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Abstract A primary cilium, made of nine microtubule doublets enclosed in a cilium membrane, is a mechanosensing organelle that bends under an external mechanical load and sends an intracellular signal through transmembrane proteins activated by cilium bending. The nine microtubule doublets are the main load‐bearing structural component, while the transmembrane proteins on the cilium membrane are the main sensing component. No distinction was made between these two components in all existing models, where the stress calculated from the structural component (nine microtubule doublets) was used to explain the sensing location, which may be totally misleading. For the first time, we developed a microstructure‐based primary cilium model by considering these two components separately. First, we refined the analytical solution of bending an orthotropic cylindrical shell for individual microtubule, and obtained excellent agreement between finite element simulations and the theoretical predictions of a microtubule bending as a validation of the structural component in the model. Second, by integrating the cilium membrane with nine microtubule doublets and simulating the tip‐anchored optical tweezer experiment on our computational model, we found that the microtubule doublets may twist significantly as the whole cilium bends. Third, besides being cilium‐length‐dependent, we found the mechanical properties of the cilium are also highly deformation‐dependent. More important, we found that the cilium membrane near the base is not under pure in‐plane tension or compression as previously thought, but has significant local bending stress. This challenges the traditional model of cilium mechanosensing, indicating that transmembrane proteins may be activated more by membrane curvature than membrane stretching. Finally, we incorporated imaging data of primary cilia into our microstructure‐based cilium model, and found that comparing to the ideal model with uniform microtubule length, the imaging‐informed model shows the nine microtubule doublets interact more evenly with the cilium membrane, and their contact locations can cause even higher bending curvature in the cilium membrane than near the base. 

Abstract The nuclear lamina is widely recognized as the most crucial component in providing mechanical stability to the nucleus. However, it is still a significant challenge to model the mechanics of this multilayered protein network. We developed a constitutive model of the nuclear lamina network based on its microstructure, which accounts for the deformation phases at the dimer level, as well as the orientational arrangement and density of lamin filaments. Instead of relying on homology modeling in the previous studies, we conducted molecular simulations to predict the force‐extension response of a highly accurate lamin dimer structure obtained through X‐ray diffraction crystallography experimentation. Furthermore, we devised a semiflexible worm‐like chain extension‐force model of lamin dimer as a substitute, incorporating phases of initial stretching, uncoiling of the dimer coiled‐coil, and transition of secondary structures. Subsequently, we developed a 2D network continuum model for the nuclear lamina by using our extension‐force lamin dimer model and derived stress resultants. By comparing with experimentally measured lamina modulus, we found that the lamina network has sharp initial strain‐hardening behavior. This also enabled us to carry out finite element simulations of the entire nucleus with an accurate microstructure‐based nuclear lamina model. Finally, we conducted simulations of transendothelial transmigration of a nucleus and investigated the impact of varying network density and uncoiling constants on the critical force required for successful transmigration. The model allows us to incorporate the microstructure characteristics of the nuclear lamina into the nucleus model, thereby gaining insights into how laminopathies and mutations affect nuclear mechanics. 

Abstract Particle migration dynamics in viscoelastic fluids in spiral channels have attracted interest in recent years due to potential applications in the 3D focusing and label-free sorting of particles and cells. Despite a number of recent studies, the underlying mechanism of Dean-coupled elasto-inertial migration in spiral microchannels is not fully understood. In this work, for the first time, we experimentally demonstrate the evolution of particle focusing behavior along a channel downstream length at a high blockage ratio. We found that flow rate, device curvature, and medium viscosity play important roles in particle lateral migration. Our results illustrate the full focusing pattern along the downstream channel length, with side-view imaging yielding observations on the vertical migration of focused streams. Ultimately, we anticipate that these results will offer a useful guide for elasto-inertial microfluidics device design to improve the efficiency of 3D focusing in cell sorting and cytometry applications. 

Abstract Various signals in tissue microenvironments are often unevenly distributed around cells. Cellular responses to asymmetric cell‐matrix adhesion in a 3D space remain generally unclear and are to be studied at the single‐cell resolution. Here, the authors developed a droplet‐based microfluidic approach to manufacture a pure population of single cells in a microscale layer of compartmentalized 3D hydrogel matrices with a tunable spatial presentation of ligands at the subcellular level. Cells elongate with an asymmetric presentation of the integrin adhesion ligand Arg‐Gly‐Asp (RGD), while cells expand isotropically with a symmetric presentation of RGD. Membrane tension is higher on the side of single cells interacting with RGD than on the side without RGD. Finite element analysis shows that a non‐uniform isotropic cell volume expansion model is sufficient to recapitulate the experimental results. At a longer timescale, asymmetric ligand presentation commits mesenchymal stem cells to the osteogenic lineage. Cdc42 is an essential mediator of cell polarization and lineage specification in response to asymmetric cell‐matrix adhesion. This study highlights the utility of precisely controlling 3D ligand presentation around single cells to direct cell polarity for regenerative engineering and medicine. 

The regulation of polymorphonuclear leukocyte (PMN) function by mechanical forces encountered during their migration across restrictive endothelial cell junctions is not well understood. Using genetic, imaging, microfluidic, and in vivo approaches, we demonstrated that the mechanosensor Piezo1 in PMN plasmalemma induced spike-like Ca2+ signals during trans-endothelial migration. Mechanosensing increased the bactericidal function of PMN entering tissue. Mice in which Piezo1 in PMNs was genetically deleted were defective in clearing bacteria, and their lungs were predisposed to severe infection. Adoptive transfer of Piezo1-activated PMNs into the lungs of Pseudomonas aeruginosa-infected mice or exposing PMNs to defined mechanical forces in microfluidic systems improved bacterial clearance phenotype of PMNs. Piezo1 transduced the mechanical signals activated during transmigration to upregulate nicotinamide adenine dinucleotide phosphate (NADPH) oxidase 4, crucial for the increased PMN bactericidal activity. Thus, Piezo1 mechanosensing of increased PMN tension, while traversing the narrow endothelial adherens junctions, is a central mechanism activating the host-defense function of transmigrating PMNs. 

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 $\mathrm{\mu }$m RBCs pass through 0.3 $\mathrm{\mu }$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 $\mathrm{\mu }$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 $\mathrm{\mu }$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 $-$1 and $-$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. 

We derived equations and closed-form solutions of transit time for a viscous droplet squeezing through a small circular pore with a finite length at microscale under constant pressures. Our analyses were motivated by the vital processes of biological cells squeezing through small pores in blood vessels and sinusoids and droplets squeezing through pores in microfluidics. First, we derived ordinary differential equations (ODEs) of a droplet squeezing through a circular pore by combining Sampson flow, Poiseuille flow, and Young–Laplace equations and took into account the lubrication layer between the droplet and the pore wall. Second, for droplets wetting the wall with small surface tension, we derived the closed-form solutions of transit time. For droplets with finite surface tension, we solved the original ODEs numerically to predict the transit time. After validations against experiments and finite element simulations, we studied the effects of pressure, viscosity, pore/droplet dimensions, and surface tension on the transit time. We found that the transit time is inversely linearly proportional to pressure when the surface tension is low compared to the critical surface tension for preventing the droplet to pass and becomes nonlinear when it approaches the critical tension. Remarkably, we showed that when a fixed percentage of surface tension to critical tension is applied, the transit time is always inversely linearly proportional to pressure, and the dependence of transit time on surface tension is nonmonotonic. Our results provided a quick way of quantitative calculations of transit time for designing droplet microfluidics and understanding cells passing through constrictions. 

Growth of the microfluidics field has triggered numerous advances in focusing and separating microparticles, with such systems rapidly finding applications in biomedical, chemical, and environmental fields. The use of shear-thinning viscoelastic fluids in microfluidic channels is leading to evolution of elasto-inertial focusing. Herein, we showed that the interplay between the elastic and shear-gradient lift forces, as well as the secondary flow transversal drag force that is caused by the non-zero second normal stress difference, lead to different particle focusing patterns in the elasto-inertial regime. Experiments and 3D simulations were performed to study the effects of flowrate, particle size, and the shear-thinning extent of the fluid on the focusing patterns. The Giesekus constitutive equation was used in the simulations to capture the shear-thinning and viscoelastic behaviors of the solution used in the experiments. At low flowrate, with Weissenberg number Wi ~ O(1), both the elastic force and secondary flow effects push particles towards the channel center. However, at a high flowrate, Wi ~ O(10), the elastic force direction is reversed in the central regions. This remarkable behavior of the elastic force, combined with the enhanced shear-gradient lift at the high flowrate, pushes particles away from the channel center. Additionally, a precise prediction of the focusing position can only be made when the shear-thinning extent of the fluid is correctly estimated in the modeling. The shear-thinning also gives rise to the unique behavior of the inertial forces near the channel walls which is linked with the ‘warped’ velocity profile in such fluids. 

Sickle cell anemia (SCA) is a disease that affects red blood cells (RBCs). Healthy RBCs are highly deformable objects that under flow can penetrate blood capillaries smaller than their typical size. In SCA there is an impaired deformability of some cells, which are much stiffer and with a different shape than healthy cells, and thereby affect regular blood flow. It is known that blood from patients with SCA has a higher viscosity than normal blood. However, it is unclear how the rigidity of cells is related to the viscosity of blood, in part because SCA patients are often treated with transfusions of variable amounts of normal RBCs and only a fraction of cells will be stiff. Here, we report systematic experimental measurements of the viscosity of a suspension varying the fraction of rigid particles within a suspension of healthy cells. We also perform systematic numerical simulations of a similar mixed suspension of soft RBCs, rigid particles, and their hydrodynamic interactions. Our results show that there is a rheological signature within blood viscosity to clearly identify the fraction of rigidified cells among healthy deformable cells down to a 5% volume fraction of rigidified cells. Although aggregation of RBCs is known to affect blood rheology at low shear rates, and our simulations mimic this effect via an adhesion potential, we show that such adhesion, or aggregation, is unlikely to provide a physical rationalization for the viscosity increase observed in the experiments at moderate shear rates due to rigidified cells. Through numerical simulations, we also highlight that most of the viscosity increase of the suspension is due to the rigidity of the particles rather than their sickled or spherical shape. Our results are relevant to better characterize SCA, provide useful insights relevant to rheological consequences of blood transfusions, and, more generally, extend to the rheology of mixed suspensions having particles with different rigidities, as well as offering possibilities for developments in the field of soft material composites.