Dynamics of leukocyte-endothelium interactions in the splanchnic microcirculation

Leukocyte margination at arteriole shear rate

We numerically investigated margination of leukocytes at arteriole shear rate in straight circular channels with diameters ranging from 10 to 22 μm. Our results demonstrated that passing motion of RBCs effectively induces leukocyte margination not only in small channels but also in large channels. A longer time is needed for margination to occur in a larger channel, but once a leukocyte has marginated, passing motion of RBCs occurs continuously independent of the channel diameter, and leukocyte margination is sustained for a long duration. We also show that leukocytes rarely approach the wall surface to within a microvillus length at arteriole shear rate.

We numerically investigated margination of leukocytes at arteriole shear rate in straight circular channels with diameters ranging from 10 to 22 µm. Our results demonstrated that passing motion of RBCs effectively induces leukocyte margination not only in small channels but also in large channels. We also show that leukocytes rarely approach the wall surface to within a microvillus length at arteriole shear rate.

The deformation of an adherent leukocyte under steady shear flow: a numerical study

Leukocyte adhesion is a pathophysiological process in which the balance between hemodynamic and adhesion forces (molecular bonds) plays a key role. In this work, we studied the deformation of an adherent leukocyte and calculated the forces exerted on it. Three model cells were proposed, considering the leukocyte as a single drop, a compound drop, and a nucleus drop, representing a cell without nucleus, a cell with a nucleus, and a nucleus only, respectively. These model cells were supposedly adherent to a smooth substrate under steady shear flow. Our numerical results showed that all three model cells deformed in function of the initial contact angle, capillary number, and Reynolds number. The single drop was the most deformable, while the nucleus drop was the most resistant to the external flow. Each of the model cells showed maximum cell deformation at a high Reynolds number. The distribution of pressure on the cell confirmed the existence of a high-pressure region downstream of the drop, which retarded further deformation of the cell and provided a positive lift force on the drop. The consideration of a highly viscous nucleus can correct the over evaluation of the cell deformation in a flow.

Molecular properties in cell adhesion: a physical and engineering perspective

The past several years have seen accelerating growth in research directed towards the understanding and control of cell adhesion processes, from a spectrum of disciplinary approaches including molecular cell biology, biochemistry, biophysics and bioengineering. Consequently, our understanding of the mechanisms involved in cell adhesion has increased substantially. Corresponding quantitative analysis and modeling of the key molecular properties governing their action in regulating dynamic cell attachment and detachment events is crucial for advancing conceptual insight along with technological applications.

The state diagram for cell adhesion under flow: leukocyte rolling and firm adhesion

Leukocyte adhesion under flow in the microvasculature is mediated by binding between cell surface receptors and complementary ligands expressed on the surface of the endothelium. Leukocytes adhere to endothelium in a two-step mechanism: rolling (primarily mediated by selectins) followed by firm adhesion (primarily mediated by integrins). Using a computational method called "Adhesive Dynamics," we have simulated the adhesion of a cell to a surface in flow, and elucidated the relationship between receptor-ligand functional properties and the dynamics of adhesion. We express this relationship in a state diagram, a one-to-one map between the biophysical properties of adhesion molecules and various adhesive behaviors. Behaviors that are observed in simulations include firm adhesion, transient adhesion (rolling), and no adhesion. We varied the dissociative properties, association rate, bond elasticity, and shear rate and found that the unstressed dissociation rate, k(r)(o), and the bond interaction length, gamma, are the most important molecular properties controlling the dynamics of adhesion. Experimental k(r)(o) and gamma values from the literature for molecules that are known to mediate rolling adhesion fall within the rolling region of the state diagram. We explain why L-selectin-mediated rolling, which has faster k(r)(o) than other selectins, is accompanied by a smaller value for gamma. We also show how changes in association rate, shear rate, and bond elasticity alter the dynamics of adhesion. The state diagram (which must be mapped for each receptor-ligand system) presents a concise and comprehensive means of understanding the relationship between bond functional properties and the dynamics of adhesion mediated by receptor-ligand bonds.

Numerical analysis of the deformation of an adherent drop under shear flow

The adhesion of leukocytes to substrates is an important biomedical problem and has drawn extensive research. In this study, employing both single and compound drop models, we investigate how hydrodynamics interacts with an adherent liquid drop in a shear flow. These liquid drop models have recently been used to describe the rheological behavior of leukocytes. Numerical simulation confirms that the drop becomes more elongated when either capillary number or initial contact angle increases. Our results show that there exists a thin region between the drop and the wall as the drop undergoes large stretching, which allows high pressure to build up and provides a lift force. In the literature, existing models regard the leukocyte as a rigid body to calculate the force and torque acting on the drop in order to characterize the binding between cell receptors and endothelial ligands. The present study indicates that such a rigid body model is inadequate and the force magnitude obtained from it is less than half of that obtained using the deformable drop models. Furthermore, because of its much higher viscosity, the cell nucleus introduces a hydrodynamic time scale orders of magnitude slower than the cytoplasm. Hence the single and compound drops experience different dynamics during stretching, but exhibit very comparable steady-state shapes. The present work offers a framework to facilitate the development of a comprehensive dynamic model for blood cells.

Rheology of rat basophilic leukemia cells

Rat basophilic leukemia (RBL) cells, decorated with IgE, have been shown to bind irreversibly to antigen-coated substrates. In this paper we measured RBL cell deformability and demonstrated that this irreversible binding is not due to a compliant cellular rheology of these cells. The rheological properties of RBL cells were assessed with single-cell micropipette aspiration. Small-sized (G1/G0 phase) cells were found to be more deformable than medium-sized (S phase) cells. No changes in cellular rheology were observed after binding of anti-dinitrophenol IgE to Fce receptors. Furthermore, cytoplasmic viscosity mu showed power-law dependence on mean shear rate gama m: mu = mu c(gamma m/gamma c)-b, where mu c is a characteristic viscosity at characteristic shear rate gamma c, and b is a material coefficient. All the cells exhibited similar dependence on shear rate (b approximately 0.5). When gamma c was set to 1 s-1. mu c = 480 +/- 10,560 +/- 40 and 490 +/- 10 Pa.s for G1/G0, S cells, and G1/G0 cells treated with the antibody, respectively. In general. RBL cells were much more rigid than normal neutrophils (mu c = 130 +/- 20 Pa, s b = 0.5). Thus the biochemistry of the adhesion molecules, not the cellular deformability of the cell, is the cause of the irreversibility of RBL cell adhesion under flow.

Dynamics of neutrophil rolling over stimulated endothelium in vitro

Prior to extravasation at sites of acute inflammation, neutrophils roll over activated endothelium. Neutrophil rolling is often characterized by the average rolling velocity. An additional dynamic feature of rolling that has been identified but not extensively studied is the fluctuation in the rolling velocity about the average. To analyze this characteristic further, we have measured the instantaneous velocity of bovine neutrophils interacting with lipopolysaccharide-stimulated bovine aortic endothelium at shear stresses of 1, 2, 3, and 4 dynes/cm2. The average velocities are quantitatively similar to those reported for human neutrophils rolling over reconstituted P-selectin at a surface density of 400 sites/microns 2. At all shear stresses tested, the population average variance in the instantaneous velocity is at least 2 orders of magnitude higher than the theoretical variance generated from experimental error, indicating that the neutrophils translate with a nonconstant velocity. Possible sources of the variance are discussed. These include "macroscopic" sources such as topological heterogeneity in the endothelium and microscopic sources, such as inherent stochastic formation and breakage of the receptor-ligand bonds that mediate the rolling. Regardless of the ultimate source of the variance, these results justify the use of mathematical models that incorporate stochastic processes to describe bond formation and breakage between the neutrophil and the endothelium and hence are able to generate variable velocity trajectories.

Effects of hydrodynamics and leukocyte-endothelium specificity on leukocyte-endothelium interactions

In vivo microscopy was used to assess the relative contribution of hydrodynamic forces (network topography and shear rate) and the specificity for leukocytes to interact with venular endothelium as determinants of leukocyte-endothelium interactions. To ascertain this, microvascular networks in the rat and rabbit mesentery were examined under normograde and mechanically induced retrograde flows to determine the effect of reversed flow on leukocyte-endothelium interactions in arterioles and venules. The data indicate that retrograde perfusion under hemodynamic (red blood cell velocity and shear rate) states equivalent to normograde flow significantly increased leukocyte marginating flux in arterioles (from 0 to 0.5 cells/5 sec) and decreased flux significantly in venules (from 1.0 to 0.2 cells/5 sec). The increased flux in arterioles under retrograde conditions, however, was significantly lower than the flux in venules under normograde conditions and the decreased flux in venules during retrograde flow was significantly greater than the flux in arterioles during normograde flow. This apparent discrepancy appears to be the result of a heterogeneous distribution of adhesive receptors on vascular endothelium. Furthermore, marginating leukocytes in arterioles made only brief contact with the endothelium before being swept away while marginating leukocytes in venules during normal and retrograde perfusion rolled along the vascular wall, with similar velocities in both directions. In conclusion, although hydrodynamic forces are important in facilitating leukocyte margination through mechanisms of radial migration, it is leukocyte-endothelium specificity in venules that ultimately determines leukocyte-endothelium interactions.

Simulation of cell rolling and adhesion on surfaces in shear flow: general results and analysis of selectin-mediated neutrophil adhesion

The receptor-mediated adhesion of cells to ligand-coated surfaces in viscous shear flow is an important step in many physiological processes, such as the neutrophil-mediated inflammatory response, lymphocyte homing, and tumor cell metastasis. This paper describes a calculational method which simulates the interaction of a single cell with a ligand-coated surface under flow. The cell is idealized as a microvilli-coated hard sphere covered with adhesive springs. The distribution of microvilli on the cell surface, the distribution of receptors on microvilli tips, and the forward and reverse reaction between receptor and ligand are all simulated using random number sampling of appropriate probability functions. The velocity of the cell at each time step in the simulation results from a balance of hydrodynamic, colloidal and bonding forces; the bonding force is derived by summing the individual contributions of each receptor-ligand tether. The model can simulate the effect of many parameters on adhesion, such as the number of receptors on microvilli tips, the density of ligand, the rates of reaction between receptor and ligand, the stiffness of the resulting receptor-ligand springs, the response of springs to strain, and the magnitude of the bulk hydrodynamic stresses. The model can successfully recreate the entire range of expected and observed adhesive phenomena, from completely unencumbered motion, to rolling, to transient attachment, to firm adhesion. Also, the method can generate meaningful statistical measures of adhesion, including the mean and variance in velocity, rate constants for cell attachment and detachment, and the frequency of adhesion. We find a critical modulating parameter of adhesion is the fractional spring slippage, which relates the strain of a bond to its rate of breakage; the higher the slippage, the faster the breakage for the same strain. Our analysis of neutrophil adhesive behavior on selectin-coated (CD62-coated) surfaces in viscous shear flow reported by Lawrence and Springer (Lawrence, M.B., and T.A. Springer 1991. Cell. 65:859-874) shows the fractional spring slippage of the CD62-LECAM-1 bond is likely below 0.01. We conclude the unique ability of this selectin bond to cause neutrophil rolling under flow is a result of its unique response to strain. Furthermore, our model can successfully recreate data on neutrophil rolling as function of CD62 surface density.