Human neutrophil surface protrusion under a point load: location independence and viscoelasticity

Acoustic radiation force on a long cylinder, and potential sound transduction by tomato trichomes

Acoustic transduction by plants has been proposed as a mechanism to enable just-in-time up-regulation of metabolically expensive defensive compounds. Although the mechanisms by which this "hearing" occurs are unknown, mechanosensation by elongated plant hair cells known as trichomes is suspected. To evaluate this possibility, we developed a theoretical model to evaluate the acoustic radiation force that an elongated cylinder can receive in response to sounds emitted by animals, including insect herbivores, and applied it to the long, cylindrical stem trichomes of the tomato plant Solanum lycopersicum. Based on perturbation theory and validated by finite element simulations, the model quantifies the effects of viscosity and frequency on this acoustic radiation force. Results suggest that acoustic emissions from certain animals, including insect herbivores, may produce acoustic radiation force sufficient to trigger stretch-activated ion channels.

Viscoelasticity, Like Forces, Plays a Role in Mechanotransduction

Viscoelasticity and its alteration in time and space has turned out to act as a key element in fundamental biological processes in living systems, such as morphogenesis and motility. Based on experimental and theoretical findings it can be proposed that viscoelasticity of cells, spheroids and tissues seems to be a collective characteristic that demands macromolecular, intracellular component and intercellular interactions. A major challenge is to couple the alterations in the macroscopic structural or material characteristics of cells, spheroids and tissues, such as cell and tissue phase transitions, to the microscopic interferences of their elements. Therefore, the biophysical technologies need to be improved, advanced and connected to classical biological assays. In this review, the viscoelastic nature of cytoskeletal, extracellular and cellular networks is presented and discussed. Viscoelasticity is conceptualized as a major contributor to cell migration and invasion and it is discussed whether it can serve as a biomarker for the cells’ migratory capacity in several biological contexts. It can be hypothesized that the statistical mechanics of intra- and extracellular networks may be applied in the future as a powerful tool to explore quantitatively the biomechanical foundation of viscoelasticity over a broad range of time and length scales. Finally, the importance of the cellular viscoelasticity is illustrated in identifying and characterizing multiple disorders, such as cancer, tissue injuries, acute or chronic inflammations or fibrotic diseases.

The Mechanics and Thermodynamics of Tubule Formation in Biological Membranes

Membrane tubulation is a ubiquitous process that occurs both at the plasma membrane and on the membranes of intracellular organelles. These tubulation events are known to be mediated by forces applied on the membrane either due to motor proteins, by polymerization of the cytoskeleton, or due to the interactions between membrane proteins binding onto the membrane. The numerous experimental observations of tube formation have been amply supported by mathematical modeling of the associated membrane mechanics and have provided insights into the force-displacement relationships of membrane tubes. Recent advances in quantitative biophysical measurements of membrane-protein interactions and tubule formation have necessitated the need for advances in modeling that will account for the interplay of multiple aspects of physics that occur simultaneously. Here, we present a comprehensive review of experimental observations of tubule formation and provide context from the framework of continuum modeling. Finally, we explore the scope for future research in this area with an emphasis on iterative modeling and experimental measurements that will enable us to expand our mechanistic understanding of tubulation processes in cells.

Biomechanics of Neutrophil Tethers

Leukocytes, including neutrophils, propelled by blood flow, can roll on inflamed endothelium using transient bonds between selectins and their ligands, and integrins and their ligands. When such receptor–ligand bonds last long enough, the leukocyte microvilli become extended and eventually form thin, 20 µm long tethers. Tether formation can be observed in blood vessels in vivo and in microfluidic flow chambers. Tethers can also be extracted using micropipette aspiration, biomembrane force probe, optical trap, or atomic force microscopy approaches. Here, we review the biomechanical properties of leukocyte tethers as gleaned from such measurements and discuss the advantages and disadvantages of each approach. We also review and discuss viscoelastic models that describe the dependence of tether formation on time, force, rate of loading, and cell activation. We close by emphasizing the need to combine experimental observations with quantitative models and computer simulations to understand how tether formation is affected by membrane tension, membrane reservoir, and interactions of the membrane with the cytoskeleton.

Squeezing through the microcirculation: survival adaptations of circulating tumour cells to seed metastasis

During metastasis, tumour cells navigating the vascular circulatory system-circulating tumour cells (CTCs)-encounter capillary beds, where they start the process of extravasation. Biomechanical constriction forces exerted by the microcirculation compromise the survival of tumour cells within capillaries, but a proportion of CTCs manage to successfully extravasate and colonise distant sites. Despite the profound importance of this step in the progression of metastatic cancers, the factors about this deadly minority of cells remain elusive. Growing evidence suggests that mechanical forces exerted by the capillaries might induce adaptive mechanisms in CTCs, enhancing their survival and metastatic potency. Advances in microfluidics have enabled a better understanding of the cell-survival capabilities adopted in capillary-mimicking constrictions. In this review, we will highlight adaptations developed by CTCs to endure mechanical constraints in the microvasculature and outline how these mechanical forces might trigger dynamic changes towards a more invasive phenotype. A better understanding of the dynamic mechanisms adopted by CTCs within the microcirculation that ultimately lead to metastasis could open up novel therapeutic avenues.

Flexural Rigidity and Shear Stiffness of Flagella Estimated from Induced Bends and Counterbends

Motile cilia and flagella are whiplike cellular organelles that bend actively to propel cells or move fluid in passages such as airways, brain ventricles, and the oviduct. Efficient motile function of cilia and flagella depends on coordinated interactions between active forces from an array of motor proteins and passive mechanical resistance from the complex cytoskeletal structure (the axoneme). However, details of this coordination, including axonemal mechanics, remain unclear. We investigated two major mechanical parameters, flexural rigidity and interdoublet shear stiffness, of the flagellar axoneme in the unicellular alga Chlamydomonas reinhardtii. Combining experiment, theory, and finite element models, we demonstrate that the apparent flexural rigidity of the axoneme depends on both the intrinsic flexural rigidity (EI) and the elastic resistance to interdoublet sliding (shear stiffness, ks). We estimated the average intrinsic flexural rigidity and interdoublet shear stiffness of wild-type Chlamydomonas flagella in vivo, rendered immotile by vanadate, to be EI = 840 ± 280 pN⋅μm(2) and ks = 79.6 ± 10.5 pN/rad, respectively. The corresponding values for the pf3; cnk11-6 double mutant, which lacks the nexin-dynein regulatory complex (N-DRC), were EI = 1011 ± 183 pN·μm(2) and ks = 39.3 ± 6.0 pN/rad under the same conditions. Finally, in the pf13A mutant, which lacks outer dynein arms and inner dynein arm c, the estimates were EI = 777 ± 184 pN·μm(2) and ks = 43.3 ± 7.7 pN/rad. In the two mutant strains, the flexural rigidity is not significantly different from wild-type (p > 0.05), but the lack of N-DRC (in pf3; cnk11-6) or dynein arms (in pf13A) significantly reduces interdoublet shear stiffness. These differences may represent the contributions of the N-DRCs (∼40 pN/rad) and residual dynein interactions (∼35 pN/rad) to interdoublet sliding resistance in these immobilized Chlamydomonas flagella.

From Surface Protrusion to Tether Extraction: A Mechanistic Model

Human leukocyte rolling on the endothelium is essential for leukocyte emigration and it is a process regulated by many factors including shear stress, receptor-ligand kinetics, and mechanical properties of cells and molecules. During this process, both leukocytes and endothelial cells (ECs) are pulled by forces due to blood flow and both may experience surface protrusion and tether extraction. In this study, we established a two-scale (cellular and molecular) model of cellular deformation because of a point pulling force and illustrated how surface protrusion makes the transition to tether extraction, either gradually or abruptly. Our simulation results matched well with what was observed in the experiments conducted with the optical trap and the atomic force microscope. We found that, although the traditional method of determining the force loading rate and the protrusional stiffness were still reasonable, the crossover force should not be simply interpreted as the rupture force of the receptor-cytoskeleton linkage. With little modification, this model can be incorporated into any leukocyte rolling model as a module for more accurate and realistic simulation.

Microfluidics-based side view flow chamber reveals tether-to-sling transition in rolling neutrophils

Neutrophils rolling at high shear stress (above 6 dyn/cm²) form tethers in the rear and slings in the front. Here, we developed a novel photo-lithographically fabricated, silicone(PDMS)-based side-view flow chamber to dynamically visualize tether and sling formation. Fluorescently membrane-labeled mouse neutrophils rolled on P-selectin substrate at 10 dyn/cm². Most rolling cells formed 5 tethers that were 2–30 μm long. Breaking of a single tether caused a reproducible forward microjump of the cell, showing that the tether was load-bearing. About 15% of all tether-breaking events resulted in slings. The tether-to-sling transition was fast (<100 ms) with no visible material extending above the rolling cell, suggesting a very low bending modulus of the tether. The sling downstream of the rolling cell aligned according to the streamlines before landing on the flow chamber. These new observations explain how slings form from tethers and provide insight into their biomechanical properties.

Endothelial Surface Protrusion by a Point Force

During leukocyte rolling on the endothelium, surface protrusion and membrane tether extraction occur consecutively on leukocytes. Both surface protrusion and tether extraction of leukocytes stabilize leukocyte rolling. Tethers can also be extracted from endothelial cells (ECs), but surface protrusion of ECs has never been confirmed to exist. In this study, we examined EC surface protrusion with the micropipette aspiration technique. We found that, like leukocytes, surface protrusion on an EC did exist when a point force was imposed. Both the protrusional stiffness and the crossover force of EC surface protrusion were dependent on the force loading rate and the cytoskeletal integrity, but neither of them was dependent on tumor necrosis factor α stimulation. Temperature (37°C) affected the protrusional stiffness only at small force loading rates. When a neutrophil was employed to directly impose the pulling force on the EC, simultaneous surface protrusion from both cells occurred, and it can be modeled as two springs connected in series, although the spring constants should be adjusted according to the force loading rate. Therefore, EC surface protrusion is an important aspect of leukocyte rolling, and it should not be ignored when leukocyte rolling stability is studied systematically.

Effect of the object 3D shape on the viscoelastic testing in optical tweezers

Viscoelastic testing of biological cells has been performed with the optical tweezers and stretcher. Historically, the cells were modeled by the spring-dashpot network or the power-law models, which can however characterize only the homogeneous, isotropic viscoelastic material, but not the 3D cell itself. Our mechanical and finite element analyses show that the cell elongations are different significantly for different cell 3D shapes in the creep testing. In the dynamic testing the loss tangent, which is measurable directly in the experiment, is not sensitive to the cell shape. However, the stress-strain hysteresis loop still depends on the cell 3D shape.

Quantitative dynamic footprinting microscopy

Quantitative dynamic footprinting (qDF) allows visualization of the footprints of live leukocytes rolling on a selectin-coated cover glass. qDF works on the principle of total internal reflection fluorescence, which involves fluorescence excitation in a thin slice (~200 nm) of the cell proximal to the cover glass while the rest of the cell remains dark. Dual color qDF (DqDF) is an advancement of qDF, which enables simultaneous visualization of two fluorochromes in the footprints of rolling leukocytes. When the fluorochrome is localized either in the cell cytoplasm or plasma membrane, the two-dimensional qDF image is used to create a three-dimensional rendition of the footprint topography. DqDF is a useful tool to study leukocyte adhesion under flow, and has recently been used to reveal mechanisms that enable neutrophils to roll at high shear stresses that prevail in venules during inflammation.

Effects of plasma membrane cholesterol level and cytoskeleton F-actin on cell protrusion mechanics

Protrusions are deformations that form at the surface of living cells during biological activities such as cell migration. Using combined optical tweezers and fluorescent microscopy, we quantified the mechanical properties of protrusions in adherent human embryonic kidney cells in response to application of an external force at the cell surface. The mechanical properties of protrusions were analyzed by obtaining the associated force-length plots during protrusion formation, and force relaxation at constant length. Protrusion mechanics were interpretable by a standard linear solid (Kelvin) model, consisting of two stiffness parameters, k0 and k1 (with k0>k1), and a viscous coefficient. While both stiffness parameters contribute to the time-dependant mechanical behavior of the protrusions, k0 and k1 in particular dominated the early and late stages of the protrusion formation and elongation process, respectively. Lowering the membrane cholesterol content by 25% increased the k0 stiffness by 74%, and shortened the protrusion length by almost half. Enhancement of membrane cholesterol content by nearly two-fold increased the protrusion length by 30%, and decreased the k0 stiffness by nearly two-and-half-fold as compared with control cells. Cytoskeleton integrity was found to make a major contribution to protrusion mechanics as evidenced by the effects of F-actin disruption on the resulting mechanical parameters. Viscoelastic behavior of protrusions was further characterized by hysteresis and force relaxation after formation. The results of this study elucidate the coordination of plasma membrane composition and cytoskeleton during protrusion formation.

Membrane tubulovesicular extensions (cytonemes): secretory and adhesive cellular organelles

In this review, we summarized data on the formation and structure of the long and highly adhesive membrane tubulovesicular extensions (TVEs, membrane tethers or cytonemes) observed in human neutrophils and other mammalian cells, protozoan parasites and bacteria. We determined that TVEs are membrane protrusions characterized by a uniform diameter (130-250 nm for eukaryotic cells and 60-90 nm for bacteria) along the entire length, an outstanding length and high rate of development and a high degree of flexibility and capacity for shedding from the cells. This review represents TVEs as protrusions of the cellular secretory process, serving as intercellular adhesive organelles in eukaryotic cells and bacteria. An analysis of the physical and chemical approaches to induce TVEs formation revealed that disrupting the actin cytoskeleton and inhibiting glucose metabolism or vacuolar-type ATPase induces TVE formation in eukaryotic cells. Nitric oxide is represented as a physiological regulator of TVE formation.

Neutrophil rolling at high shear: flattening, catch bond behavior, tethers and slings

Neutrophil recruitment to sites of inflammation involves neutrophil rolling along the inflamed endothelium in the presence of shear stress imposed by blood flow. Neutrophil rolling in post-capillary venules in vivo is primarily mediated by P-selectin on the endothelium binding to P-selectin glycoprotein ligand-1 (PSGL-1) constitutively expressed on neutrophils. Blood flow exerts a hydrodynamic drag on the rolling neutrophil which is partially or fully balanced by the adhesive forces generated in the P-selectin-PSGL-1 bonds. Rolling is the result of rapid formation and dissociation of P-selectin-PSGL-1 bonds at the center and rear of the rolling cell, respectively. Neutrophils roll stably on P-selectin in post-capillary venules in vivo and flow chambers in vitro at wall shear stresses greater than 6 dyn cm(-2). However, the mechanisms that enable neutrophils to roll at such high shear stress are not completely understood. In vitro and in vivo studies have led to the discovery of four potential mechanisms, viz. cell flattening, catch bond behavior, membrane tethers, and slings. Rolling neutrophils undergo flattening at high shear stress, which not only increases the size of the cell footprint but also reduces the hydrodynamic drag experienced by the rolling cell. P-selectin-PSGL-1 bonds behave as catch bonds at small detachment forces and thus become stronger with increasing force. Neutrophils rolling at high shear stress form membrane tethers which can be longer than the cell diameter and promote the survival of P-selectin-PSGL-1 bonds. Finally, neutrophils rolling at high shear stress form 'slings', which act as cell autonomous adhesive substrates and support step-wise peeling. Tethers and slings act together and contribute to the forces balancing the hydrodynamic drag. How the synergy between the four mechanisms leads to stable rolling at high shear stress is an area that needs further investigation.

Constitutively active ezrin increases membrane tension, slows migration, and impedes endothelial transmigration of lymphocytes in vivo in mice

ERM (ezrin, radixin moesin) proteins in lymphocytes link cortical actin to plasma membrane, which is regulated in part by ERM protein phosphorylation. To assess whether phosphorylation of ERM proteins regulates lymphocyte migration and membrane tension, we generated transgenic mice whose T-lymphocytes express low levels of ezrin phosphomimetic protein (T567E). In these mice, T-cell number in lymph nodes was reduced by 27%. Lymphocyte migration rate in vitro and in vivo in lymph nodes decreased by 18% to 47%. Lymphocyte membrane tension increased by 71%. Investigations of other possible underlying mechanisms revealed impaired chemokine-induced shape change/lamellipod extension and increased integrin-mediated adhesion. Notably, lymphocyte homing to lymph nodes was decreased by 30%. Unlike most described homing defects, there was not impaired rolling or sticking to lymph node vascular endothelium but rather decreased migration across that endothelium. Moreover, decreased numbers of transgenic T cells in efferent lymph suggested defective egress. These studies confirm the critical role of ERM dephosphorylation in regulating lymphocyte migration and transmigration. Of particular note, they identify phospho-ERM as the first described regulator of lymphocyte membrane tension, whose increase probably contributes to the multiple defects observed in the ezrin T567E transgenic mice.

Biomechanics of leukocyte rolling

Leukocyte rolling on endothelial cells and other P-selectin substrates is mediated by P-selectin binding to P-selectin glycoprotein ligand-1 expressed on the tips of leukocyte microvilli. Leukocyte rolling is a result of rapid, yet balanced formation and dissociation of selectin-ligand bonds in the presence of hydrodynamic shear forces. The hydrodynamic forces acting on the bonds may either increase (catch bonds) or decrease (slip bonds) their lifetimes. The force-dependent 'catch-slip' bond kinetics are explained using the 'two pathway model' for bond dissociation. Both the 'sliding-rebinding' and the 'allosteric' mechanisms attribute 'catch-slip' bond behavior to the force-induced conformational changes in the lectin-EGF domain hinge of selectins. Below a threshold shear stress, selectins cannot mediate rolling. This 'shear-threshold' phenomenon is a consequence of shear-enhanced tethering and catch bond-enhanced rolling. Quantitative dynamic footprinting microscopy has revealed that leukocytes rolling at venular shear stresses (>0.6 Pa) undergo cellular deformation (large footprint) and form long tethers. The hydrodynamic shear force and torque acting on the rolling cell are thought to be synergistically balanced by the forces acting on tethers and stressed microvilli, however, their relative contribution remains to be determined. Thus, improvement beyond the current understanding requires in silico models that can predict both cellular and microvillus deformation and experiments that allow measurement of forces acting on individual microvilli and tethers.

Cell protrusions and tethers: a unified approach

Low pulling forces applied locally to cell surface membranes produce viscoelastic cell surface protrusions. As the force increases, the membrane can locally separate from the cytoskeleton and a tether forms. Tethers can grow to great lengths exceeding the cell diameter. The protrusion-to-tether transition is known as the crossover. Here we propose a unified approach to protrusions and tethers providing, to our knowledge, new insights into their biomechanics. We derive a necessary and sufficient condition for a crossover to occur, a formula for predicting the crossover time, conditions for a tether to establish a dynamic equilibrium (characterized by constant nonzero pulling force and tether extension rate), a general formula for the tether material after crossover, and a general modeling method for tether pulling experiments. We introduce two general protrusion parameters, the spring constant and effective viscosity, valid before and after crossover. Their first estimates for neutrophils are 50 pN μm(-1) and 9 pN s μm(-1), respectively. The tether elongation after crossover is described as elongation of a viscoelastic-like material with a nonlinearly decaying spring (NLDs-viscoelastic material). Our model correctly describes the results of the published protrusion and tether pulling experiments, suggesting that it is universally applicable to such experiments.

Three powerful research tools from single cells into single molecules: AFM, laser tweezers, and Raman spectroscopy

By using three physical techniques (atomic force microscopy (AFM), laser tweezers, and Raman spectroscopy), many excellent works in single-cell/molecule research have been accomplished. In this review, we present a brief introduction to the principles of these three techniques, and their capabilities toward single-cell/molecule research are highlighted. Afterward, the advances in single-cell/molecule research that have been facilitated by these three techniques are described. Following this, their complementary assets for single-cell/molecule research are analyzed, and the necessity of integrating the functions of these three techniques into one instrument is proposed.

A semianalytical model to study the effect of cortical tension on cell rolling

Cell rolling on the vascular endothelium plays an important role in trafficking of leukocytes, stem cells, and cancer cells. We describe a semianalytical model of cell rolling that focuses on the microvillus as the unit of cell-substrate interaction and integrates microvillus mechanics, receptor clustering, force-dependent receptor-ligand kinetics, and cortical tension that enables incorporation of cell body deformation. Using parameters obtained from independent experiments, the model showed excellent agreement with experimental studies of neutrophil rolling on P-selectin and predicted different regimes of cell rolling, including spreading of the cells on the substrate under high shear. The cortical tension affected the cell-surface contact area and influenced the rolling velocity, and modulated the dependence of rolling velocity on microvillus stiffness. Moreover, at the same shear stress, microvilli of cells with higher cortical tension carried a greater load compared to those with lower cortical tension. We also used the model to obtain a scaling dependence of the contact radius and cell rolling velocity under different conditions of shear stress, cortical tension, and ligand density. This model advances theoretical understanding of cell rolling by incorporating cortical tension and microvillus extension into a versatile, semianalytical framework.

Unfolding the A2 domain of von Willebrand factor with the optical trap

Von Willebrand factor (VWF) is a multimeric plasma glycoprotein involved in both hemostasis and thrombosis. VWF conformational changes, especially unfolding of the A2 domain, may be required for efficient enzymatic cleavage in vivo. It has been shown that a single A2 domain unfolds at most probable unfolding forces of 7-14 pN at force loading rates of 0.35-350 pN/s and A2 unfolding facilitates A2 cleavage in vitro. However, it remains unknown how much force is required to unfold the A2 domain in the context of a VWF multimer where A2 may be stabilized by other domains like A1 and A3. With the optical trap, we stretched VWF multimers and a poly-protein (A1A2A3)3 that contains three repeats of the triplet A1A2A3 domains at constant speeds of 2000 nm/s and 400 nm/s, respectively, which yielded corresponding average force loading rates of 90 and 22 pN/s. We found that VWF multimers became stiffer when they were stretched and extended by force. After force increased to a certain level, sudden extensional jumps that signify domain unfolding were often observed. Histograms of the unfolding force and the unfolded contour length showed two or three peaks that were integral multiples of approximately 21 pN and approximately 63 nm, respectively. Stretching of (A1A2A3)3 yielded comparable distributions of unfolding force and unfolded contour length, showing that unfolding of the A2 domain accounts for the behavior of VWF multimers under tension. These results show that the A2 domain can be indeed unfolded in the presence of A1, A3, and other domains. Compared with the value in the literature, the larger most probable unfolding force measured in this study suggests that the A2 domain is mechanically stabilized by A1 or A3 although variations in experimental setups and conditions may complicate this interpretation.

Validation, In-Depth Analysis, and Modification of the Micropipette Aspiration Technique

The micropipette aspiration technique (MAT) has been successfully applied to many studies in cell adhesion such as leukocyte-endothelium interactions. However, this technique has never been validated experimentally and it has been only employed to impose constant forces. In this study, we validated the force measurement of the MAT with the optical trap and analyzed two technical issues of the MAT, force-transducer offset and cell-micropipette gap, with finite element simulation. We also modified the MAT so that increasing or decreasing forces can be applied. With the modified MAT, we studied tether extraction from endothelial cells by pulling single tethers at increasing velocities and constant force loading rates. Before the onset of tether extraction, an apparently-linear surface protrusion of a few hundred nanometers was observed, which is likely related to membrane receptors pulling on the underlying cytoskeleton. The strength of the modified MAT lies in its capability and consistency to apply a wide range of force loading rates from several piconewtons per second up to thousands of piconewtons per second. With this modification, the MAT becomes more versatile in the study of single molecule and single cell biophysics.