A computational study of leukocyte adhesion and its effect on flow pattern in microvessels

The role of adhesive receptor patterns on cell transport in complex microvessels

Cell transport is governed by the interaction of fluid dynamic forces and biochemical factors such as adhesion receptor expression and concentration. Although the effect of endothelial receptor density is well understood, it is not clear how the spacing and local spatial distribution of receptors affect cell adhesion in three-dimensional microvessels. To elucidate the effect of vessel shape on cell trajectory and the arrangement of endothelial receptors on cell adhesion, we employed a three-dimensional deformable cell model that incorporates microscale interactions between the cell and the endothelium. Computational cellular adhesion models are systematically altered to assess the influence of receptor spacing. We demonstrate that the patterns of receptors on the vessel walls are a key factor guiding cell movement. In straight microvessels, we show a relationship between cell velocity and the spatial distribution of adhesive endothelial receptors, with larger receptor patches producing lower translational velocities. The joint effect of the complex vessel topology seen in microvessel shapes such as curved and bifurcated vessels when compared to straight tubes is explored with results which showed the spatial distribution of receptors affecting cell trajectory. Our findings here represent demonstration of the previously undescribed relationship between receptor pattern and geometry that guides cellular movement in complex microenvironments.

A computational study of amoeboid motility in 3D: the role of extracellular matrix geometry, cell deformability, and cell-matrix adhesion

Amoeboid cells often migrate using pseudopods, which are membrane protrusions that grow, bifurcate, and retract dynamically, resulting in a net cell displacement. Many cells within the human body, such as immune cells, epithelial cells, and even metastatic cancer cells, can migrate using the amoeboid phenotype. Amoeboid motility is a complex and multiscale process, where cell deformation, biochemistry, and cytosolic and extracellular fluid motions are coupled. Furthermore, the extracellular matrix (ECM) provides a confined, complex, and heterogeneous environment for the cells to navigate through. Amoeboid cells can migrate without significantly remodeling the ECM using weak or no adhesion, instead utilizing their deformability and the microstructure of the ECM to gain enough traction. While a large volume of work exists on cell motility on 2D substrates, amoeboid motility is 3D in nature. Despite recent progress in modeling cellular motility in 3D, there is a lack of systematic evaluations of the role of ECM microstructure, cell deformability, and adhesion on 3D motility. To fill this knowledge gap, here we present a multiscale, multiphysics modeling study of amoeboid motility through 3D-idealized ECM. The model is a coupled fluid‒structure and coarse-grain biochemistry interaction model that accounts for large deformation of cells, pseudopod dynamics, cytoplasmic and extracellular fluid motion, stochastic dynamics of cell-ECM adhesion, and microstructural (pore-scale) geometric details of the ECM. The key finding of the study is that cell deformation and matrix porosity strongly influence amoeboid motility, while weak adhesion and microscale structural details of the ECM have secondary but subtle effects.

The influence of adherent cell morphology on hydrodynamic recruitment of leukocytes

Innate immunity is characterized by the coordinated activity of multiple leukocytes mobilizing at or near the site of tissue injury. Slow rolling and/or adherent leukocytes have been shown to hydrodynamically recruit free-stream leukocytes to a model of inflamed tissue. In this paper, we numerically investigate the hydrodynamic recruitment of free-stream leukocytes due to the presence of a nearby adherent, deformed leukocyte by using a computational model developed from first principles to simulate these types of interactions. For free-stream cells at least one diameter above the surface and subsequently involved in a glancing (out-of-plane) collision with one or more adherent cell, the simulation indicated that the free-stream cell was driven closer to the surface as a function of increasing glancing distance. Further, with increasing deformation of the adherent cell a similar effect was observed beginning at smaller glancing offsets. The influence of binary interactions on the trajectories of free-stream cells that were less than one diameter above the surface was also examined. For fixed glancing distance, increased adherent cell deformation led to enhanced recruiting effectiveness which was quantified by determining the time needed for the free-stream cell to enter the reactive zone; that is, a membrane separation distance such that receptor-ligand binding was possible. This effectiveness was only moderately influenced by variations in shear rate and cell buoyancy. Finally, for large glancing offset the domain of influence of the adherent cell diminished and the trajectory of the free-stream cell was unaffected by the adherent cell, with regard to hydrodynamic recruitment.

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.

Hydrodynamics of a free-flowing leukocyte toward the endothelial wall

Leukocyte recruitment is an essential stage of the inflammatory response and although the molecular mechanisms of this process are relatively well known, the influence of the hydrodynamic effects that govern the inflammatory response are still under study. In this paper we made use of the images and experimental parameters obtained by intravital microscopy in an in vivo animal model of inflammation to track the leukocytes trajectories and measure their velocities and diameters. Using a recent validated mathematical model describing the coupled deformation-flow of an individual leukocyte in a microchannel, numerical simulations of an individual and of two leukocytes under flow were performed. The results showed that velocity plays an important role in the motion, deformation and attraction of the cells during an inflammatory response. In fact, for higher inlet velocities the cell movement along the endothelial wall is accelerated and the attraction forces break faster. These results highlight the role of the mechanical properties of the blood, namely the ones influenced by the velocity field, in the case of inflammation.

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.

Effects of flowing RBCs on adhesion of a circulating tumor cell in microvessels

Adhesion of circulating tumor cells (CTCs) to the microvessel wall largely depends on the blood hydrodynamic conditions, one of which is the blood viscosity. Since blood is a non-Newtonian fluid, whose viscosity increases with hematocrit, in the microvessels at low shear rate. In this study, the effects of hematocrit, vessel size, flow rate and red blood cell (RBC) aggregation on adhesion of a CTC in the microvessels were numerically investigated using dissipative particle dynamics. The membrane of cells was represented by a spring-based network connected by elastic springs to characterize its deformation. RBC aggregation was modeled by a Morse potential function based on depletion-mediated assumption, and the adhesion of the CTC to the vessel wall was achieved by the interactions between receptors and ligands at the CTC and those at the endothelial cells forming the vessel wall. The results demonstrated that in the microvessel of [Formula: see text] diameter, the CTC has an increasing probability of adhesion with the hematocrit due to a growing wall-directed force, resulting in a larger number of receptor-ligand bonds formed on the cell surface. However, with the increase in microvessel size, an enhanced lift force at higher hematocrit detaches the initial adherent CTC quickly. If the microvessel is comparable to the CTC in diameter, CTC adhesion is independent of Hct. In addition, the velocity of CTC is larger than the average blood flow velocity in smaller microvessels and the relative velocity of CTC decreases with the increase in microvessel size. An increased blood flow resistance in the presence of CTC was also found. Moreover, it was found that the large deformation induced by high flow rate and the presence of aggregation promote the adhesion of CTC.

Effects of cellular viscoelasticity in lifetime extraction of single receptor-ligand bonds

Single-molecule force spectroscopy is widely used to determine kinetic parameters of dissociation by analyzing bond rupture data obtained via applying mechanical force to cells, capsules, and beads that are attached to an intermolecular bond. The bond rupture data are obtained in experiments either at a constant force or at a constant loading rate. We explore the effect of cellular viscoelasticity in constant-force experiments. Specifically, we perform Monte Carlo simulations of bond rupture at a given constant force to obtain the bond lifetime as a function of force in the absence and in the presence of bond force modulation due to cellular viscoelasticity, to explore its effect on the bond lifetime.

Effects of cellular viscoelasticity in multiple-bond force spectroscopy

Receptor-ligand bonds are often subjected to forces that regulate their detachment via modulating off-rates. Though 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 have an effect on it as well. In this work, Monte Carlo simulation of the rupture of multiple receptor-ligand bonds between substrate and a polymorphonuclear leukocyte (PMN) cell suspended in a Newtonian fluid is performed. It is demonstrated via various micromechanical models of the PMN cell adhered to the substrate by multiple receptor-ligand bonds that viscous drag caused by relative motion of cell suspended in a Newtonian fluid and cellular viscoelasticity modulate transmission of an applied external load to receptor-ligand bonds. It is demonstrated that due to cellular viscoelasticity the instantaneous intermolecular bond force is lower than the instantaneous applied force. It is also demonstrated that due to cellular viscoelasticity, the mean intermolecular bond rupture forces are lowered while the mean bond lifetime increases.

EFFECT OF FLOW ACCELERATION ON DEFORMATION AND ADHESION DYNAMICS OF CAPTURED CELLS

Cell deformation and adhesion under shear flows play an important role in both cell migration in vivo and capture based microfluidic devices in vitro. Adhesion dynamics of captured cell (e.g., firm adhesion, cell rolling and cell detachment) under steady shear flows have been studied extensively. However, cell adhesion under accelerating flows is common both in vivo and in vitro, and dynamics of cell adhesion under accelerating flows remains unknown. As such, we used a mathematical model based on the front tracking method and investigated the effect of flow acceleration on deformation and adhesion dynamics of captured cells, including cell deformation index, cell shape evolution, the velocities of cell center, contact time and wall shear stress for cell rolling and detachment by using a series of parameter values for leukocyte. The results showed that the cell presented three dynamics states (i.e., firm adhesion, rolling and detachment) with increasing wall shear stress under uniform flows. Wall shear stresses were < 0.56 Pa and > 1.12 Pa for firm adhesion and detachment, respectively. The wall shear stresses were at the range 1.48–1.63 Pa (higher than 1.12 Pa) when cell left the bottom surface of the channel under flow accelerations (a = 0.975–1.625 m/s2). The minimum of deformation index under accelerating flow was smaller than that under uniform flow. In conclusion, the flow acceleration promotes the deformation and adhesion of captured cells. These findings could further the understanding of cell migration in vivo and promote the development of capture based microfluidic devices in vitro.

Clonal variants of Plasmodium falciparum exhibit a narrow range of rolling velocities to host receptor CD36 under dynamic flow conditions

Cytoadhesion of Plasmodium falciparum parasitized red blood cells (pRBCs) has been implicated in the virulence of malaria infection. Cytoadhesive interactions are mediated by the protein family of Plasmodium falciparum erythrocyte membrane protein 1 (PfEMP1). The PfEMP1 family is under strong antibody and binding selection, resulting in extensive sequence and size variation of the extracellular domains. Here, we investigated cytoadhesion of pRBCs to CD36, a common receptor of P. falciparum field isolates, under dynamic flow conditions. Isogeneic parasites, predominantly expressing single PfEMP1 variants, were evaluated for binding to recombinant CD36 under dynamic flow conditions using microfluidic devices. We tested if PfEMP1 size (number of extracellular domains) or sequence variation affected the pRBC-CD36 interaction. Our analysis showed that clonal parasite variants varied ∼5-fold in CD36 rolling velocity despite extensive PfEMP1 sequence polymorphism. In addition, adherent pRBCs exhibited a characteristic hysteresis in rolling velocity at microvascular flow rates, which was accompanied by changes in pRBC shape and may represent important adaptations that favor stable binding.

Effects of microfluidic channel geometry on leukocyte rolling assays

Microfluidic cell adhesion assays have emerged as a means to increase throughput as well as reduce the amount of costly reagents. However as dimensions of the flow chamber are reduced and approach the diameter of a cell (D(c)), theoretical models have predicted that mechanical stress, force, and torque on a cell will be amplified. We fabricated a series of microfluidic devices that have a constant width:height ratio (10:1) but with varying heights. The smallest microfluidic device (200 μm ×20 μm) requires perfusion rates as low as 40 nL/min to generate wall shear stresses of 0.5 dynes/cm(2). When neutrophils were perfused through P-selectin coated chambers at equivalent wall shear stress, rolling velocities decreased by approximately 70 % as the ratio of cell diameter to chamber height (D(c)/H) increased from 0.08 (H = 100 μm) to 0.40 (H = 20 μm). Three-dimensional numerical simulations of neutrophil rolling in channels of different heights showed a similar trend. Complementary studies with PSGL-1 coated microspheres and paraformaldehyde-fixed neutrophils suggested that changes in rolling velocity were related to cell deformability. Using interference reflection microscopy, we observed increases in neutrophil contact area with increasing chamber height (9-33 %) and increasing wall shear stress (28-56 %). Our results suggest that rolling velocity is dependent not only on wall shear stress but also on the shear stress gradient experienced by the rolling cell. These results point to the D(c)/H ratio as an important design parameter of leukocyte microfluidic assays, and should be applicable to rolling assays that involve other cell types such as platelets or cancer cells.

Matrix geometry determines optimal cancer cell migration strategy and modulates response to interventions

The molecular requirements and morphology of migrating cells can vary depending on matrix geometry; therefore, predicting the optimal migration strategy or the effect of experimental perturbation is difficult. We present a model of cell motility that encompasses actin-polymerization-based protrusions, actomyosin contractility, variable actin-plasma membrane linkage leading to membrane blebbing, cell-extracellular-matrix adhesion and varying extracellular matrix geometries. This is used to explore the theoretical requirements for rapid migration in different matrix geometries. Confined matrix geometries cause profound shifts in the relationship of adhesion and contractility to cell velocity; indeed, cell-matrix adhesion is dispensable for migration in discontinuous confined environments. The model is challenged to predict the effect of different combinations of kinase inhibitors and integrin depletion in vivo, and in confined matrices based on in vitro two-dimensional measurements. Intravital imaging is used to verify bleb-driven migration at tumour margins, and the predicted response to single and combinatorial manipulations.

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.

Microfluidics for in vitro biomimetic shear stress-dependent leukocyte adhesion assays

Recruitment of leukocytes from blood to tissues is a multi-step process playing a major role in the activation of inflammatory responses. Tethering and rolling of leukocytes along the vessel wall, followed by arrest and transmigration through the endothelium result from chemoattractant-dependent signals, inducing adhesive and migratory events. Shear forces exerted by the blood flow on leukocytes induce rolling via selectin-mediated interactions with endothelial cells and increase the probability of leukocytes to engage their chemokine receptors, facilitating integrin activation and consequent arrest. Flow-derived shear forces generate mechanical stimuli concurring with biochemical signals in the modulation of leukocyte-endothelial cell interactions. In the last few years, a host of in vitro studies have clarified the biochemical adhesion cascade and the role of shear stress in leukocyte extravasation. The limitation of the static environment in Boyden devices has been overcome both by the use of parallel-plate flow chambers and by custom models mimicking the in vivo conditions, along with widespread microfluidic approaches to in vitro modeling. These devices create an in vitro biomimetic environment where the multi-step transmigration process can be imaged and quantified under mechanical and biochemical controlled conditions, including fluid dynamic settings, channel design, materials and surface coatings. This paper reviews the technological solutions recently proposed to model, observe and quantify leukocyte adhesion behavior under shear flow, with a final survey of high-throughput solutions featuring multiple parallel assays as well as thorough and time-saving statistical interpretation of the experimental results.

Elastic capsule deformation in general irrotational linear flows

Knowledge of the response of elastic capsules to imposed fluid flow is necessary for predicting deformation and motion of biological cells and synthetic capsules in microfluidic devices and in the microcirculation. Capsules have been studied in shear, planar extensional, and axisymmetric extensional flows. Here, the flow gradient matrix of a general irrotational linear flow is characterized by two parameters, its strain rate, defined as the maximum of the principal strain rates, and by a new term, q, the difference in the two lesser principal strain rates, scaled by the maximum principal strain rate; this characterization is valid for ellipsoids in irrotational linear flow, and it gives good results for spheres in general linear flows at low capillary numbers. We demonstrate that deformable non-spherical particles align with the principal axes of an imposed irrotational flow. Thus, it is most practical to model deformation of non-spherical particles already aligned with the flow, rather than considering each arbitrary orientation. Capsule deformation was modeled for a sphere, a prolate spheroid, and an oblate spheroid, subjected to combinations of uniaxial, biaxial, and planar extensional flows; modeling was performed using the immersed boundary method. The time response of each capsule to each flow was found, as were the steady-state deformation factor, mean strain energy, and surface area. For a given capillary number, planar flows led to more deformation than uniaxial or biaxial extensional flows. Capsule behavior in all cases was bounded by the response of capsules to uniaxial, biaxial, and planar extensional flow.

DIRECT NUMERICAL SIMULATION OF DETACHMENT OF SINGLE CAPTURED LEUKOCYTE UNDER DIFFERENT FLOW CONDITIONS

Antibody-based cell isolation using microfluidics finds widespread applications in disease diagnostics and treatment monitoring at point of care (POC) for global health. However, the lack of knowledge on underlying mechanisms of cell capture greatly limits their developments. To address this, in this study, we developed a mathematical model using a direct numerical simulation for the detachment of single leukocyte captured on a functionalized surface in a rectangular microchannel under different flow conditions. The captured leukocyte was modeled as a simple liquid drop and its deformation was tracked using a level set method. The kinetic adhesion model was used to calculate the adhesion force and analyze the detachment of single captured leukocyte. The results demonstrate that the detachment of single captured leukocyte was dependent on both the magnitude of flow rate and flow acceleration, while the latter provides more significant effects. Pressure gradient was found to represent as another critical factor promoting leukocyte detachment besides shear stress. Cytoplasmic viscosity plays a much more important role in the deformation and detachment of captured leukocyte than cortex tension. Besides, better deformability (represented as lower cytoplasmic viscosity) noteworthy accelerates leukocyte detachment. The model presented here provides an enabling tool to clarify the interaction of target cells with functional surface and could help for developing more effective POC devices for global health.

Effects of Membrane Rheology on Leuko-polymersome Adhesion to Inflammatory Ligands

A strategy for treating inflammatory disease is to create micro-particles with the adhesive properties of leukocytes. The underlying rheology of deformable adhesive microspheres would be an important factor in the adhesive performance of such particles. In this work the effect of particle deformability on the selectin-mediated rolling of polymer vesicles (polymersomes) is evaluated. The rheology of the polymersome membrane was modulated by cross-linking unsaturated side-chains within the hydrophobic core of the membrane. Increased membrane rigidity resulted in decreased rates of particle recruitment rather than decreased average rolling velocities. Reflective interference contrast microscopy of rolling vesicles confirmed that neither flaccid nor rigid vesicles sustained close contacts with the substrate during rolling adhesion. A variable-shear rate parallel-plate flow chamber was employed to evaluate individual vesicles rolling on substrates under different flow conditions. Analysis of the trajectories of single flaccid vesicles revealed several distinct populations of rolling vesicles; however, some of these populations disappear when the vesicle membranes are made rigid. This work shows that membrane mechanics affects the capture, but not the rolling dynamics, of adherent leuko-polymersomes.