Dynamic states of cells adhering in shear flow: from slipping to rolling

Deciphering circulating tumor cells binding in a microfluidic system thanks to a parameterized mathematical model

The spread of metastases is a crucial process in which some questions remain unanswered. In this work, we focus on tumor cells circulating in the bloodstream, the so-called Circulating Tumor Cells (CTCs). Our aim is to characterize their trajectories under the influence of hemodynamic and adhesion forces. We focus on already available in vitro measurements performed with a microfluidic device corresponding to the trajectories of CTCs - without or with different protein depletions - interacting with an endothelial layer. A key difficulty is the weak knowledge of the fluid velocity that has to be reconstructed. Our strategy combines a differential equation model - a Poiseuille model for the fluid velocity and an ODE system for the cell adhesion model - and a robust and well-designed calibration procedure. The parameterized model quantifies the strong influence of fluid velocity on adhesion and confirms the expected role of several proteins in the deceleration of CTCs. Finally, it enables the generation of synthetic cells, even for unobserved experimental conditions, opening the way to a digital twin for flowing cells with adhesion.

Electric field-mediated adhesive dynamics of cells inside bio-functionalised microchannels offers important cues for active control of cell-substrate adhesion

Adhesive dynamics of cells plays a critical role in determining different biophysical processes orchestrating health and disease in living systems. While the rolling of cells on functionalised substrates having similarity with biophysical pathways appears to be extensively discussed in the literature, the effect of an external stimulus in the form of an electric field on the same remains underemphasized. Here, we bring out the interplay of fluid shear and electric field on the rolling dynamics of adhesive cells in biofunctionalised micro-confinements. Our experimental results portray that an electric field, even restricted to low strengths within the physiologically relevant regimes, can significantly influence the cell adhesion dynamics. We quantify the electric field-mediated adhesive dynamics of the cells in terms of two key parameters, namely, the voltage-altered rolling velocity and the frequency of adhesion. The effect of the directionality of the electric field with respect to the flow direction is also analysed by studying cellular migration with electrical effects acting both along and against the flow. Our experiment, on one hand, demonstrates the importance of collagen functionalisation in the adhesive dynamics of cells through micro channels, while on the other hand, it reveals how the presence of an axial electric field can lead to significant alteration in the kinetic rate of bond breakage, thereby modifying the degree of cell-substrate adhesion and quantifying in terms of the adhesion frequency of the cells. Proceeding further forward, we offer a simple theoretical explanation towards deriving the kinetics of cellular bonding in the presence of an electric field, which corroborates favourably with our experimental outcome. These findings are likely to offer fundamental insights into the possibilities of local control of cellular adhesion via electric field mediated interactions, bearing critical implications in a wide variety of medical conditions ranging from wound healing to cancer metastasis.

Effects of cell deformability and adhesion strength on dynamic cell seeding: Cell-scale investigation via mesoscopic modeling

The flow of cell suspension through a porous scaffold is a common process in dynamic cell seeding, which determines the initial distribution of cells for constructing tissue-engineered grafts. Physical insights into the transport and adhesion behaviors of cells in this process are of great significance to the precise control of cell density and its distribution in the scaffold. Revealing of dynamic mechanisms underlying these cell behaviors through experiments is still difficult. The numerical approach therefore plays an important role in such studies. However, existing studies have mostly focused on external factors (e.g., flow conditions and scaffold architecture) but ignored the intrinsic biomechanical properties of cells as well as their associated effects. The present work utilized a well-established mesoscopic model to simulate the dynamic cell seeding within a porous scaffold, based on which a thorough investigation of the effects of cell deformability and cell-scaffold adhesion strength on the seeding process was carried out. The results show that the increase in either the stiffness or the bond strength of cells would augment the firm-adhesion rate and thus enhance seeding efficiency. In comparison to cell deformability, bond strength seems to play a more dominant role. Especially in the cases with weak bond strength, remarkable losses of seeding efficiency and distribution uniformity are observed. Noteworthily, it is found that both the firm-adhesion rate and the seeding efficiency are quantiatively related to the adhesion strength which is measured as the detachment force, suggesting a straightforward way to estimate the seeding outcome.

Mass Changes the Diffusion Coefficient of Particles with Ligand-Receptor Contacts in the Overdamped Limit

Inertia does not generally affect the long-time diffusion of passive overdamped particles in fluids. Yet a model starting from the Langevin equation predicts a surprising property of particles coated with ligands that bind reversibly to surface receptors: heavy particles diffuse more slowly than light ones of the same size. We show this by simulation and by deriving an analytic formula for the mass-dependent diffusion coefficient in the overdamped limit. We estimate the magnitude of this effect for a range of biophysical ligand-receptor systems, and find it is potentially observable for tailored micronscale DNA-coated colloids.

A general numerical model of leukocyte adhesion in microchannels

Leukocyte adhesion on the vascular endothelium plays an important role in human immune system and reflects the physiological condition of a human body. In this paper, a generally implementable dynamic adhesion model based on the length limit of microvilli was developed to explore the behavior of a suspended leukocyte's adhesion process under microchannel shear flow. Simulations showed that the whole adhesion process can be divided into cell sedimentation, preliminary adhesion and stable dynamic adhesion stages. The cell tumbling kinetics, cell deformation, cell adhesion area and adhesion force were studied under the conditions of various bond strength, cell membrane surface tension, inlet flow velocity and cytoplasmic viscosity. Results showed that the bond strength affects the cell tumbling behaviors differently by changing the adhesion force. The cell with lower membrane surface tension induces a larger adhesion area, and eventually results in a greater adhesion and a lower cell tumbling velocity. The flow velocity changes cell velocity through the flow viscous force during the whole adhesion process. The cytoplasmic viscosity affects adhesion mainly in the preliminary adhesion stage by changing the cell deformation rate but has slight effect on the stabilized dynamic adhesion on cells. This study provides a simple theoretical basis to further clarify the mechanism of cell behaviors under stress and adhesion and becomes one of the prerequisites for study of tissue inflammation, wound healing, and disease treatments.

Physics of self-rolling viruses

Viruses are right at the interface of inanimate matter and life. However, recent experiments [Sakai et al., J. Virol. 92, e01522-17 (2018)0022-538X10.1128/JVI.01522-17] have shown that some influenza strains can actively roll on glycan-covered surfaces. In a previous letter [Ziebert and Kulić, Phys. Rev. Lett. 126, 218101 (2021)0031-900710.1103/PhysRevLett.126.218101] we suggested this to be a form of viral surface metabolism: a collection of spike proteins that attach to and cut the glycans act as a self-organized mechano-chemical motor. Here we study in more depth the physics of the emergent self-rolling states. We give scaling arguments how the motion arises, substantiated by a detailed analytical theory that yields the full torque-angular velocity relation of the self-organized motor. Stochastic Gillespie simulations are used to validate the theory and to quantify stochastic effects like virus detachment and reversals of its direction. Finally, we also cross-check several approximations made previously and show that the proposed mechanism is very robust. All these results point together to the statistical inevitability of viral rolling in the presence of enzymatic activity.

The nanocaterpillar's random walk: diffusion with ligand-receptor contacts

Particles with ligand-receptor contacts bind and unbind fluctuating "legs" to surfaces, whose fluctuations cause the particle to diffuse. Quantifying the diffusion of such "nanoscale caterpillars" is a challenge, since binding events often occur on very short time and length scales. Here we derive an analytical formula, validated by simulations, for the long time translational diffusion coefficient of an overdamped nanocaterpillar, under a range of modeling assumptions. We demonstrate that the effective diffusion coefficient, which depends on the microscopic parameters governing the legs, can be orders of magnitude smaller than the background diffusion coefficient. Furthermore it varies rapidly with temperature, and reproduces the striking variations seen in existing data and our own measurements of the diffusion of DNA-coated colloids. Our model gives insight into the mechanism of motion, and allows us to ask: when does a nanocaterpillar prefer to move by sliding, where one leg is always linked to the surface, and when does it prefer to move by hopping, which requires all legs to unbind simultaneously? We compare a range of systems (viruses, molecular motors, white blood cells, protein cargos in the nuclear pore complex, bacteria such as Escherichia coli, and DNA-coated colloids) and present guidelines to control the mode of motion for materials design.

Functionalized supported membranes for quantifying adhesion of P. falciparum-infected erythrocytes

The pathology of Plasmodium falciparum malaria is largely defined by the cytoadhesion of infected erythrocytes to the microvascular endothelial lining. The complexity of the endothelial surface and the large range of interactions available for the infected erythrocyte via parasite-encoded adhesins make analysis of critical contributions during cytoadherence challenging to define. Here, we have explored supported membranes functionalized with two important adhesion receptors, ICAM1 or CD36, as a quantitative biomimetic surface to help understand the processes involved in cytoadherence. Parasitized erythrocytes bound to the receptor-functionalized membranes with high efficiency and selectivity under both static and flow conditions, with infected wild-type erythrocytes displaying a higher binding capacity than do parasitized heterozygous sickle cells. We further show that the binding efficiency decreased with increasing intermolecular receptor distance and that the cell-surface contacts were highly dynamic and increased with rising wall shear stress as the cell underwent a shape transition. Computer simulations using a deformable cell model explained the wall-shear-stress-induced dynamic changes in cell shape and contact area via the specific physical properties of erythrocytes, the density of adhesins presenting knobs, and the lateral movement of receptors in the supported membrane.

How Influenza's Spike Motor Works

While often believed to be a passive agent that merely exploits its host's metabolism, the influenza virus has recently been shown to actively move across glycan-coated surfaces. This form of enzymatically driven surface motility is currently not well understood and has been loosely linked to burnt-bridge Brownian ratchet mechanisms. Starting from known properties of influenza's spike proteins, we develop a physical model that quantitatively describes the observed motility. It predicts a collectively emerging dynamics of spike proteins and surface-bound ligands that combined with the virus' geometry give rise to a self-organized rolling propulsion. We show that in contrast to a Brownian ratchet, the rotary spike drive is not fluctuation driven but operates optimally as a macroscopic engine in the deterministic regime. The mechanism also applies to relatives of influenza and to man-made analogs like DNA monowheels and should give guidelines for their optimization.

Quantitative interpretation of cell rolling velocity distribution

Leukocyte rolling adhesion, facilitated by selectin-mediated interactions, is a highly dynamic process in which cells roll along the endothelial surface of blood vessel walls to reach the site of infection. The most common approach to investigate cell-substrate adhesion is to analyze the cell rolling velocity in response to shear stress changes. It is assumed that changes in rolling velocity indicate changes in adhesion strength. In general, cell rolling velocity is studied at the population level as an average velocity corresponding to given shear stress. However, no statistical investigation has been performed on the instantaneous velocity distribution. In this study, we first developed a method to remove systematic noise and revealed the true velocity distribution to exhibit a log-normal profile. We then demonstrated that the log-normal distribution describes the instantaneous velocity at both the population and single-cell levels across the physiological flow rates. The log-normal parameters capture the cell motion more accurately than the mean and median velocities, which are prone to systematic error. Lastly, we connected the velocity distribution to the molecular adhesion force distribution and showed that the slip-bond regime of the catch-slip behavior of the P-selectin/PSGL-1 interaction is responsible for the variation of cell velocity.

Numerical investigation of adhesion dynamics of a deformable cell pair on an adhesive substrate in shear flow

Adhesion dynamics of cells is of great value to biological systems and adhesion-based biomedical applications. Although adhesion of a single cell or capsule has been widely studied, physical insights into the adhesion dynamics of aggregates containing two or more cells remain elusive. In this paper, we numerically investigate the dynamic adhesion of a deformable cell pair to a flat substrate under shear flow. Specifically, the immersed boundary-lattice Boltzmann method is utilized as the flow solver, and the stochastic receptor-ligand kinetics model is implemented to recover cell-substrate and cell-cell adhesive interactions. Special attention is paid to the roles of the cell deformability and adhesion strengths in cellular motion. Four distinct adhesion states, namely, rolling, tumbling, firm adhesion, and detachment, are identified and presented in phase diagrams as a function of the adhesion strengths for cell pairs with different deformabilities. The simulation results suggest that both the cell-cell and cell-substrate adhesion strengths act as the resistance to the rolling motion, and dominate the transition among various adhesion states. The cell deformability not only enhances the resistance effect, but also contributes to detachment or fast tumbling of the cell pair. These findings enrich the understanding of adhesion dynamics of cell aggregates, which could shed light on complex adhesion processes and provide instructions in developing adhesion-based applications.

State diagram for wall adhesion of red blood cells in shear flow: from crawling to flipping

Red blood cells in shear flow show a variety of different shapes due to the complex interplay between hydrodynamics and membrane elasticity. Malaria-infected red blood cells become generally adhesive and less deformable. Adhesion to a substrate leads to a reduction in shape variability and to a flipping motion of the non-spherical shapes during the mid-stage of infection. Here, we present a complete state diagram for wall adhesion of red blood cells in shear flow obtained by simulations, using a particle-based mesoscale hydrodynamics approach, multiparticle collision dynamics. We find that cell flipping at a substrate is replaced by crawling beyond a critical shear rate, which increases with both membrane stiffness and viscosity contrast between the cytosol and suspending medium. This change in cell dynamics resembles the transition between tumbling and tank-treading for red blood cells in free shear flow. In the context of malaria infections, the flipping-crawling transition would strongly increase the adhesive interactions with the vascular endothelium, but might be suppressed by the combined effect of increased elasticity and viscosity contrast.

Coarse-Grain Modeling of Shear-Induced Binding between von Willebrand Factor and Collagen

Von Willebrand factor (VWF) is a large multimeric protein that aids in blood clotting. Near injury sites, hydrodynamic force from increased blood flow elongates VWF, exposing binding sites for platelets and collagen. To investigate VWF binding to collagen that is exposed on injured arterial surfaces, Brownian dynamics simulations are performed with a coarse-grain molecular model. Accounting for hydrodynamic interactions in the presence of a stationary surface, shear flow conditions are modeled. Binding between beads in coarse-grain VWF and collagen sites on the surface is described via reversible ligand-receptor-type bond formation, which is governed via Bell model kinetics. For conditions in which binding is energetically favored, the model predicts a high probability for binding at low shear conditions; this is counter to experimental observations but in agreement with what prior modeling studies have revealed. To address this discrepancy, an additional binding criterion that depends on the conformation of a submonomer feature in the model local to a given VWF binding site is implemented. The modified model predicts shear-induced binding, in very good agreement with experimental observations; this is true even for conditions in which binding is significantly favored energetically. Biological implications of the model modification are discussed in terms of mechanisms of VWF activity.

The sickle cell trait affects contact dynamics and endothelial cell activation in Plasmodium falciparum-infected erythrocytes

Sickle cell trait, a common hereditary blood disorder, protects carriers from severe disease in infections with the human malaria parasite Plasmodium falciparum. Protection is associated with a reduced capacity of parasitized erythrocytes to cytoadhere to the microvascular endothelium and cause vaso-occlusive events. However, the underpinning cellular and biomechanical processes are only partly understood and the impact on endothelial cell activation is unclear. Here, we show, by combining quantitative flow chamber experiments with multiscale computer simulations of deformable cells in hydrodynamic flow, that parasitized erythrocytes containing the sickle cell haemoglobin displayed altered adhesion dynamics, resulting in restricted contact footprints on the endothelium. Main determinants were cell shape, knob density and membrane bending. As a consequence, the extent of endothelial cell activation was decreased. Our findings provide a quantitative understanding of how the sickle cell trait affects the dynamic cytoadhesion behavior of parasitized erythrocytes and, in turn, endothelial cell activation.

Adhesion-based sorting of blood cells: an adhesive dynamics simulation study

Blood cells can be sorted in microfluidic devices not only based on their sizes and deformability, but also based on their adhesive properties. In particular, white blood cells have been shown to be sorted out by using adhesive micropatterns made from stripes that are tilted in regard to the direction of shear flow. Here we use adhesive dynamics simulations for round cells to quantitatively investigate this effect and to predict the optimal tilt angle. We then apply our method to predict optimal sorting conditions for malaria-infected red blood cells, which like white blood cells also adhere to and roll on adhesive substrates.

Mechanical properties of P-selectin PSGL-1 bonds

The accurate determination of the mechanical properties of P-selectin and PSGL-1 is crucial for design and optimization of applications utilizing such bonds, e.g. biosensors and targeted drug delivery systems, as adhesion and mechanical interactions play a critical role in several key functions of biological cells. In current work, the spring constant and rupture force of a single P-selectin PSGL-1 ligand receptor bond and the Young's modulus of a layer made of these ligand receptors are reported. The work-of-adhesion of the P-selectin PSGL-1 interface is also characterized. In the reported experiments, PSGL-1 coated particles are deposited on a P-selectin coated substrate and their transient nanometer scale out-of-plane displacements are acquired employing a laser Doppler vibrometer as they are excited by an ultrasonic field. From the spectral response of a single particle, the resonance frequencies of its vibrational motion are identified, and with help of a particle adhesion model, the average rupture force and stiffness of a single P-selectin PSGL-1 ligand receptor are determined as F^rupt = 171 ± 56 pN and k^b = 0.56 ± 0.04 mN/m, respectively. Furthermore, the Young's modulus and work-of-adhesion of a layer of P-selectin PSGL-1 ligand receptors are extracted as E = 28.74 ± 3.96 MPa and W^A = 70.0 ± 8.0 mJ/m², respectively. Unlike Atomic Force Microscopy (AFM) and other probe-based techniques, the reported approach eliminates the need for direct contact with the sample, which could compromise the accuracy of the results by imposing unspecified additional contact interactions. Further, the current technique can be employed for measurements under various fluid flow conditions.

On Stability of Specific Adhesion of Particles to Membranes in Simple Shear Flow

Adhesion of carrier particles to the luminal surface of endothelium under hemodynamic flow conditions is critical for successful vascular drug delivery. Endothelial cells line the inner surface of blood vessels. The effect of mechanical behavior of this compliant surface on the adhesion of blood-borne particles is unknown. In this contribution, we use a phase-plane method, first developed by Hammer and Lauffenburger [Biophysical Journal, 52, 475 (1987)], to analyze the stability of specific adhesion of a spherical particle to a compliant interface layer. We construct a phase diagram that predicts the state of particle adhesion, subjected to an incident simple shear flow, in terms of interfacial elasticity, shear rate, binding affinity of cell adhesive molecules, and their surface density. The main conclusion is that the local deformation of the flexible interface inhibits the stable adhesion of the particle. In comparison with adhesion to a rigid substrate, a greater ligand density is required to establish a stable adhesion between a particle and a compliant interface. The results can be used for the rational design of particles in vascular drug delivery.

Analysis of adhesion kinetics of cancer cells on inflamed endothelium using a microfluidic platform

Metastasis is the ultimate cause of death among the vast majority of cancer patients. This process is comprised of multiple steps, including the migration of circulating cancer cells across microvasculature. This trans-endothelial migration involves the adhesion and eventual penetration of cancer cells to the vasculature of the target organ. Many of these mechanisms remain poorly understood due to poor control of pathophysiological conditions in tumor models. In this work, a microfluidic device was developed to support the culture and observation of engineered microvasculature with systematic control of the environmental characteristics. This device was then used to study the adhesion of circulating cancer cells to an endothelium under varying conditions to delineate the effects of hemodynamics and inflammations. The resulting understanding will help to establish a quantitative and biophysical mechanism of interactions between cancer cells and endothelium.

Mechanism in External Field-mediated Trapping of Bacteria Sensitive to Nanoscale Surface Chemical Structure

Molecular imprinting technique enables the selective binding of nanoscale target molecules to a polymer film, within which their chemical structure is transcribed. Here, we report the successful production of mixed bacterial imprinted film (BIF) from several food poisoning bacteria by the simultaneous imprinting of their nanoscale surface chemical structures (SCS), and provide highly selective trapping of original micron-scale bacteria used in the production process of mixed BIF even for multiple kinds of bacteria in real samples. Particularly, we reveal the rapid specific identification of E. coli group serotypes (O157:H7 and O26:H11) using an alternating electric field and a quartz crystal microbalance. Furthermore, we have performed the detailed physicochemical analysis of the specific binding of SCS and molecular recognition sites (MRS) based on the dynamic Monte Carlo method under taking into account the electromagnetic interaction. The dielectrophoretic selective trapping greatly depends on change in SCS of bacteria damaged by thermal treatment, ultraviolet irradiation, or antibiotic drugs, which can be well explained by the simulation results. Our results open the avenue for an innovative means of specific and rapid detection of unknown bacteria for food safety and medicine from a nanoscale viewpoint.

Effects of membrane deformability and bond formation/dissociation rates on adhesion dynamics of a spherical capsule in shear flow

Cellular adhesion plays a critical role in biological systems and biomedical applications. Cell deformation and biophysical properties of adhesion molecules are of significance for the adhesion behavior. In the present work, dynamic adhesion of a deformable capsule to a planar substrate, in a linear shear flow, is numerically simulated to investigate the combined influence of membrane deformability (quantified by the capillary number) and bond formation/dissociation rates on the adhesion behavior. The computational model is based on the immersed boundary-lattice Boltzmann method for the capsule-fluid interaction and a probabilistic adhesion model for the capsule-substrate interaction. Three distinct adhesion states, detachment, rolling adhesion and firm adhesion, are identified and presented in a state diagram as a function of capillary number and bond dissociation rate. The impact of bond formation rate on the state diagram is further investigated. Results show that the critical bond dissociation rate for the transition of rolling or firm adhesion to detachment is strongly related to the capsule deformability. At the rolling-adhesion state, smaller off rates are needed for larger capillary number to increase the rolling velocity and detach the capsule. In contrast, the critical off rate for firm-to-detach transition slightly increases with the capillary number. With smaller on rate, the effect of capsule deformability on the critical off rates is more pronounced and capsules with moderate deformability are prone to detach by the shear flow. Further increasing of on rate leads to large expansion of both rolling-adhesion and firm-adhesion regions. Even capsules with relatively large deformability can maintain stable rolling adhesion at certain off rate.

Tumor cell capture patterns around aptamer-immobilized microposts in microfluidic devices

Circulating tumor cells (CTCs) have shown potential for cancer diagnosis and prognosis. Affinity-based CTC isolation methods have been proved to be efficient for CTC detection in clinical blood samples. One of the popular choices for affinity-based CTC isolation is to immobilize capture agents onto an array of microposts in microchannels, providing high CTC capture efficiency due to enhanced interactions between tumor cells and capture agents on the microposts. However, how the cells interact with microposts under different flow conditions and what kind of capture pattern results from the interactions have not been fully investigated; a full understanding of these interactions will help to design devices and choose experimental conditions for higher CTC capture effeciency. We report our study on their interaction and cell distribution patterns around microposts under different flow conditions. Human acute lymphoblastic leukemia cells (CCRF-CEM) were used as target cancer cells in this study, while the Sgc8 aptamer that has specific binding with CCRF-CEM cells was employed as a capture agent. We investigated the effects of flow rates and micropost shapes on the cell capture efficiency and capture patterns on microposts. While a higher flow rate decreased cell capture efficiency, we found that the capture pattern around microposts also changed, with much more cells captured in the front half of a micropost than at the back half. We also found the ratio of cells captured on microposts to the cells captured by both microposts and channel walls increased as a function of the flow rate. We compared circular microposts with an elliptical shape and found that the geometry affected the capture distribution around microposts. In addition, we have developed a theoretical model to simulate the interactions between tumor cells and micropost surfaces, and the simulation results are in agreement with our experimental observation.

Rolling Adhesion of Schizont Stage Malaria-Infected Red Blood Cells in Shear Flow

To avoid clearance by the spleen, red blood cells infected with the human malaria parasite Plasmodium falciparum (iRBCs) adhere to the vascular endothelium through adhesive protrusions called "knobs" that the parasite induces on the surface of the host cell. However, the detailed relation between the developing knob structure and the resulting movement in shear flow is not known. Using flow chamber experiments on endothelial monolayers and tracking of the parasite inside the infected host cell, we find that trophozoites (intermediate-stage iRBCs) tend to flip due to their biconcave shape, whereas schizonts (late-stage iRBCs) tend to roll due to their almost spherical shape. We then use adhesive dynamics simulations for spherical cells to predict the effects of knob density and receptor multiplicity per knob on rolling adhesion of schizonts. We find that rolling adhesion requires a homogeneous coverage of the cell surface by knobs and that rolling adhesion becomes more stable and slower for higher knob density. Our experimental data suggest that schizonts are at the border between transient and stable rolling adhesion. They also allow us to establish an estimate for the molecular parameters for schizont adhesion to the vascular endothelium and to predict bond dynamics in the contact region.

Mapping cell surface adhesion by rotation tracking and adhesion footprinting

Rolling adhesion, in which cells passively roll along surfaces under shear flow, is a critical process involved in inflammatory responses and cancer metastasis. Surface adhesion properties regulated by adhesion receptors and membrane tethers are critical in understanding cell rolling behavior. Locally, adhesion molecules are distributed at the tips of membrane tethers. However, how functional adhesion properties are globally distributed on the individual cell’s surface is unknown. Here, we developed a label-free technique to determine the spatial distribution of adhesive properties on rolling cell surfaces. Using dark-field imaging and particle tracking, we extract the rotational motion of individual rolling cells. The rotational information allows us to construct an adhesion map along the contact circumference of a single cell. To complement this approach, we also developed a fluorescent adhesion footprint assay to record the molecular adhesion events from cell rolling. Applying the combination of the two methods on human promyelocytic leukemia cells, our results surprisingly reveal that adhesion is non-uniformly distributed in patches on the cell surfaces. Our label-free adhesion mapping methods are applicable to the variety of cell types that undergo rolling adhesion and provide a quantitative picture of cell surface adhesion at the functional and molecular level.

Mobility and shape adaptation of neutrophil in the microchannel flow

This paper presents motion of neutrophil in a confined environment. Many experimental and theoretical studies were performed to show mechanics and basic principles of the white blood cell motion. However, they were mostly performed on flat plates without boundaries. More realistic model of flow in the capillaries based on confinement, curvature and adequate dimensions is applied in our experiments. These conditions lead to cell motion with deformability and three-dimensional character of that movement. Neutrophils are important cells for human immune system. Their motion and attachment often influence several diseases and immune response. Hence, studies focus on that particular cell type. We have shown that deformability of the cell influences its velocity. Cells actively participate in the flow using the shear gradient to advance control motion. The observed neutrophil velocity was from 1 up to 100μm/s.

State diagram for adhesion dynamics of deformable capsules under shear flow

Due to the significance of understanding the underlying mechanisms of cell adhesion in biological processes and cell capture in biomedical applications, we numerically investigate the adhesion dynamics of deformable capsules under shear flow by using a three-dimensional computational fluid dynamic model. This model is based on the coupling of the front tracking-finite element method for elastic mechanics of the capsule membrane and the adhesion kinetics simulation for adhesive interactions between capsules and functionalized surfaces. Using this model, three distinct adhesion dynamic states are predicted, such as detachment, rolling and firm-adhesion. Specifically, the effects of capsule deformability quantified by the capillary number on the transitions of these three dynamic states are investigated by developing an adhesion dynamic state diagram for the first time. At low capillary numbers (e.g. Ca < 0.0075), whole-capsule deformation confers the capsule a flattened bottom in contact with the functionalized surface, which hence promotes the rolling-to-firm-adhesion transition. It is consistent with the observations from previous studies that cell deformation promotes the adhesion of cells lying in the rolling regime. However, it is surprising to find that, at relatively high capillary numbers (e.g. 0.0075 < Ca < 0.0175), the effect of capsule deformability on its adhesion dynamics is far more complex than just promoting adhesion. High deformability of capsules makes their bottom take a concave shape with no adhesion bond formation in the middle. The appearance of this specific capsule shape inhibits the transitions of both rolling-to-firm-adhesion and detachment-to-rolling, and it means that capsule deformation no longer promotes the capsule adhesion. Besides, it is interesting to note that, when the capillary number exceeds a critical value (e.g. Ca = 0.0175), the rolling state no longer appears, since capsules exhibit large deviation from the spherical shape.

Force and torque on spherical particles in micro-channel flows using computational fluid dynamics

To delineate the influence of hemodynamic force on cell adhesion processes, model in vitro fluidic assays that mimic physiological conditions are commonly employed. Herein, we offer a framework for solution of the three-dimensional Navier-Stokes equations using computational fluid dynamics (CFD) to estimate the forces resulting from fluid flow near a plane acting on a sphere that is either stationary or in free flow, and we compare these results to a widely used theoretical model that assumes Stokes flow with a constant shear rate. We find that while the full three-dimensional solutions using a parabolic velocity profile in CFD simulations yield similar translational velocities to those predicted by the theoretical method, the CFD approach results in approximately 50% larger rotational velocities over the wall shear stress range of 0.1-5.0 dynes cm(-2). This leads to an approximately 25% difference in force and torque calculations between the two methods. When compared with experimental measurements of translational and rotational velocities of microspheres or cells perfused in microfluidic channels, the CFD simulations yield significantly less error. We propose that CFD modelling can provide better estimations of hemodynamic force levels acting on perfused microspheres and cells in flow fields through microfluidic devices used for cell adhesion dynamics analysis.

Circulating Tumor Cell Isolation and Analysis

Isolation and analysis of cancer cells from body fluids have significant implications in diagnosis and therapeutic treatment of cancers. Circulating tumor cells (CTCs) are cancer cells circulating in the peripheral blood or spreading iatrogenically into blood vessels, which is an early step in the cascade of events leading to cancer metastasis. Therefore, CTCs can be used for diagnosing for therapeutic treatment, prognosing a given anticancer intervention, and estimating the risk of metastatic relapse. However, isolation of CTCs is a significant technological challenge due to their rarity and low recovery rate using traditional purification techniques. Recently microfluidic devices represent a promising platform for isolating cancer cells with high efficiency in processing complex cellular fluids, with simplicity, sensitivity, and throughput. This review summarizes recent methods of CTC isolation and analysis, as well as their applications in clinical studies.

Modeling cytoadhesion of Plasmodium falciparum-infected erythrocytes and leukocytes-common principles and distinctive features

Cytoadhesion of Plasmodium falciparum‐infected erythrocytes to the microvascular endothelial lining shares striking similarities to cytoadhesion of leukocytes. In both cases, adhesins are presented in structures that raise them above the cell surface. Another similarity is the enhancement of adhesion under physical force (catch bonding). Here, we review recent advances in our understanding of the molecular and biophysical mechanisms underlying cytoadherence in both cellular systems. We describe how imaging, flow chamber experiments, single‐molecule measurements, and computational modeling have been used to decipher the relevant processes. We conclude that although the parasite seems to induce processes that resemble the cytoadherence of leukocytes, the mechanics of erythrocytes is such that the resulting behavior in shear flow is fundamentally different.

Shear-enhanced adsorption of a homopolymeric globule mediated by surface catch bonds

The adsorption of a single collapsed homopolymer onto a planar smooth surface in shear flow is investigated by means of Brownian hydrodynamics simulation. While cohesive intra-polymer forces are modeled by Lennard-Jones potentials, surface-monomer interactions are described by stochastic bonds whose two-state kinetics is characterized by three parameters: bond formation rate, bond dissociation rate and an effective catch bond parameter that describes how the force acting on a surface-monomer bond influences the dissociation rate. We construct adsorption state diagrams as a function of shear rate and all three surface-monomer bond parameters. We find shear-induced adsorption in a small range of parameters for low dissociation and association rates and only when the surface-monomer bond is near the transition between slip and catch bond behavior. By mapping on a simple surface-monomer interaction model with conservative pair potentials we try to estimate the conservative potential parameters necessary to observe shear-induced surface adsorption phenomena.

Significance of thermal fluctuations and hydrodynamic interactions in receptor-ligand-mediated adhesive dynamics of a spherical particle in wall-bound shear flow

The dynamics of adhesion of a spherical microparticle to a ligand-coated wall, in shear flow, is studied using a Langevin equation that accounts for thermal fluctuations, hydrodynamic interactions, and adhesive interactions. Contrary to the conventional assumption that thermal fluctuations play a negligible role at high Péclet numbers, we find that for particles with low surface densities of receptors, rotational diffusion caused by fluctuations about the flow and gradient directions aids in bond formation, leading to significantly greater adhesion on average, compared to simulations where thermal fluctuations are completely ignored. The role of wall hydrodynamic interactions on the steady-state motion of a particle, when the particle is close to the wall, has also been explored. At high Péclet numbers, the shear induced force that arises due to the stresslet part of the Stokes dipole plays a dominant role, reducing the particle velocity significantly and affecting the states of motion of the particle. The coupling between the translational and rotational degrees of freedom of the particle, brought about by the presence of hydrodynamic interactions, is found to have no influence on the binding dynamics. On the other hand, the drag coefficient, which depends on the distance of the particle from the wall, plays a crucial role at low rates of bond formation. A significant difference in the effect of both the shear force and the position-dependent drag force on the states of motion of the particle is observed when the Péclet number is small.

Shear-induced dynamics of polymeric globules at adsorbing homogeneous and inhomogeneous surfaces

The dynamics and adsorption behavior of a single collapsed homopolymer on a surface in shear flow is investigated by means of Brownian hydrodynamics simulations. We study different homogeneous and inhomogeneous surface models and determine dynamic state diagrams as a function of the cohesive strength, the adhesive strength, and the shear rate. We find distinct dynamical adsorbed states that are classified into rolling and slipping states, globular and coil-like states, as well as isotropic and prolate states. We identify two different cyclic processes based on trajectories of the polymer stretching and the polymer separation from the surface. For adsorption on an inhomogeneous surface consisting of discrete binding sites, we observe stick-roll motion for highly corrugated surface potentials. Although the resulting high surface friction leads to low drift velocities and reduced hydrodynamic lift forces on such inhomogeneous surfaces, a shear-induced adsorption is not found in the presence of full hydrodynamic interactions. A hydrodynamically stagnant surface model is introduced for which shear-induced adsorption is observed in the absence of hydrodynamic interactions.

Isolation of viable cancer cells in antibody-functionalized microfluidic devices

Microfluidic devices functionalized with EpCAM antibodies were utilized for the capture of target cancer cells representing circulating tumor cells (CTCs). The fraction of cancer cells captured from homogeneous suspensions is mainly a function of flow shear rate, and can be described by an exponential function. A characteristic shear rate emerges as the most dominant parameter affecting the cell attachment ratio. Utilizing this characteristic shear rate as a scaling factor, all attachment ratio results for various combinations of receptor and ligand densities collapsed onto a single curve described by the empirical formula. The characteristic shear rate increases with both cell-receptor and surface-ligand densities, and empirical formulae featuring a product of two independent cumulative distributions described well these relationships. The minimum detection limit in isolation of target cancer cells from binary mixtures was experimentally explored utilizing microchannel arrays that allow high-throughput processing of suspensions about 0.5 ml in volume, which are clinically relevant, within a short time. Under a two-step attachment/detachment flow rate, both high sensitivity (almost 1.0) and high specificity (about 0.985) can be achieved in isolating target cancer cells from binary mixtures even for the lowest target/non-target cell concentration ratio of 1:100 000; this is a realistic ratio between CTCs and white blood cells in blood of cancer patients. Detection of CTCs from blood samples was also demonstrated using whole blood from healthy donors spiked with cancer cells. Finally, the viability of target cancer cells released after capture was confirmed by observing continuous cell growth in culture.

Multiscale modeling of blood flow: from single cells to blood rheology

Mesoscale simulations of blood flow, where the red blood cells are described as deformable closed shells with a membrane characterized by bending rigidity and stretching elasticity, have made much progress in recent years to predict the flow behavior of blood cells and other components in various flows. To numerically investigate blood flow and blood-related processes in complex geometries, a highly efficient simulation technique for the plasma and solutes is essential. In this review, we focus on the behavior of single and several cells in shear and microcapillary flows, the shear-thinning behavior of blood and its relation to the blood cell structure and interactions, margination of white blood cells and platelets, and modeling hematologic diseases and disorders. Comparisons of the simulation predictions with existing experimental results are made whenever possible, and generally very satisfactory agreement is obtained.

Attomolar protein detection using a magnetic bead surface coverage assay

We demonstrate a microfluidic method for ultra-sensitive protein detection in serum. First, 'large' (2.8 μm) antibody-functionalized magnetic beads specifically capture antigen from a serum matrix under active microfluidic mixing. Subsequently, the large beads loaded with the antigens are gently exposed to a surface pattern of fixed 'small' (1.0 μm) antibody-coated magnetic beads. During the exposure, attractive magnetic bead dipole-dipole interactions improve the contact between the two bead types and help the antigen-antibody immunocomplex formation, while non-specific large bead adsorption is limited by exploiting viscous drag forces in the microfluidic channel on the small-bead pattern. This efficient antigen-antibody recognition and binding mechanism mimics a biological process of selective recognition of tissue molecules, like is the case when leukocytes roll and slow down on blood vessel walls by selectin-mediated adhesion. After exposure of the large beads to the pattern of small beads, the antigen concentration is detected by simply counting the number of surface pattern-bound large magnetic beads. The new technique allows detection of proteins down to the sub-zeptomole range. In particular, we demonstrate detection of only 200 molecules of Tumor Necrosis Factor-α (TNF-α) in a serum sample volume of 5 μL, corresponding to a concentration of 60 attomolar or 1 fg mL(-1).

Glycomechanics of the metastatic cascade: tumor cell-endothelial cell interactions in the circulation

Hydrodynamic shear force plays an important role in the leukocyte adhesion cascade that involves the tethering and rolling of cells along the endothelial layer, their firm adhesion or arrest, and their extravasation or escape from the circulatory system by inducing passive deformation, or cell flattening, and microvilli stretching, as well as regulating the expression, distribution, and conformation of adhesion molecules on leukocytes and the endothelial layer. Similarly, the dissemination of circulating tumor cells (CTCs) from the primary tumor sites is believed to involve tethering, rolling, and firm adhesion steps before their eventual extravasation which leads to secondary tumor sites (metastasis). Of particular importance to both the leukocyte adhesion cascade and the extravasation of CTCs, glycoproteins are involved in all three steps (capture, rolling, and firm adhesion) and consist of a variety of important selectin ligands. This review article provides an overview of glycoprotein glycosylation associated with the abnormal glycan expression on cancer cell surfaces, where well-established and novel selectin ligands that are cancer related are discussed. An overview of computational approaches on the effects of fluid mechanical force on glycoprotein mediated cancer cell rolling and adhesion is presented with a highlight of recent flow-based and selectin-mediated cell capturing/enriching devices. Finally, as an important branch of the glycoprotein family, mucins, specifically MUC1, are discussed in the context of their aberrant expression on cancer cells and their role as cancer cell adhesion molecules. Since metastasis relies heavily on glycoprotein interactions in the bloodstream where the fluid shear stress highly regulates cell adhesion forces, it is important to study and understand the glycomechanics of all relevant glycoproteins (well-established and novel) as they relate to the metastatic cascade.

Cell receptor and surface ligand density effects on dynamic states of adhering circulating tumor cells

Dynamic states of cancer cells moving under shear flow in an antibody-functionalized microchannel are investigated experimentally and theoretically. The cell motion is analyzed with the aid of a simplified physical model featuring a receptor-coated rigid sphere moving above a solid surface with immobilized ligands. The motion of the sphere is described by the Langevin equation accounting for the hydrodynamic loadings, gravitational force, receptor-ligand bindings, and thermal fluctuations; the receptor-ligand bonds are modeled as linear springs. Depending on the applied shear flow rate, three dynamic states of cell motion have been identified: (i) free motion, (ii) rolling adhesion, and (iii) firm adhesion. Of particular interest is the fraction of captured circulating tumor cells, defined as the capture ratio, via specific receptor-ligand bonds. The cell capture ratio decreases with increasing shear flow rate with a characteristic rate. Based on both experimental and theoretical results, the characteristic flow rate increases monotonically with increasing either cell-receptor or surface-ligand density within certain ranges. Utilizing it as a scaling parameter, flow-rate dependent capture ratios for various cell-surface combinations collapse onto a single curve described by an exponential formula.

Effect of cell and microvillus mechanics on the transmission of applied loads to single bonds in dynamic force spectroscopy

Receptor-ligand interactions that mediate cellular adhesion are often subjected to forces that regulate their detachment via modulating off-rates. Although the dynamics of detachment is primarily controlled by the physical chemistry of adhesion molecules, cellular features such as cell deformability and microvillus viscoelasticity have been shown to affect the rolling velocity of leukocytes in vitro through experiments and simulation. In this work, we demonstrate via various micromechanical models of two cells adhered by a single (intramolecular) bond that cell deformability and microvillus viscoelasticity modulate transmission of an applied external load to an intramolecular bond, and thus the dynamics of detachment. Specifically, it is demonstrated that the intermolecular bond force is not equivalent to the instantaneous applied force and that the instantaneous bond force decreases with cellular and microvillus compliance. As cellular compliance increases, not only does the time lag between the applied load and the bond force increase, an initial response time is observed during which cell deformation is observed without transfer of force to the bond. It is further demonstrated that following tether formation the instantaneous intramoleular bond force increases linearly at a rate dependent on microvillus viscosity. Monte Carlo simulations with fixed kinetic parameters predict that both cell and microvillus compliance increase the average rupture time, although the average rupture force based on bond length remains nearly unchanged.

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.

Examining the lateral displacement of HL60 cells rolling on asymmetric P-selectin patterns

The lateral displacement of cells orthogonal to a flow stream by rolling on asymmetrical receptor patterns presents a new opportunity for the label-free separation and analysis of cells. Understanding the nature of cell rolling trajectories on such substrates is necessary to the engineering of substrates and the design of devices for cell separation and analysis. Here, we investigate the statistical nature of cell rolling and the effect of pattern geometry and flow shear stress on cell rolling trajectories using micrometer-scale patterns of biomolecular receptors with well-defined edges. Leukemic myeloid HL60 cells expressing the PSGL-1 ligand were allowed to flow across a field of patterned lines fabricated using microcontact printing and functionalized with the P-selectin receptor, leveraging both the specific adhesion of this ligand-receptor pair and the asymmetry of the receptor pattern inclination angle with respect to the fluid shear flow direction (α = 5, 10, 15, and 20°). The effects of the fluid shear stress magnitude (τ = 0.5, 1, 1.5, and 2.0 dyn/cm(2)), α, and P-selectin incubation concentration were quantified in terms of the rolling velocity and edge tracking length. Rolling cells tracked along the inclined edges of the patterned lines before detaching and reattaching on another line. The detachment of rolling cells after tracking along the edge was consistent with a Poisson process of history-independent interactions. Increasing the edge inclination angle decreased the edge tracking length in an exponential manner, contrary to the shear stress magnitude and P-selectin incubation concentration, which did not have a significant effect. On the basis of these experimental data, we constructed an empirical model that predicted the occurrence of the maximum lateral displacement at an edge angle of 7.5°. We also used these findings to construct a Monte Carlo simulation for the prediction of rolling trajectories of HL60 cells on P-selectin-patterned substrates with a specified edge inclination angle. The prediction of lateral displacement in the range of 200 μm within a 1 cm separation length supports the feasibility of label-free cell separation via asymmetric receptor patterns in microfluidic devices.

Models of dynamic extraction of lipid tethers from cell membranes

When a ligand that is bound to an integral membrane receptor is pulled, the membrane and the underlying cytoskeleton can deform before either the membrane delaminates from the cytoskeleton or the ligand detaches from the receptor. If the membrane delaminates from the cytoskeleton, it may be further extruded and form a membrane tether. We develop a phenomenological model for this process by assuming that deformations obey Hooke's law up to a critical force at which the cell membrane locally detaches from the cytoskeleton and a membrane tether forms. We compute the probability of tether formation and show that tethers can be extruded only within an intermediate range of force loading rates and pulling velocities. The mean tether length that arises at the moment of ligand detachment is computed as are the force loading rates and pulling velocities that yield the longest tethers.

Stochastic simulations of cargo transport by processive molecular motors

We use stochastic computer simulations to study the transport of a spherical cargo particle along a microtubule-like track on a planar substrate by several kinesin-like processive motors. Our newly developed adhesive motor dynamics algorithm combines the numerical integration of a Langevin equation for the motion of a sphere with kinetic rules for the molecular motors. The Langevin part includes diffusive motion, the action of the pulling motors, and hydrodynamic interactions between sphere and wall. The kinetic rules for the motors include binding to and unbinding from the filament as well as active motor steps. We find that the simulated mean transport length increases exponentially with the number of bound motors, in good agreement with earlier results. The number of motors in binding range to the motor track fluctuates in time with a Poissonian distribution, both for springs and cables being used as models for the linker mechanics. Cooperativity in the sense of equal load sharing only occurs for high values for viscosity and attachment time.

Numerical study of the phase separation in binary lipid membrane containing protein inclusions under stationary shear flow

The phase separation of lipids is believed to be responsible for the formation of lipid rafts in biological cell membrane. In the present work, a continuum model and a particle model are constructed to study the phase separation in binary lipid membrane containing inclusions under stationary shear flow. In each model, employing the cell dynamical system (CDS) approach, the kinetic equations of the confusion-advection process are numerically solved. Snapshot figures of the phase morphology are performed to intuitively display such phase evolving process. Considering the effects from both the inclusions and the shear flow, the time growth law of the characteristic domain size is discussed.