Roles of cell and microvillus deformation and receptor-ligand binding kinetics in cell rolling

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.

A Theoretical Analysis of Receptor-Mediated Endocytosis of Nanoparticles in Wall Shear Flow

This study theoretically investigates receptor–ligand-mediated endocytosis of nanoparticles (NPs) in wall shear flow. The endocytosis is modeled as a birth–death process and relationships between coefficients in the model and the wall shear rate have been derived to deal with the effects of the shear flow. Model predictions show that flow-induced alteration in bond formation rates does not affect the endocytosis significantly, and the suppression of hydrodynamic load on endocytosis is eminent only when diameters of NPs are large (around 700[Formula: see text]nm) and the shear rate is sufficiently high. In the latter case, it is shown that the hydrodynamic load suppresses the initial attachment of NPs to cells more than the following internalization. The model also predicts that shear-promoted expression of certain ligands can lead to observable increase in the number of endocytozed NPs in typical flow-chamber experiments, and the promotion can also cause selective endocytosis of NPs by cells at high shear rate regions if the ligand surface density on NPs or the original expression of receptors on cells in the absence of flow is low.

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.

Isolating the influences of fluid dynamics on selectin-mediated particle rolling at venular junctional regions

The objective of this study was to isolate the impact of hydrodynamics on selectin-mediated cell rolling in branched microvessels. Significant advancements have been made in furthering the understanding of complex interactions between biochemical and physical factors in the inflammatory cascade in simplified planar geometries. However, few studies have sought to quantify the effects of branched configurations and to isolate the effects of associated fluid forces. Experimental techniques were developed to perform in vitro adhesion experiments in Y-shaped micro-slides. The micro-slides were coated with P-selectin and microspheres coated with Sialyl-Lewis^x were observed as they rolled in the chambers at different wall shear stresses. Study results revealed that microsphere rolling velocities and rolling flux were lowest in regions closest to the apex of a junctional region and were dependent on both branch angle and wall shear stress. The regions closest to the junctional region were shown to have low bulk flow velocities and shear stresses using computational fluid dynamics (CFD) modeling. Collectively, the study demonstrates that despite the presence of a uniform coating of P-selectin, hydrodynamic factors associated with the chamber geometry yield non-uniform effects on particle behavior. These findings could explain why cells have been observed to preferentially adhere or transmigrate near junctional regions. Future characterization of inflammatory processes in microvascular network configurations is therefore crucial for furthering our fundamental understanding of inflammation.

Computational study of cell adhesion and rolling in flow channel by meshfree method

Tethering and rolling of circulating leukocytes on the surface of endothelium are critical steps during an inflammatory response. A soft solid cell model was proposed to study monocytes tethering and rolling behaviors on substrate surface in shear flow. The interactions between monocytes and micro-channel surface were modeled by a coarse-grained molecular adhesive potential. The computational model was implemented in a Lagrange-type meshfree Galerkin formulation to investigate the monocyte tethering and rolling process with different flow rates. From the simulation results, it was found that the flow rate has profound effects on the rolling velocity, contact area and effective stress of monocytes. As the flow rate increased, the rolling velocity would increase linearly, whereas the contact area and average effective stress in monocyte showed nonlinear increase.

Localized Modeling of Biochemical and Flow Interactions during Cancer Cell Adhesion

This work focuses on one component of a larger research effort to develop a simulation tool to model populations of flowing cells. Specifically, in this study a local model of the biochemical interactions between circulating melanoma tumor cells (TC) and substrate adherent polymorphonuclear neutrophils (PMN) is developed. This model provides realistic three-dimensional distributions of bond formation and attendant attraction and repulsion forces that are consistent with the time dependent Computational Fluid Dynamics (CFD) framework of the full system model which accounts local pressure, shear and repulsion forces. The resulting full dynamics model enables exploration of TC adhesion to adherent PMNs, which is a known participating mechanism in melanoma cell metastasis. The model defines the adhesion molecules present on the TC and PMN cell surfaces, and calculates their interactions as the melanoma cell flows past the PMN. Biochemical rates of reactions between individual molecules are determined based on their local properties. The melanoma cell in the model expresses ICAM-1 molecules on its surface, and the PMN expresses the β-2 integrins LFA-1 and Mac-1. In this work the PMN is fixed to the substrate and is assumed fully rigid and of a prescribed shear-rate dependent shape obtained from micro-PIV experiments. The melanoma cell is transported with full six-degrees-of-freedom dynamics. Adhesion models, which represent the ability of molecules to bond and adhere the cells to each other, and repulsion models, which represent the various physical mechanisms of cellular repulsion, are incorporated with the CFD solver. All models are general enough to allow for future extensions, including arbitrary adhesion molecule types, and the ability to redefine the values of parameters to represent various cell types. The model presented in this study will be part of a clinical tool for development of personalized medical treatment programs.

COMPUTATIONAL DETERMINATION OF THE DETACHMENT TIME OF THE LEUKOCYTE UNDER DIFFERENT KINETIC DISSOCIATION RATE PARAMETERS

Three-dimensional simulation of the leukocyte detachment subjected to blood flow is presented. The initially captured leukocyte is modeled as a sphere adhered to the bottom wall of a cylindrical vessel via receptor/ligand bonds (P-selectin/PSGL-1). Ansys Parametric Design Language is used to create the geometrical model and couple the Navier–Stokes flow solver with structural equations and the Monte Carlo equation to define the stochastic breakage of the bonds. The assumption of equal forces on bonds has been ignored and the force on each bond is obtained from the balance between hydrodynamic forces and cellular viscoelasticity at every time step. In this model, catch-slip behavior of the P-selectin/PSGL-1 is considered by using the two-pathway dissociation model instead of the Bell model to define the rate of dissociation of each bond. Detachment time of the leukocyte is the time elapsed until all the bonds break. The effects of various values of blood inlet velocities, bond stiffness and kinetic properties of the catch bonds on the detachment time of the leukocyte are studied.

Multi-scale biological and physical modelling of the tumour micro-environment

Paced by advances in high performance computing, and algorithms for multi-physics and multi-scale simulation, a number of groups have recently established numerical models of flowing blood systems, where cell-scale interactions are explicitly resolved. To be biologically representative, these models account for some or all of: (1) fluid dynamics of the carrier flow, (2) structural dynamics of the cells and vessel walls, (3) interaction and transport biochemistry, and, (4) methods for scaling to physiologically representative numbers of cells. In this article, our interest is the modelling of the tumour micro-environment. We review the broader area of cell-scale resolving blood flow modelling, while focusing on the particular interactions of tumour cells and white blood cells, known to play an important role in metastasis.

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.

Yielding elastic tethers stabilize robust cell adhesion

Many bacteria and eukaryotic cells express adhesive proteins at the end of tethers that elongate reversibly at constant or near constant force, which we refer to as yielding elasticity. Here we address the function of yielding elastic adhesive tethers with Escherichia coli bacteria as a model for cell adhesion, using a combination of experiments and simulations. The adhesive bond kinetics and tether elasticity was modeled in the simulations with realistic biophysical models that were fit to new and previously published single molecule force spectroscopy data. The simulations were validated by comparison to experiments measuring the adhesive behavior of E. coli in flowing fluid. Analysis of the simulations demonstrated that yielding elasticity is required for the bacteria to remain bound in high and variable flow conditions, because it allows the force to be distributed evenly between multiple bonds. In contrast, strain-hardening and linear elastic tethers concentrate force on the most vulnerable bonds, which leads to failure of the entire adhesive contact. Load distribution is especially important to noncovalent receptor-ligand bonds, because they become exponentially shorter lived at higher force above a critical force, even if they form catch bonds. The advantage of yielding is likely to extend to any blood cells or pathogens adhering in flow, or to any situation where bonds are stretched unequally due to surface roughness, unequal native bond lengths, or conditions that act to unzip the bonds.

Cells adhere to surfaces and each other in the presence of forces that would easily overpower the individual noncovalent receptor-ligand bonds that mediate this adhesion, raising the question as to how these bonds cooperate to withstand such high forces. Here we show that cooperation and robust adhesion depends on the elastic properties of the bonds. A type of nonlinear elasticity referred to as elastic yielding ensures that the total force is distributed equally across the individual bonds regardless of geometry. In contrast, with linear or strain-hardening elasticity, the bonds that are stretched the most are exposed to higher forces, which cause them to fail sequentially. This work explains why elastic yielding is found in structurally and evolutionarily diverse adhesive complexes.

Effect of extracellular pH on selectin adhesion: theory and experiment

Selectins mediate circulatory leukocyte trafficking to sites of inflammation and trauma, and the extracellular microenvironments at these sites often become acidic. In this study, we investigated the influence of slightly acidic pH on the binding dynamics of selectins (P-, L-, and E-selectin) to P-selectin glycoprotein ligand-1 (PSGL-1) via computational modeling (molecular dynamics) and experimental rolling assays under shear in vitro. The P-selectin/PSGL-1 binding is strengthened at acidic pH, as evidenced by the formation of a new hydrogen bond (seen computationally) and the observed decrease in the rolling velocities of model cells. In the case of L-selectin/PSGL-1 binding dynamics, the binding strength and frequency increase at acidic pH, as indicated by the greater cell-rolling flux of neutrophils and slower rolling velocities of L-selectin-coated microspheres, respectively. The cell flux is most likely due to an increased population of L-selectin in the high-affinity conformation as pH decreases, whereas the velocities are due to increased L-selectin/PSGL-1 contacts. In contrast to P- and L-selectin, the E-selectin/PSGL-1 binding does not exhibit significant changes at acidic pH levels, as shown both experimentally and computationally.

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.

Dynamic modeling of cell migration and spreading behaviors on fibronectin coated planar substrates and micropatterned geometries

An integrative cell migration model incorporating focal adhesion (FA) dynamics, cytoskeleton and nucleus remodeling, actin motor activity, and lamellipodia protrusion is developed for predicting cell spreading and migration behaviors. This work is motivated by two experimental works: (1) cell migration on 2-D substrates under various fibronectin concentrations and (2) cell spreading on 2-D micropatterned geometries. These works suggest (1) cell migration speed takes a maximum at a particular ligand density (∼1140 molecules/µm(2)) and (2) that strong traction forces at the corners of the patterns may exist due to combined effects exerted by actin stress fibers (SFs). The integrative model of this paper successfully reproduced these experimental results and indicates the mechanism of cell migration and spreading. In this paper, the mechanical structure of the cell is modeled as having two elastic membranes: an outer cell membrane and an inner nuclear membrane. The two elastic membranes are connected by SFs, which are extended from focal adhesions on the cortical surface to the nuclear membrane. In addition, the model also includes ventral SFs bridging two focal adhesions on the cell surface. The cell deforms and gains traction as transmembrane integrins distributed over the outer cell membrane bond to ligands on the ECM surface, activate SFs, and form focal adhesions. The relationship between the cell migration speed and fibronectin concentration agrees with existing experimental data for Chinese hamster ovary (CHO) cell migrations on fibronectin coated surfaces. In addition, the integrated model is validated by showing persistent high stress concentrations at sharp geometrically patterned edges. This model will be used as a predictive model to assist in design and data processing of upcoming microfluidic cell migration assays.

NUMERICAL SIMULATION OF CELL ADHESION AND DETACHMENT IN MICROFLUIDICS

Inspired by the complex biophysical processes of cell adhesion and detachment under blood flow in vivo, numerous novel microfluidic devices have been developed to manipulate, capture, and separate bio-particles for various applications, such as cell analysis and cell enumeration. However, the underlying physical mechanisms are yet unclear, which has limited the further development of microfluidic devices and point-of-care (POC) systems. Mathematical modeling is an enabling tool to study the physical mechanisms of biological processes for its relative simplicity, low cost, and high efficiency. Recent development in computation technology for multiphase flow simulation enables the theoretical study of the complex flow processes of cell adhesion and detachment in microfluidics. Various mathematical methods (e.g., front tracking method, level set method, volume of fluid (VOF) method, fluid–solid interaction method, and particulate modeling method) have been developed to investigate the effects of cell properties (i.e., cell membrane, cytoplasma, and nucleus), flow conditions, and microchannel structures on cell adhesion and detachment in microfluidic channels. In this paper, with focus on our own simulation results, we review these methods and compare their advantages and disadvantages for cell adhesion/detachment modeling. The mathematical approaches discussed here would allow us to study microfluidics for cell capture and separation, and to develop more effective POC devices for disease diagnostics.

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.

A low-dimensional deformation model for cancer cells in flow

A low-dimensional parametric deformation model of a cancer cell under shear flow is developed. The model is built around an experiment in which MDA-MB-231 adherent cells are subjected to flow with increasing shear. The cell surface deformation is imaged using differential interference contrast microscopy imaging techniques until the cell releases into the flow. We post-process the time sequence of images using an active shape model from which we obtain the principal components of deformation. These principal components are then used to obtain the parameters in an empirical constitutive equation determining the cell deformations as a function of the fluid normal and shear forces imparted. The cell surface is modeled as a 2D Gaussian interface which can be deformed with three active parameters: H (height), σ(x) (x-width), and σ(y) (y-width). Fluid forces are calculated on the cell surface by discretizing the surface with regularized Stokeslets, and the flow is driven by a stochastically fluctuating pressure gradient. The Stokeslet strengths are obtained so that viscous boundary conditions are enforced on the surface of the cell and the surrounding plate. We show that the low-dimensional model is able to capture the principal deformations of the cell reasonably well and argue that active shape models can be exploited further as a useful tool to bridge the gap between experiments, models, and numerical simulations in this biological setting.

Study of local hydrodynamic environment in cell-substrate adhesion using side-view μPIV technology

Tumor cell adhesion to the endothelium under shear flow conditions is a critical step that results in circulation-mediated tumor metastasis. This study presents experimental and computational techniques for studying the local hydrodynamic environment around adherent cells and how local shear conditions affect cell-cell interactions on the endothelium in tumor cell adhesion. To study the local hydrodynamic profile around heterotypic adherent cells, a side-view flow chamber assay coupled with micro particle imaging velocimetry (μPIV) technique was developed, where interactions between leukocytes and tumor cells in the near-endothelial wall region and the local shear flow environment were characterized. Computational fluid dynamics (CFD) simulations were also used to obtain quantitative flow properties around those adherent cells. Results showed that cell dimension and relative cell-cell positions had strong influence on local shear rates. The velocity profile above leukocytes and tumor cells displayed very different patterns. Larger cell deformations led to less disturbance to the flow. Local shear rates above smaller cells were observed to be more affected by relative positions between two cells.

Effect of loading conditions on the dissociation behaviour of catch bond clusters

Under increasing tensile load, the lifetime of a single catch bond counterintuitively increases up to a maximum and then decreases exponentially like a slip bond. So far, the characteristics of single catch bond dissociation have been extensively studied. However, it remains unclear how a cluster of catch bonds behaves under tensile load. We perform computational analysis on the following models to examine the characteristics of clustered catch bonds: (i) clusters of catch bonds with equal load sharing, (ii) clusters of catch bonds with linear load sharing, and (iii) clusters of catch bonds in micropipette-manipulated cell detachment. We focus on the differences between the slip and catch bond clusters, identifying the critical factors for exhibiting the characteristics of catch bond mechanism for the multiple-bond system. Our computation reveals that for a multiple-bond cluster, the catch bond behaviour could only manifest itself under relatively uniform loading conditions and at certain stages of decohesion, explaining the difficulties in observing the catch bond mechanism under real biological conditions.

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.

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.

Biophysics of selectin-ligand interactions in inflammation and cancer

Selectins (L-, E- and P-selectin) are calcium-dependent transmembrane glycoproteins that are expressed on the surface of circulating leukocytes, activated platelets, and inflamed endothelial cells. Selectins bind predominantly to sialofucosylated glycoproteins and glycolipids (E-selectin only) present on the surface of apposing cells, and mediate transient adhesive interactions pertinent to inflammation and cancer metastasis. The rapid turnover of selectin-ligand bonds, due to their fast on- and off-rates along with their remarkably high tensile strengths, enables them to mediate cell tethering and rolling in shear flow. This paper presents the current body of knowledge regarding the role of selectins in inflammation and cancer metastasis, and discusses experimental methodologies and mathematical models used to resolve the biophysics of selectin-mediated cell adhesion. Understanding the biochemistry and biomechanics of selectin-ligand interactions pertinent to inflammatory disorders and cancer metastasis may provide insights for developing promising therapies and/or diagnostic tools to combat these disorders.

Shear-stabilized rolling behavior of E. coli examined with simulations

Escherichia coli exhibit both shear-stabilized rolling and a transition to stationary adhesion while adhering in fluid flow. Understanding the mechanism by which this shear-enhanced adhesion occurs is an important step in understanding bacterial pathogenesis. In this work, simulations are used to investigate the relative contributions of fimbrial deformation and bond transitions to the rolling and stationary adhesion of E. coli. Each E. coli body is surrounded by many long, thin fimbriae terminating in a single FimH receptor that is capable of forming a catch bond with mannose. As simulated cells progress along a mannosylated surface under flow, the fimbriae bend and buckle as they interact with the surface, and FimH-mannose bonds form and break according to a two-state, allosteric catch-bond model. In simulations, shear-stabilized rolling resulted from an increase in the low-affinity bond number due to increased fimbrial deformation with shear. Catch-bond formation did not occur during cell rolling, but instead led to the transition to stationary adhesion. In contrast, in leukocyte and platelet systems, catch bonds appear to be involved in the stabilization of rolling, and integrin activation is required for stationary adhesion.

Linear diode laser bar optical stretchers for cell deformation

To investigate the use of linear diode laser bars to optically stretch cells and measure their mechanical properties, we present numerical simulations using the immersed boundary method (IBM) coupled with classic ray optics. Cells are considered as three-dimensional (3D) spherical elastic capsules immersed in a fluid subjected to both optical and hydrodynamic forces in a periodic domain. We simulate cell deformation induced by both single and dual diode laser bar configurations and show that a single diode laser bar induces significant stretching but also induces cell translation of speed < 10 µm/sec for applied 6.6 mW/µm power in unconfined systems. The dual diode laser bar configuration, however, can be used to both stretch and optically trap cells at a fixed position. The net cell deformation was found to be a function of the total laser power and not the power distribution between single or dual diode laser bar configurations.

Dynamic ray tracing for modeling optical cell manipulation

Current methods for predicting stress distribution on a cell surface due to optical trapping forces are based on a traditional ray optics scheme for fixed geometries. Cells are typically modeled as solid spheres as this facilitates optical force calculation. Under such applied forces however, real and non-rigid cells can deform, so assumptions inherent in traditional ray optics methods begin to break down. In this work, we implement a dynamic ray tracing technique to calculate the stress distribution on a deformable cell induced by optical trapping. Here, cells are modeled as three-dimensional elastic capsules with a discretized surface with associated hydrodynamic forces calculated using the Immersed Boundary Method. We use this approach to simulate the transient deformation of spherical, ellipsoidal and biconcave capsules due to external optical forces induced by a single diode bar optical trap for a range of optical powers.

Cell deformation cytometry using diode-bar optical stretchers

The measurement of cell elastic parameters using optical forces has great potential as a reagent-free method for cell classification, identification of phenotype, and detection of disease; however, the low throughput associated with the sequential isolation and probing of individual cells has significantly limited its utility and application. We demonstrate a single-beam, high-throughput method where optical forces are applied anisotropically to stretch swollen erythrocytes in microfluidic flow. We also present numerical simulations of model spherical elastic cells subjected to optical forces and show that dual, opposing optical traps are not required and that even a single linear trap can induce cell stretching, greatly simplifying experimental implementation. Last, we demonstrate how the elastic modulus of the cell can be determined from experimental measurements of the equilibrium deformation. This new optical approach has the potential to be readily integrated with other cytometric technologies and, with the capability of measuring cell populations, enabling true mechanical-property-based cell cytometry.

Cell deformation cytometry using diode-bar optical stretchers

The measurement of cell elastic parameters using optical forces has great potential as a reagent-free method for cell classification, identification of phenotype, and detection of disease; however, the low throughput associated with the sequential isolation and probing of individual cells has significantly limited its utility and application. We demonstrate a single-beam, high-throughput method where optical forces are applied anisotropically to stretch swollen erythrocytes in microfluidic flow. We also present numerical simulations of model spherical elastic cells subjected to optical forces and show that dual, opposing optical traps are not required and that even a single linear trap can induce cell stretching, greatly simplifying experimental implementation. Last, we demonstrate how the elastic modulus of the cell can be determined from experimental measurements of the equilibrium deformation. This new optical approach has the potential to be readily integrated with other cytometric technologies and, with the capability of measuring cell populations, enabling true mechanical-property-based cell cytometry.

Multi-scale simulation of L-selectin-PSGL-1-dependent homotypic leukocyte binding and rupture

L-selectin-PSGL-1-mediated polymorphonuclear (PMN) leukocyte homotypic interactions potentiate the extent of PMN recruitment to endothelial sites of inflammation. Cell-cell adhesion is a complex phenomenon involving the interplay of bond kinetics and hydrodynamics. As a first step, a 3-D computational model based on the Immersed Boundary Method is developed to simulate adhesion-detachment of two PMN cells in quiescent conditions. Our simulations predict that the total number of bonds formed is dictated by the number of available receptors (PSGL-1) when ligands (L-selectin) are in excess, while the excess amount of ligands influences the rate of bond formation. Increasing equilibrium bond length results in a higher number of receptor-ligand bonds due to an increased intercellular contact area. On-rate constants determine the rate of bond formation, while off-rates control the average number of bonds by modulating bond lifetimes. Application of an external pulling force leads to time-dependent on- and off-rates and causes bond rupture. Moreover, the time required for bond rupture in response to an external force is inversely proportional to the applied load and decreases with increasing off-rate.

Dynamics of Microvillus Extension and Tether Formation in Rolling Leukocytes

P-selectin glycoprotein ligand-1 (PSGL-1) binding to P-selectin mediates leukocyte rolling under conditions of flow. In human neutrophils, a type of leukocyte belonging to the innate immune system, PSGL-1 molecules are located on the neutrophil's surface ruffles, called microvilli. Each newly formed P-selectin-PSGL-1 bond can become load bearing, imposing on its microvillus a pulling force that deforms the microvillus. Depending on the magnitude of the bond force, a microvillus can be extended, or a thin membrane cylinder (a tether) can be formed at the tip of the microvillus. Here we propose a Kelvin-Voigt viscoelastic material as an improved model for microvillus extension. Using a modified version of our Event-Tracking Model of Adhesion (ETMA), we demonstrate how P-selectin-PSGL-1 load-bearing bonds shape microvillus deformation during neutrophil rolling at low shear (wall shear rate of 50 s(-1), P-selectin site density of 150 molecules μm(-2)). We also discuss the impact of microvillus deformability on neutrophil rolling. We find that the average microvillus extension constitutes 65% of the total microvillus-tether complex extension, and that the rolling neutrophil may never fully rest. A quantitative comparison with the corresponding non-deformable microvilli case supports a concept that the ability of the microvillus to deform stabilizes cell rolling.

Adhesive dynamics simulations of the mechanical shedding of L-selectin from the neutrophil surface

Here we accurately recreate the mechanical shedding of L-selectin and its effect on the rolling behavior of neutrophils in vitro using the adhesive dynamics simulation by incorporating the shear-dependent shedding of L-selectin. We have previously shown that constitutively expressed L-selectin is cleaved from the neutrophil surface during rolling on a sialyl Lewis x-coated planar surface at physiological shear rates without the addition of exogenous stimuli. Utilizing a Bell-like model to describe a shedding rate which presumably increases exponentially with force, we were able to reconstruct the characteristics of L-selectin-mediated neutrophil rolling observed in the experiments. First, the rolling velocity was found to increase during rolling due to the mechanical shedding of L-selectin. When most of the L-selectin concentrated on the tips of deformable microvilli was cleaved by force exerted on the L-selectin bonds, the cell detached from the reactive plane to join the free stream as observed in the experiments. In summary, we show through detailed computational modeling that the force-dependent shedding of L-selectin can explain the rolling behavior of neutrophils mediated by L-selectin in vitro.