 Pa, ϕ has values of 82 and 72° for RBCs with average densities of 1.097 and 1.115, respectively. Surprisingly, we show that SCD RBCs display the same ϕ-evolution as healthy RBCs of same density, showing that the flip-flopping behavior is unaffected by the SCD pathology. When the shear stress is increased further (above 0.1 Pa), healthy RBCs start going through a transition to a fluid-like motion, called tank-treading, where the RBC has a quasi-constant orientation relatively to the flow and the membrane rotates around the center of mass of the cell. This transition occurs at higher shear stresses (above 0.2 Pa) for denser cells. This shift toward higher stresses is even more remarkable in the case of SCD RBCs, showing that the transition to the tank-treading regime is highly dependent on the SCD pathology. Indeed, at a shear stress of 0.2 Pa, for RBCs with a density of 1.097, 100% of healthy RBCs have transited to the tank-treading regime vs. less than 50% SCD RBCs. We correlate the observed differences in dynamics to the alterations of RBC mechanical properties with regard to density and SCD pathology reported in the literature. Our results suggest that it might be possible to develop simple non-invasive assays for diagnosis purpose based on the RBC motion in shear flow and relying on this millifluidic approach.

Mechanical adaptation of monocytes in model lung capillary networks.

Proper circulation of white blood cells (WBCs) in the pulmonary vascular bed is crucial for an effective immune response. In this branched vascular network, WBCs have to strongly deform to pass through the narrowest capillaries and bifurcations. Although it is known that this process depends on the cell mechanical properties, it is still poorly understood due to the lack of a comprehensive model of cell mechanics and of physiologically relevant experiments. Here, using an in-house microfluidic device mimicking the pulmonary capillary bed, we show that the dynamics of THP1 monocytes evolves along successive capillary-like channels, from a nonstationary slow motion with hops to a fast and smooth efficient one. We used actin cytoskeleton drugs to modify the traffic dynamics. This led us to propose a simple mechanical model that shows that a very finely tuned cortical tension combined with a high cell viscosity governs the fast transit through the network while preserving cell integrity. We finally highlight that the cortical tension controls the steady-state cell velocity via the viscous friction between the cell and the channel walls.

Hydrodynamic model of directional ciliary-beat organization in human airways.

In the lung, the airway surface is protected by mucus, whose transport and evacuation is ensured through active ciliary beating. The mechanisms governing the long-range directional organization of ciliary beats, required for effective mucus transport, are much debated. Here, we experimentally show on human bronchial epithelium reconstituted in-vitro that the dynamics of ciliary-beat orientation is closely connected to hydrodynamic effects. To examine the fundamental mechanisms of this self-organization process, we build a two-dimensional model in which the hydrodynamic coupling between cilia is provided by a streamwise-alignment rule governing the local orientation of the ciliary forcing. The model reproduces the emergence of the mucus swirls observed in the experiments. The predicted swirl sizes, which scale with the ciliary density and mucus viscosity, are in agreement with in-vitro measurements. A transition from the swirly regime to a long-range unidirectional mucus flow allowing effective clearance occurs at high ciliary density and high mucus viscosity. In the latter case, the mucus flow tends to spontaneously align with the bronchus axis due to hydrodynamic effects.

Self-organization of red blood cell suspensions under confined 2D flows.

Dynamic self-organized structures with long-range order have been observed in emulsions and suspensions of particles under confined flows. Here, experiments on red blood cell suspensions under quasi-2D confined flows and numerical simulations were combined to explore long-distance self-organization as a function of the channel width, red blood cell concentration and flow rate. They reveal and quantitatively describe the existence of red blood cell long-range alignments and heterogeneous cross-stream concentration profiles characterized by red blood cell-enriched bands parallel to the flow. Numerical simulations show that, in addition to the degree of lateral confinement, the key factor for the structural self-organization of a suspension of particles under a confined flow is the deformability of the constituent particles.

Spatiotemporal organization of cilia drives multiscale mucus swirls in model human bronchial epithelium.

Mucociliary clearance is a biomechanical mechanism of airway protection. It consists of the active transport along the bronchial tree of the mucus, a fluid propelled by the coordinated beating of a myriad of cilia on the epithelial surface of the respiratory tract. The physics of mucus transport is poorly understood because it involves complex phenomena such as long-range hydrodynamic interactions, active collective ciliary motion, and the complex rheology of mucus. We propose a quantitative physical analysis of the ciliary activity and mucus transport on a large panel of human bronchial cultures from control subjects, patients with asthma and chronic obstructive pulmonary disease obtained from endobronchial biopsies. Here we report on the existence of multiple ciliary domains with sizes ranging from the tens of a micron to the centimeter, where ciliary beats present a circular orientational order. These domains are associated with circular mucus flow patterns, whose size scales with the average cilia density. In these domains, we find that the radial increase of the ciliated cell density coupled with the increase in the orientational order of ciliary beats result in a net local force proportional to the mucus velocity. We propose a phenomenological physical model that supports our results.

High Aspect Ratio Sub-Micrometer Channels Using Wet Etching: Application to the Dynamics of Red Blood Cell Transiting through Biomimetic Splenic Slits.

Nanoparticles delivering drugs, disseminating cancer cells, and red blood cells (RBCs) during splenic filtration must deform and pass through the sub-micrometer and high aspect ratio interstices between the endothelial cells lining blood vessels. The dynamics of passage of particles/cells through these slit-like interstices remain poorly understood because the in vitro reproduction of slits with physiological dimensions in devices compatible with optical microscopy observations requires expensive technologies. Here, novel microfluidic PDMS devices containing high aspect ratio slits with sub-micrometer width are molded on silicon masters using a simple, inexpensive, and highly flexible method combining standard UV lithography and anisotropic wet etching. These devices enabled revealing novel modes of deformations of healthy and diseased RBCs squeezing through splenic-like slits (0.6-2 × 5-10 × 1.6-11 µm3 ) under physiological interstitial pressures. At the slit exit, the cytoskeleton of spherocytic RBCs seemed to be detached from the lipid membrane whereas RBCs from healthy donors and patients with sickle cell disease exhibited peculiar tips at their front. These tips disappeared much slower in patients' cells, allowing estimating a threefold increase in RBC cytoplasmic viscosity in sickle cell disease. Measurements of time and rate of RBC sequestration in the slits allowed quantifying the massive trapping of spherocytic RBCs.

A simple model to understand the effect of membrane shear elasticity and stress-free shape on the motion of red blood cells in shear flow.

An analytical model was proposed by Keller and Skalak in 1982 to understand the motion of red blood cells in shear flow. The cell was described as a fluid ellipsoid of fixed shape. This model was extended in 2007 to introduce shear elasticity of the red blood cell membrane. Here, this model is further extended to take into account that the cell discoid shape physiologically observed is not a stress-free shape. The model shows that spheroid stress-free shapes allow us to fit the experimental data with the values of shear elasticity typical to that found with micropipette and optical tweezer experiments. In the range of moderate shear rates (for which RBCs keep their discoid shape) this model enables us to quantitatively determine (i) an effective cell viscosity, which combines membrane and hemoglobin viscosities and (ii) an effective shear modulus of the membrane that combines the shear modulus and the stress-free shape. This model can also be used to determine RBC mechanical parameters not only in the tanktreading regime when cells are suspended in medium of high viscosity but also in the tumbling regime characteristic of cells suspended in media of low viscosity. In this regime, a transition is predicted between a rigid-like tumbling motion and a fluid-like tumbling motion above a critical shear rate, which is directly related to the mechanical parameters of the cell.

Serum pantetheinase/vanin levels regulate erythrocyte homeostasis and severity of malaria.

Tissue pantetheinase, encoded by the VNN1 gene, regulates response to stress, and previous studies have shown that VNN genes contribute to the susceptibility to malaria. Herein, we evaluated the role of pantetheinase on erythrocyte homeostasis and on the development of malaria in patients and in a new mouse model of pantetheinase insufficiency. Patients with cerebral malaria have significantly reduced levels of serum pantetheinase activity (PA). In mouse, we show that a reduction in serum PA predisposes to severe malaria, including cerebral malaria and severe anemia. Therefore, scoring pantetheinase in serum may serve as a severity marker in malaria infection. This disease triggers an acute stress in erythrocytes, which enhances cytoadherence and hemolysis. We speculated that serum pantetheinase might contribute to erythrocyte resistance to stress under homeostatic conditions. We show that mutant mice with a reduced serum PA are anemic and prone to phenylhydrazine-induced anemia. A cytofluorometric and spectroscopic analysis documented an increased frequency of erythrocytes with an autofluorescent aging phenotype. This is associated with an enhanced oxidative stress and shear stress-induced hemolysis. Red blood cell transfer and bone marrow chimera experiments show that the aging phenotype is not cell intrinsic but conferred by the environment, leading to a shortening of red blood cell half-life. Therefore, serum pantetheinase level regulates erythrocyte life span and modulates the risk of developing complicated malaria.

Encapsulation of Living Leishmania Promastigotes in Artificial Lipid Vacuoles.

After phagocytosis by mammalian macrophages, promastigote forms of Leishmania parasites settle inside intracellular parasitophorous vacuoles (PVs) in which they transform into amastigote forms and replicate. Here, using a variant of the 'inverted emulsion' method, we succeeded in encapsulating living L. amazonensis parasites in giant artificial liposomes that serve as model PVs. We were able to control the size of liposomes, the pH and the composition of their internal volume, and the number of internalized parasites per liposome. L. amazonensis promastigotes encapsulated in liposomes filled with RPMI-Dextran solution at pH 7.5 or 6.5 survived up to 96 h at 24°C. At 37°C and pH 5.5, parasites survived 48h. This method paves the way to identifying certain effectors secreted by the parasite and to unraveling specific mechanisms of fusion between the PV and intracellular vesicles of the host cell. This method will also facilitate the study of the temporal evolution of biophysical properties of the PV during its maturation.

Full dynamics of a red blood cell in shear flow.

At the cellular scale, blood fluidity and mass transport depend on the dynamics of red blood cells in blood flow, specifically on their deformation and orientation. These dynamics are governed by cellular rheological properties, such as internal viscosity and cytoskeleton elasticity. In diseases in which cell rheology is altered genetically or by parasitic invasion or by changes in the microenvironment, blood flow may be severely impaired. The nonlinear interplay between cell rheology and flow may generate complex dynamics, which remain largely unexplored experimentally. Under simple shear flow, only two motions, "tumbling" and "tank-treading," have been described experimentally and relate to cell mechanics. Here, we elucidate the full dynamics of red blood cells in shear flow by coupling two videomicroscopy approaches providing multidirectional pictures of cells, and we analyze the mechanical origin of the observed dynamics. We show that contrary to common belief, when red blood cells flip into the flow, their orientation is determined by the shear rate. We discuss the "rolling" motion, similar to a rolling wheel. This motion, which permits the cells to avoid energetically costly deformations, is a true signature of the cytoskeleton elasticity. We highlight a hysteresis cycle and two transient dynamics driven by the shear rate: an intermittent regime during the "tank-treading-to-flipping" transition and a Frisbee-like "spinning" regime during the "rolling-to-tank-treading" transition. Finally, we reveal that the biconcave red cell shape is highly stable under moderate shear stresses, and we interpret this result in terms of stress-free shape and elastic buckling.

Gel phase vesicles buckle into specific shapes.

Osmotic deflation of giant vesicles in the rippled gel phase P(ß') gives rise to a large variety of novel faceted shapes. These shapes are also found from a numerical approach by using an elastic surface model. A shape diagram is proposed based on the model that accounts for the vesicle size and ratios of three mechanical constants: in-plane shear elasticity and compressibility (usually neglected) and out-of-plane bending of the membrane. The comparison between experimental and simulated vesicle morphologies reveals that they are governed by a typical elasticity length, of the order of 1   µm, and must be described with a large Poisson's ratio.

Chaotic dynamics of red blood cells in a sinusoidal flow.

We show that the motion of individual red blood cells in an oscillating moderate shear flow is described by a nonlinear system of three coupled oscillators. Our experiments reveal that the cell tank treads and tumbles either in a stable way with synchronized cell inclination, membrane rotation and hydrodynamic oscillations, or in an irregular way, very sensitively to initial conditions. By adapting our model described previously, we determine the theoretical diagram for the red cell motion in a sinusoidal flow close to physiological shear stresses and flow variation frequencies and reveal large domains of chaotic motions. Finally, fitting our observations allows a characterization of cell viscosity and membrane elasticity.

Vesicles and red blood cells in shear flow.

We describe the similarities and the specificities of the behaviour of individual soft particles, namely, drops, lipid vesicles and red blood cells subjected to a shear flow. We highlight that their motion depends in a non-trivial way on the particle mechanical properties. We detail the effect of the presence of a wall with or without wall-particle attractive interaction from a biological perspective.