The reaction-limited kinetics of membrane-to-surface adhesion and detachment

E-cadherin junctions as active mechanical integrators in tissue dynamics

During epithelial morphogenesis, E-cadherin adhesive junctions play an important part in mechanically coupling the contractile cortices of cells together, thereby distributing the stresses that drive cell rearrangements at both local and tissue levels. Here we discuss the concept that cellular contractility and E-cadherin-based adhesion are functionally integrated by biomechanical feedback pathways that operate on molecular, cellular and tissue scales.

Catch-slip bonds can be dispensable for motor force regulation during skeletal muscle contraction

It is intriguing how multiple molecular motors can perform coordinated and synchronous functions, which is essential in various cellular processes. Recent studies on skeletal muscle might have shed light on this issue, where rather precise motor force regulation was partly attributed to the specific stochastic features of a single attached myosin motor. Though attached motors can randomly detach from actin filaments either through an adenosine triphosphate (ATP) hydrolysis cycle or through "catch-slip bond" breaking, their respective contribution in motor force regulation has not been clarified. Here, through simulating a mechanical model of sarcomere with a coupled Monte Carlo method and finite element method, we find that the stochastic features of an ATP hydrolysis cycle can be sufficient while those of catch-slip bonds can be dispensable for motor force regulation.

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.

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.

Global contraction or local growth, bleb shape depends on more than just cell structure

When the plasma membrane of a cell locally delaminates from its actin cortex the membrane is pushed outwards due to the cell׳s internal fluid pressure. The resulting spherical protrusion is known as a bleb. A cell׳s ability to function correctly is highly dependent on the production of such protrusions with the correct size and shape. Here, we investigate the nucleation of large blebs from small, local neck regions. A mathematical model of a cell׳s membrane, cortex and interconnecting adhesions demonstrates that these three components are unable to capture experimentally observed bleb shapes without the addition of further assumptions. We have identified that combinations of global cortex contraction and localised membrane growth are the most promising methods for generating prototypical blebs. Currently, neither proposed mechanism has been fully tested experimentally and, thus, we propose experiments that will distinguish between the two methods of bleb production.

Dynamics of receptor-mediated nanoparticle internalization into endothelial cells

Nanoparticles offer a promising medical tool for targeted drug delivery, for example to treat inflamed endothelial cells during the development of atherosclerosis. To inform the design of such therapeutic strategies, we develop a computational model of nanoparticle internalization into endothelial cells, where internalization is driven by receptor-ligand binding and limited by the deformation of the cell membrane and cytoplasm. We specifically consider the case of nanoparticles targeted against ICAM-1 receptors, of relevance for treating atherosclerosis. The model computes the kinetics of the internalization process, the dynamics of binding, and the distribution of stresses exerted between the nanoparticle and the cell membrane. The model predicts the existence of an optimal nanoparticle size for fastest internalization, consistent with experimental observations, as well as the role of bond characteristics, local cell mechanical properties, and external forces in the nanoparticle internalization process.

Molecular force spectroscopy on cells

Molecular force spectroscopy has become a powerful tool to study how mechanics regulates biology, especially the mechanical regulation of molecular interactions and its impact on cellular functions. This force-driven methodology has uncovered a wealth of new information of the physical chemistry of molecular bonds for various biological systems. The new concepts, qualitative and quantitative measures describing bond behavior under force, and structural bases underlying these phenomena have substantially advanced our fundamental understanding of the inner workings of biological systems from the nanoscale (molecule) to the microscale (cell), elucidated basic molecular mechanisms of a wide range of important biological processes, and provided opportunities for engineering applications. Here, we review major force spectroscopic assays, conceptual developments of mechanically regulated kinetics of molecular interactions, and their biological relevance. We also present current challenges and highlight future directions.

Force-induced remodelling of proteins and their complexes

Force can drive conformational changes in proteins, as well as modulate their stability and the affinity of their complexes, allowing a mechanical input to be converted into a biochemical output. These properties have been utilised by nature and force is now recognised to be widely used at the cellular level. The effects of force on the biophysical properties of biological systems can be large and varied. As these effects are only apparent in the presence of force, studies on the same proteins using traditional ensemble biophysical methods can yield apparently conflicting results. Where appropriate, therefore, force measurements should be integrated with other experimental approaches to understand the physiological context of the system under study.

Probing time-dependent mechanical behaviors of catch bonds based on two-state models

With lifetime counter-intuitively being prolonged under forces, catch bonds can play critical roles in various sub-cellular processes. By adopting different “catching” strategies within the framework of two-state models, we construct two types of catch bonds that have a similar force-lifetime profile upon a constant force-clamp load. However, when a single catch bond of either type is subjected to varied forces, we find that they can behave very differently in both force history dependence and bond strength. We further find that a cluster of catch bonds of either type generally becomes unstable when subjected to a periodically oscillating force, which is consistent with experimental results. These results provide important insights into versatile time-dependent mechanical behaviors of catch bonds. We suggest that it is necessary to further differentiate those bonds that are all phenomenologically referred to as “Catch bonds”.

The speed of an inclined ruck

Steady rucks in an elastic beam can roll at constant speed down an inclined plane. We examine the dynamics of these travelling-wave structures and argue that their speed can be dictated by a combination of the physical conditions arising in the vicinity of the 'contact points' where the beam is peeled off the underlying plane and stuck back down. We provide three detailed models for the contact dynamics: viscoelastic fracture, a thermodynamic model for bond formation and detachment and adhesion mediated by a thin liquid film. The results are compared with experiments.

Evaluation of agglutination strength by a flow-induced cell movement assay based surface plasmon resonance (SPR) technique

Flow-induced cell movement assay based on an SPR biosensor for the quantification of the strength of RBC agglutination via the velocity of RBCs moving on immobilized antibodies.

Enhancing sensitivity and specificity in rare cell capture microdevices with dielectrophoresis

The capture and subsequent analysis of rare cells, such as circulating tumor cells from a peripheral blood sample, has the potential to advance our understanding and treatment of a wide range of diseases. There is a particular need for high purity (i.e., high specificity) techniques to isolate these cells, reducing the time and cost required for single-cell genetic analyses by decreasing the number of contaminating cells analyzed. Previous work has shown that antibody-based immunocapture can be combined with dielectrophoresis (DEP) to differentially isolate cancer cells from leukocytes in a characterization device. Here, we build on that work by developing numerical simulations that identify microfluidic obstacle array geometries where DEP-immunocapture can be used to maximize the capture of target rare cells, while minimizing the capture of contaminating cells. We consider geometries with electrodes offset from the array and parallel to the fluid flow, maximizing the magnitude of the resulting electric field at the obstacles' leading and trailing edges, and minimizing it at the obstacles' shoulders. This configuration attracts cells with a positive DEP (pDEP) response to the leading edge, where the shear stress is low and residence time is long, resulting in a high capture probability; although these cells are also repelled from the shoulder region, the high local fluid velocity at the shoulder minimizes the impact on the overall transport and capture. Likewise, cells undergoing negative DEP (nDEP) are repelled from regions of high capture probability and attracted to regions where capture is unlikely. These simulations predict that DEP can be used to reduce the probability of capturing contaminating peripheral blood mononuclear cells (using nDEP) from 0.16 to 0.01 while simultaneously increasing the capture of several pancreatic cancer cell lines from 0.03-0.10 to 0.14-0.55, laying the groundwork for the experimental study of hybrid DEP-immunocapture obstacle array microdevices.

Adhesive dynamics

Adhesive dynamics (AD) is a method for simulating the dynamic response of biological systems in response to force. Biological bonds are mechanical entities that exert force under strain, and applying forces to biological bonds modulates their rate of dissociation. Since small numbers of events usually control biological interactions, we developed a simple method for sampling probability distributions for the formation or failure of individual bonds. This method allows a simple coupling between force and strain and kinetics, while capturing the stochastic response of biological systems. Biological bonds are dynamically reconfigured in response to applied mechanical stresses, and a detailed spatio-temporal map of molecules and the forces they exert emerges from AD. The shape or motion of materials bearing the molecules is easily calculated from a mechanical energy balance provided the rheology of the material is known. AD was originally used to simulate the dynamics of adhesion of leukocytes under flow, but new advances have allowed the method to be extended to many other applications, including but not limited to the binding of viruses to surface, the clustering of adhesion molecules driven by stiff substrates, and the effect of cell-cell interaction on cell capture and rolling dynamics. The technique has also been applied to applications outside of biology. A particular exciting recent development is the combination of signaling with AD (so-called integrated signaling adhesive dynamics, or ISAD), which allows facile integration of signaling networks with mechanical models of cell adhesion and motility. Potential opportunities in applying AD are summarized.

Force and affinity in ligand discrimination by the TCR

T cell recognition of antigen is a physical process that requires formation of a cell-cell junction that is rich in active force generation. Recently a biomolecular force probe was used to examine how the T cell receptor (TCR)-pMHC interaction responds to force and the consequences of force-dependent interactions for T cell activation. While adhesion and costimulatory molecules in the immunological synapse impact upon the overall force of the interaction, these results suggest that the TCR uses a force-dependent bond - a catch bond - and that it may therefore be important to consider the TCR-pMHC interaction in isolation in the early phases of the decision process. We discuss here these findings in the context of other work on the impact of forces on the TCR and the quantification of interaction in interfaces.

Simulation of the microscopic process during initiation of stent thrombosis

OBJECTIVE

Coronary stenting is one of the most commonly used approaches to open coronary arteries blocked due to atherosclerosis. However, stent struts can induce stent thrombosis due to altered hemodynamics and endothelial dysfunction, and the microscopic process is poorly understood. The objective of this study was to determine the microscale processes during the initiation of stent thrombosis.

METHODS

We utilized a discrete element computational model to simulate the transport, collision, adhesion, and activation of thousands of individual platelets and red blood cells in thrombus formation around struts and dysfunctional endothelium.

RESULTS

As strut height increased, the area of endothelium activated by low shear stress increased, which increased the number of platelets in mural thrombi. These thrombi were generally outside regions of recirculation for shorter struts. For the tallest strut, wall shear stress was sufficiently low to activate the entire endothelium. With the entire endothelium activated by injury or denudation, the number of platelets in mural thrombi was largest for the shortest strut. The type of platelet activation (by high shear stress or contact with activated endothelium) did not greatly affect results.

CONCLUSIONS

During the initiation of stent thrombosis, platelets do not necessarily enter recirculation regions or deposit on endothelium near struts, as suggested by previous computational fluid dynamics simulations. Rather, platelets are more likely to deposit on activated endothelium outside recirculation regions and deposit directly on struts. Our study elucidated the effects of different mechanical factors on the roles of platelets and endothelium in stent thrombosis.

Hemodynamics in the microcirculation and in microfluidics

Hemodynamics in microcirculation is important for hemorheology and several types of circulatory disease. Although hemodynamics research has a long history, the field continues to expand due to recent advancements in numerical and experimental techniques at the micro-and nano-scales. In this paper, we review recent computational and experimental studies of blood flow in microcirculation and microfluidics. We first focus on the computational studies of red blood cell (RBC) dynamics, from the single cellular level to mesoscopic multiple cellular flows, followed by a review of recent computational adhesion models for white blood cells, platelets, and malaria-infected RBCs, in which the cell adhesion to the vascular wall is essential for cellular function. Recent developments in optical microscopy have enabled the observation of flowing blood cells in microfluidics. Experimental particle image velocimetry and particle tracking velocimetry techniques are described in this article. Advancements in micro total analysis system technologies have facilitated flowing cell separation with microfluidic devices, which can be used for biomedical applications, such as a diagnostic tool for breast cancer or large intestinal tumors. In this paper, cell-separation techniques are reviewed for microfluidic devices, emphasizing recent advances and the potential of this fast-evolving research field in the near future.

Physics of nail conditions: why do ingrown nails always happen in the big toes?

Although surgical treatment of nail conditions can be traced back centuries to the writings of Paul Aegineta (625-690 AC), little is known about the physical laws governing nail growth. Such a poor understanding together with the increasing number of nail salons in the high street should raise legitimate concerns regarding the different procedures applied to nails. An understanding of the physics of nail growth is therefore essential to engage with human medicine and to understand the aetiology of nail conditions. In this context, a theory of nail plate adhesion, including a physical description of nail growth can be used to determine the transverse and longitudinal curvatures of the nail plate that are so important in the physical diagnosis of some nail conditions. As a result physics sheds light on: (a) why/how nails/hooves adhere strongly, yet grow smoothly; (b) why hoof/claw/nail growth rates are similar across species; (c) potential nail damage incurred by poor trimming; (d) the connection between three previously unrelated nail conditions, i.e. spoon-shaped, pincer and ingrown nails and; last but not least, (e) why ingrown nails occur preferentially in the big toes.

Stochastic simulation of single-molecule pulling experiments

Single-molecule pulling experiments are widely used for studying the structure, dynamics, and function of single biological molecules via applying mechanical forces on them in a controlled way. Pulling at a constant speed or at a constant force builds up a mechanical force on a molecule or molecular complex leading to a molecular transition such as the dissociation of a molecular complex, unfolding of a protein, or unwrapping of a higher-order structure. We perform Brownian dynamics and Monte Carlo simulations of single-molecule pulling experiments. Through our simulations we demonstrate that the molecular transition rate based on the Kramers theory in the high-barrier limit becomes unsuitable as the applied force approaches the critical force at which the barrier disappears. We also demonstrate that use of molecular transition rate based on mean first passage time (MFPT) approach would be more relevant in describing molecular transition especially as the applied force approaches the critical force.

Parametric control of collision rates and capture rates in geometrically enhanced differential immunocapture (GEDI) microfluidic devices for rare cell capture

The enrichment and isolation of rare cells from complex samples, such as circulating tumor cells (CTCs) from whole blood, is an important engineering problem with widespread clinical applications. One approach uses a microfluidic obstacle array with an antibody surface functionalization to both guide cells into contact with the capture surface and to facilitate adhesion; geometrically enhanced differential immunocapture is a design strategy in which the array is designed to promote target cell–obstacle contact and minimize other interactions (Gleghorn et al. 2010; Kirby et al. 2012). We present a simulation that uses capture experiments in a simple Hele-Shaw geometry (Santana et al. 2012) to inform a target-cell-specific capture model that can predict capture probability in immunocapture microdevices of any arbitrary complex geometry. We show that capture performance is strongly dependent on the array geometry, and that it is possible to select an obstacle array geometry that maximizes capture efficiency (by creating combinations of frequent target cell–obstacle collisions and shear stress low enough to support capture), while simultaneously enhancing purity by minimizing nonspecific adhesion of both smaller contaminant cells (with infrequent cell–obstacle collisions) and larger contaminant cells (by focusing those collisions into regions of high shear stress).

Cell surface topography is a regulator of molecular interactions during chemokine-induced neutrophil spreading

Adhesive interactions between neutrophils and endothelium involve chemokine-induced neutrophil spreading and subsequent crawling on the endothelium to sites of transmigration. We investigated the importance of cell topography in this process using immunofluorescence, scanning electron microscopy, and live-cell imaging using total internal reflectance microscopy to observe redistribution of key membrane proteins, both laterally and relative to surface topography, during neutrophil spreading onto glass coated with interleukin 8. During formation of the lamellipod, L-selectin is distributed on microvilli tips along the top of the lamellipodium, whereas the interleukin 8 receptors CXCR1 and CXCR2 and the integrin LFA-1 (αLβ2) were present at the interface between the lamellipodium and the substrate. Total internal reflection fluorescence imaging indicated that LFA-1 and both chemokine receptors redistributed into closer contact with the substrate as the cells spread onto the surface and remodeled their topography. A geometric model of the surface remodeling with nonuniform distribution of molecules and a realistic distribution of microvilli heights was matched to the data, and the fits indicated a 1000-fold increase in the concentration of chemokine receptors and integrins available for bond formation at the interface. These observations imply that topographical remodeling is a key mechanism for regulating cell adhesion and surface-induced activation of cells.

Active elastic dimers: cells moving on rigid tracks

Experiments suggest that the migration of some cells in the three-dimensional extracellular matrix bears strong resemblance to one-dimensional cell migration. Motivated by this observation, we construct and study a minimal one-dimensional model cell made of two beads and an active spring moving along a rigid track. The active spring models the stress fibers with their myosin-driven contractility and α-actinin-driven extendability, while the friction coefficients of the two beads describe the catch and slip-bond behaviors of the integrins in focal adhesions. In the absence of active noise, net motion arises from an interplay between active contractility (and passive extendability) of the stress fibers and an asymmetry between the front and back of the cell due to catch-bond behavior of integrins at the front of the cell and slip-bond behavior of integrins at the back. We obtain reasonable cell speeds with independently estimated parameters. We also study the effects of hysteresis in the active spring, due to catch-bond behavior and the dynamics of cross linking, and the addition of active noise on the motion of the cell. Our model highlights the role of α-actinin in three-dimensional cell motility and does not require Arp2/3 actin filament nucleation for net motion.

Biomechanics of cell adhesion: how force regulates the lifetime of adhesive bonds at the single molecule level

Cell adhesion proteins play critical roles in positioning cells during development, segregating cells into distinct tissue compartments and in maintaining tissue integrity. The principle function of these proteins is to bind cells together and resist mechanical force. Adhesive proteins also enable migrating cells to adhere and roll on surfaces even in the presence of shear forces exerted by fluid flow. Recently, several experimental and theoretical studies have provided quantitative insights into the physical mechanisms by which adhesion proteins modulate their unbinding kinetics in response to tensile force. This perspective reviews these biophysical investigations. We focus on single molecule studies of cadherins, selectins, integrins, the von Willebrand factor and FimH adhesion proteins; the effect of mechanical force on the lifetime of these interactions has been extensively characterized. We review both theoretical models and experimental investigations and discuss future directions in this exciting area of research.

Sticky surface: sphere-sphere adhesion dynamics

We present a multi-scale model to study the attachment of spherical particles with a rigid core, coated with binding ligands and suspended in the surrounding, quiescent fluid medium. This class of fluid-immersed adhesion is widespread in many natural and engineering settings, particularly in microbial surface adhesion. Our theory highlights how the micro-scale binding kinetics of these ligands, as well as the attractive/repulsive surface potential in an ionic medium affects the eventual macro-scale size distribution of the particle aggregates (flocs). The bridge between the micro-macro model is made via an aggregation kernel. Results suggest that the presence of elastic ligands on the particle surface lead to the formation of larger floc aggregates via efficient inter-floc collisions (i.e. non-zero sticking probability, g). Strong electrolytic composition of the surrounding fluid favours large floc formation as well. The kernel for the Brownian diffusion for hard spheres is recovered in the limit of perfect binding effectiveness (g→1) and in a neutral solution with no dissolved salts.

Three-dimensional multi-scale model of deformable platelets adhesion to vessel wall in blood flow

When a blood vessel ruptures or gets inflamed, the human body responds by rapidly forming a clot to restrict the loss of blood. Platelets aggregation at the injury site of the blood vessel occurring via platelet-platelet adhesion, tethering and rolling on the injured endothelium is a critical initial step in blood clot formation. A novel three-dimensional multi-scale model is introduced and used in this paper to simulate receptor-mediated adhesion of deformable platelets at the site of vascular injury under different shear rates of blood flow. The novelty of the model is based on a new approach of coupling submodels at three biological scales crucial for the early clot formation: novel hybrid cell membrane submodel to represent physiological elastic properties of a platelet, stochastic receptor-ligand binding submodel to describe cell adhesion kinetics and lattice Boltzmann submodel for simulating blood flow. The model implementation on the GPU cluster significantly improved simulation performance. Predictive model simulations revealed that platelet deformation, interactions between platelets in the vicinity of the vessel wall as well as the number of functional GPIbα platelet receptors played significant roles in platelet adhesion to the injury site. Variation of the number of functional GPIbα platelet receptors as well as changes of platelet stiffness can represent effects of specific drugs reducing or enhancing platelet activity. Therefore, predictive simulations can improve the search for new drug targets and help to make treatment of thrombosis patient-specific.

Plasticity of hydrogen bond networks regulates mechanochemistry of cell adhesion complexes

Mechanical forces acting on cell adhesion receptor proteins regulate a range of cellular functions by formation and rupture of noncovalent interactions with ligands. Typically, force decreases the lifetimes of intact complexes ("slip bonds"), making the discovery that these lifetimes can also be prolonged ("catch bonds") a surprise. We created a microscopic analytic theory by incorporating the structures of selectin and integrin receptors into a conceptual framework based on the theory of stochastic equations, which quantitatively explains a wide range of experimental data (including catch bonds at low forces and slip bonds at high forces). Catch bonds arise due to force-induced remodeling of hydrogen bond networks, a finding that also accounts for unbinding in structurally unrelated integrin-fibronectin and actomyosin complexes. For the selectin family, remodeling of hydrogen bond networks drives an allosteric transition resulting in the formation of the maximum number of hydrogen bonds determined only by the structure of the receptor and independent of the ligand. A similar transition allows us to predict the increase in the number of hydrogen bonds in a particular allosteric state of α5β1 integrin-fibronectin complex, a conformation which is yet to be crystallized. We also make a testable prediction that a single point mutation (Tyr51Phe) in the ligand associated with selectin should dramatically alter the nature of the catch bond compared with the wild type. Our work suggests that nature uses a ductile network of hydrogen bonds to engineer function over a broad range of forces.

Mechanical regulation of T-cell functions

T cells are key players of the mammalian adaptive immune system. They experience different mechanical microenvironments during their life cycle, from the thymus, secondary lymph organs, and peripheral tissues that are free of externally applied force, but display variable substrate rigidities to the blood and lymphatic circulation systems, where complicated hydrodynamic forces are present. Regardless of whether T cells are subject to external forces or generate their own internal forces, they respond and adapt to different biomechanical cues to modulate their adhesion, migration, trafficking, and triggering of immune functions through mechanical regulation of various molecules that bear force. These include adhesive receptors, immunoreceptors, motor proteins, cytoskeletal proteins, and their associated molecules. Here, we discuss the forces acting on various surface and cytoplasmic proteins of a T cell in different mechanical milieus. We review existing data on how force regulates protein conformational changes and interactions with counter molecules, including integrins, actin, and the T-cell receptor, and how each relates to T-cell functions.

Contractile fibers and catch-bond clusters: a biological force sensor?

Catch bonds are cellular receptor-ligand pairs whose lifetime, counterintuitively, increases with increasing load. Although their existence was initially pure theoretical speculation, recent years have seen several experimental demonstrations of catch-bond behavior in biologically relevant and functional protein-protein bonds. Particularly notable among these established catch-bond formers is the integrin α5β1, the primary receptor for fibronectin and, as such, a crucial determinant for the characteristics of the mechanical coupling between cell and matrix. In this work, we explore the implications of single catch-bond characteristics for the behavior of a load-sharing cluster of such bonds: These clusters are shown to possess a regime of strengthening with increasing applied force, similar to the manner in which focal adhesions become selectively reinforced. Our results may shed new light on the fundamental processes that allow cells to sense and respond to the mechanical properties of their environment and in particular show how single focal adhesions may act, autonomously, as local rigidity sensors.

Catch and release: how do kinetochores hook the right microtubules during mitosis?

Sport fishermen keep tension on their lines to prevent hooked fish from releasing. A molecular version of this angler's trick, operating at kinetochores, ensures accuracy during mitosis: the mitotic spindle attaches randomly to chromosomes and then correctly bioriented attachments are stabilized due to the tension exerted on them by opposing microtubules. Incorrect attachments, which lack tension, are unstable and release quickly, allowing another chance for biorientation. Stabilization of molecular interactions by tension also occurs in other physiological contexts, such as cell adhesion, motility, hemostasis, and tissue morphogenesis. Here, we review models for the stabilization of kinetochore attachments with an eye toward emerging models for other force-activated systems. Although attention in the mitosis field has focused mainly on one kinase-based mechanism, multiple mechanisms may act together to stabilize properly bioriented kinetochores and some principles governing other tension-sensitive systems may also apply to kinetochores.

Estimating the probability of polyreactive antibodies 4E10 and 2F5 disabling a gp41 trimer after T cell-HIV adhesion

A few broadly neutralizing antibodies, isolated from HIV-1 infected individuals, recognize epitopes in the membrane proximal external region (MPER) of gp41 that are transiently exposed during viral entry. The best characterized, 4E10 and 2F5, are polyreactive, binding to the viral membrane and their epitopes in the MPER. We present a model to calculate, for any antibody concentration, the probability that during the pre-hairpin intermediate, the transient period when the epitopes are first exposed, a bound antibody will disable a trivalent gp41 before fusion is complete. When 4E10 or 2F5 bind to the MPER, a conformational change is induced that results in a stably bound complex. The model predicts that for these antibodies to be effective at neutralization, the time to disable an epitope must be shorter than the time the antibody remains bound in this conformation, about five minutes or less for 4E10 and 2F5. We investigate the role of avidity in neutralization and show that 2F5 IgG, but not 4E10, is much more effective at neutralization than its Fab fragment. We attribute this to 2F5 interacting more stably than 4E10 with the viral membrane. We use the model to elucidate the parameters that determine the ability of these antibodies to disable epitopes and propose an extension of the model to analyze neutralization data. The extended model predicts the dependencies of for neutralization on the rate constants that characterize antibody binding, the rate of fusion of gp41, and the number of gp41 bridging the virus and target cell at the start of the pre-hairpin intermediate. Analysis of neutralization experiments indicate that only a small number of gp41 bridges must be disabled to prevent fusion. However, the model cannot determine the exact number from neutralization experiments alone.

Most people who become infected with HIV generate a strong antibody response to the infecting virus population. Unfortunately, the protection offered by the antibody is short lived as the virus rapidly mutates and renders the antibodies impotent in preventing further infection. There are a few antibodies, however, that have been isolated from infected individuals that can block infection by many different viral strains. Among these are several that target sites on the HIV that are exposed only after the virus has attached to a cell. These antibodies have a brief window of time to prevent fusion of the virus and cell. They are special in that they bind both to the viral membrane and to sequences on the gp41 protein that lie along the viral surface. Here, we present a model that predicts the concentrations at which these antibodies effectively neutralize the virus. The model tells us what properties of antibody binding are key in determining efficient neutralization and what properties have little influence. A prediction of the model is that in a standard neutralization assay there are only a small number of attachments between virus and cell and disabling these is sufficient to prevent infection.

Effect of Red Blood Cells on Platelet Activation and Thrombus Formation in Tortuous Arterioles

Thrombosis is a major contributor to cardiovascular disease, which can lead to myocardial infarction and stroke. Thrombosis may form in tortuous microvessels, which are often seen throughout the human body, but the microscale mechanisms and processes are not well understood. In straight vessels, the presence of red blood cells (RBCs) is known to push platelets toward walls, which may affect platelet aggregation and thrombus formation. However in tortuous vessels, the effects of RBC interactions with platelets in thrombosis are largely unknown. Accordingly, the objective of this work was to determine the physical effects of RBCs, platelet size, and vessel tortuosity on platelet activation and thrombus formation in tortuous arterioles. A discrete element computational model was used to simulate the transport, collision, adhesion, aggregation, and shear-induced platelet activation of hundreds of individual platelets and RBCs in thrombus formation in tortuous arterioles. Results showed that high shear stress near the inner sides of curved arteriole walls activated platelets to initiate thrombosis. RBCs initially promoted platelet activation, but then collisions of RBCs with mural thrombi reduced the amount of mural thrombus and the size of emboli. In the absence of RBCs, mural thrombus mass was smaller in a highly tortuous arteriole compared to a less tortuous arteriole. In the presence of RBCs however, mural thrombus mass was larger in the highly tortuous arteriole compared to the less tortuous arteriole. As well, smaller platelet size yielded less mural thrombus mass and smaller emboli, either with or without RBCs. This study shed light on microscopic interactions of RBCs and platelets in tortuous microvessels, which have implications in various pathologies associated with thrombosis and bleeding.

Receptor concentration and diffusivity control multivalent binding of Sv40 to membrane bilayers

Incoming Simian Virus 40 particles bind to their cellular receptor, the glycolipid GM1, in the plasma membrane and thereby induce membrane deformation beneath the virion leading to endocytosis and infection. Efficient membrane deformation depends on receptor lipid structure and the organization of binding sites on the internalizing particle. To determine the role of receptor diffusion, concentration and the number of receptors required for stable binding in this interaction, we analyze the binding of SV40 to GM1 in supported membrane bilayers by computational modeling based on experimental data. We measure the diffusion rates of SV40 virions in solution by fluorescence correlation spectroscopy and of the receptor in bilayers by single molecule tracking. Quartz-crystal microbalance with dissipation (QCM-D) is used to measure binding of SV40 virus-like particles to bilayers containing the viral receptor GM1. We develop a phenomenological stochastic dynamics model calibrated against this data, and use it to investigate the early events of virus attachment to lipid membranes. Our results indicate that SV40 requires at least 4 attached receptors to achieve stable binding. We moreover find that receptor diffusion is essential for the establishment of stable binding over the physiological range of receptor concentrations and that receptor concentration controls the mode of viral motion on the target membrane. Our results provide quantitative insight into the initial events of virus-host interaction at the nanoscopic level.

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.

Mechanochemitry: a molecular biomechanics view of mechanosensing

Molecular biomechanics includes two themes: the study of mechanical aspects of biomolecules and the study of molecular biology of the cell using mechanical tools. The two themes are interconnected for obvious reasons. The present review focuses on one of the interconnected areas-the mechanical regulation of molecular interaction and conformational change. Recent conceptual developments are summarized, including catch bonds, regulation of molecular interaction by the history of force application, and cyclic mechanical reinforcement. These studies elucidate the mechanochemistry of some of the candidate mechanosensing molecules, thereby providing a natural connection to mechanobiology.

Spatial-temporal event adaptive characteristics of nanocarrier drug delivery in cancer therapy

In cancer therapy, drug delivery is a complex process that aims to transit the cargo to the destination with as little damage to the normal tissue as possible. In the last decade, tremendous development and research on nanomedicine have been exploring an ideal system with efficient drug transportation and release property. For this end, series of barriers need to be circumvented by nanomedicine, including systemic barriers, such as biosurface adsorption, phagocytic clearance, bloodstream washing, interstitial pressure, degradation, as well as intracellular barriers, such as cell membrane reorganization and internalization, endo/lysosomal escape, cytosolic or subcellular localization. Rather than being random, these barriers follow a specific spatial-temporal sequence. Therefore, the nanocarriers have to be endowed with characteristics that are adaptive to particular biological milieu on systemic and intracellular levels. To this end, we reviewed the correlations between the spatial-temporal sequences of drug delivery and nanocarrier characteristics in cancer therapy, as well as strategies to achieve efficient drug delivery upon both systemic and intracellular levels.

Platelet size and density affect shear-induced thrombus formation in tortuous arterioles

Thrombosis accounts for 80% of deaths in patients with diabetes mellitus. Diabetic patients demonstrate tortuous microvessels and larger than normal platelets. Large platelets are associated with increased platelet activation and thrombosis, but the physical effects of large platelets in the microscale processes of thrombus formation are not clear. Therefore, the objective of this study was to determine the physical effects of mean platelet volume (MPV), mean platelet density (MPD) and vessel tortuosity on platelet activation and thrombus formation in tortuous arterioles. A computational model of the transport, shear-induced activation, collision, adhesion and aggregation of individual platelets was used to simulate platelet interactions and thrombus formation in tortuous arterioles. Our results showed that an increase in MPV resulted in a larger number of activated platelets, though MPD and level of tortuosity made little difference on platelet activation. Platelets with normal MPD yielded the lowest amount of mural thrombus. With platelets of normal MPD, the amount of mural thrombus decreased with increasing level of tortuosity but did not have a simple monotonic relationship with MPV. The physical mechanisms associated with MPV, MPD and arteriole tortuosity play important roles in platelet activation and thrombus formation.

Impact of flow on ligand-mediated bacterial flocculation

To understand the adhesion-fragmentation dynamics of bacterial aggregates (i.e., flocs), we model the aggregates as two ligand-covered rigid spheres. We develop and investigate a model for the attachment/detachment dynamics in a fluid subject to a homogeneous planar shear-flow. The binding ligands on the surface of the flocs experience attractive and repulsive surface forces in an ionic medium and exhibit finite resistance to rotation (via bond tilting). For certain range of material and fluid parameters, our results predict a nonlinear or hysteretic relationship between the binding/unbinding of the floc surface and the net floc velocity (translational plus rotational velocity). We show that the surface adhesion is promoted by increased fluid flow until a critical value, beyond which the bonds starts to yield. Moreover, adhesion is not promoted in a medium with low ionic strength, or flocs with bigger size or higher binder stiffness. The numerical simulations of floc-aggregate number density studies support these findings.

Dynamic bonds and polar ejection force distribution explain kinetochore oscillations in PtK1 cells

A computational model of kinetochore dynamics suggests that differences in the distribution of polar ejection forces at the periphery and in the middle of PtK1 cell spindles underlie the observed position-dependence of metaphase chromosome behavior.

Duplicated mitotic chromosomes aligned at the metaphase plate maintain dynamic attachments to spindle microtubules via their kinetochores, and multiple motor and nonmotor proteins cooperate to regulate their behavior. Depending on the system, sister chromatids may display either of two distinct behaviors, namely (1) the presence or (2) the absence of oscillations about the metaphase plate. Significantly, in PtK1 cells, in which chromosome behavior appears to be dependent on the position along the metaphase plate, both types of behavior are observed within the same spindle, but how and why these distinct behaviors are manifested is unclear. Here, we developed a new quantitative model to describe metaphase chromosome dynamics via kinetochore–microtubule interactions mediated by nonmotor viscoelastic linkages. Our model reproduces all the key features of metaphase sister kinetochore dynamics in PtK1 cells and suggests that differences in the distribution of polar ejection forces at the periphery and in the middle of PtK1 cell spindles underlie the observed dichotomy of chromosome behavior.

AXIAL-SYMMETRIC MODELING AND KINEMATIC ANALYSIS OF SPREADING OF SPARSELY CULTURED FIBROBLASTS

Cell spreading plays an important role in the modulation of physiological functions such as inflammation and cancer metastasis. The Brownian ratchet model and Bell's model have been used to simulate actin dynamics and bond kinetics for focal adhesion dynamics, respectively. In the present study, these models were modified and two additional subcellular mechanisms, integrin and myosin kinetics, were incoporated. An integrin recruitment function was introduced to determine the size of a focal adhesion associated with the substrate stiffness. The relationship between myosin concentration and the actin protrusion velocity was described by a first-order differential equation. Subcellular processes, including cell protrusion, focal adhesion formation, and stress fiber formation, were integrated into an axial-symmetric biophysical model, while inputs to the model were kinematic data from time-lapse experiments. Numerical simulations of the model using the Gillespie algorithm showed that dynamics of cell spreading can be well described by the model.

Tuning the kinetics of cadherin adhesion

Cadherins are Ca(2+)-dependent cell-cell adhesion proteins that maintain the structural integrity of the epidermis; their principle function is to resist mechanical force. This review summarizes the biophysical mechanisms by which classical cadherins tune adhesion and withstand mechanical stress. We first relate the structure of classical cadherins to their equilibrium binding properties. We then review the role of mechanical perturbations in tuning the kinetics of cadherin adhesion. In particular, we highlight recent studies that show that cadherins form three types of adhesive bonds: catch bonds, which become longer lived and lock in the presence of tensile force; slip bonds, which become shorter lived when pulled; and ideal bonds, which are insensitive to tugging.

Coupled Particulate and Continuum Model for Nanoparticle Targeted Delivery

Prediction of nanoparticle (NP) distribution in a vasculature involves transport phenomena at various scales and is crucial for the evaluation of NP delivery efficiency. A combined particulate and continuum model is developed to model NP transport and delivery processes. In the particulate model ligand-receptor binding kinetics is coupled with Brownian dynamics to study NP binding on a microscale. An analytical formula is derived to link molecular level binding parameters to particulate level adhesion and detachment rates. The obtained NP adhesion rates are then coupled with a convection-diffusion-reaction model to study NP transport and delivery at macroscale. The binding results of the continuum model agree well with those from the particulate model. The effects of shear rate, particle size and vascular geometry on NP adhesion are investigated. Attachment rates predicted by the analytical formula also agree reasonably well with the experimental data reported in literature. The developed coupled model that links ligand-receptor binding dynamics to NP adhesion rate along with macroscale transport and delivery processes may serve as a faster evaluation and prediction tool to determine NP distribution in complex vascular networks.

Elongated membrane tethers, individually anchored by high affinity α4β1/VCAM-1 complexes, are the quantal units of monocyte arrests

The α4β1 integrin facilitates both monocyte rolling and adhesion to the vascular endothelium and is physiologically activated by monocyte chemoattractant protein (MCP-1). The current study investigated the initial events in the adhesion of THP-1 cells to immobilized Vascular Cell Adhesion Molecule 1 (VCAM-1). Using AFM force measurements, cell adhesion was shown to be mediated by two populations of α4β1/VCAM-1 complexes. A low affinity form of α4β1 was anchored to the elastic elements of the cytoskeleton, while a higher affinity conformer was coupled to the viscous elements of the cell membrane. Within 100 ms of contact, THP-1 cells, stimulated by co-immobilized MCP-1, exhibited a tremendous increase in adhesion to VCAM-1. Enhanced cell adhesion was accompanied by a local decoupling of the cell membrane from the cytoskeleton and the formation of long membrane tethers. The tethers were individually anchored by multiple α4β1/VCAM-1 complexes that prolonged the extension of the viscous tethers. In vivo, the formation of these membrane tethers may provide the quantal structural units for the arrest of rolling monocytes within the blood vessels.

Biophysical description of multiple events contributing blood leukocyte arrest on endothelium

Blood leukocytes have a remarkable capacity to bind to and stop on specific blood vessel areas. Many studies have disclosed a key role of integrin structural changes following the interaction of rolling leukocytes with surface-bound chemoattractants. However, the functional significance of structural data and mechanisms of cell arrest are incompletely understood. Recent experiments revealed the unexpected complexity of several key steps of cell-surface interaction: (i) ligand-receptor binding requires a minimum amount of time to proceed and this is influenced by forces. (ii) Also, molecular interactions at interfaces are not fully accounted for by the interaction properties of soluble molecules. (iii) Cell arrest depends on nanoscale topography and mechanical properties of the cell membrane, and these properties are highly dynamic. Here, we summarize these results and we discuss their relevance to recent functional studies of integrin-receptor association in cells from a patient with type III leukocyte adhesion deficiency. It is concluded that an accurate understanding of all physical events listed in this review is needed to unravel the precise role of the multiple molecules and biochemical pathway involved in arrest triggering.

A review of numerical methods for red blood cell flow simulation

In this review, we provide an overview of the simulation techniques employed for modelling the flow of red blood cells (RBCs) in blood plasma. The scope of this review omits the fluid modelling aspect while focusing on other key components in the RBC-plasma model such as (1) describing the RBC deformation with shell-based and spring-based RBC models, (2) constitutive models for RBC aggregation based on bridging theory and depletion theory and (3) additional strategies required for completing the RBC-plasma flow model. These include topics such as modelling fluid-structure interaction with the immersed boundary method and boundary integral method, and updating the variations in multiphase fluid property through the employment of index field methods. Lastly, we summarily discuss the current state and aims of RBC modelling and suggest some research directions for the further development of this field of modelling.

Amyloid-β peptide on sialyl-Lewis(X)-selectin-mediated membrane tether mechanics at the cerebral endothelial cell surface

Increased deposition of amyloid-β peptide (Aβ) at the cerebral endothelial cell (CEC) surface has been implicated in enhancement of transmigration of monocytes across the brain blood barrier (BBB) in Alzheimer's disease (AD). In this study, quantitative immunofluorescence microscopy (QIM) and atomic force microscopy (AFM) with cantilevers biofunctionalized by sialyl-Lewis(x) (sLe(x)) were employed to investigate Aβ-altered mechanics of membrane tethers formed by bonding between sLe(x) and p-selectin at the CEC surface, the initial mechanical step governing the transmigration of monocytes. QIM results indicated the ability for Aβ to increase p-selectin expression at the cell surface and promote actin polymerization in both bEND3 cells (immortalized mouse CECs) and human primary CECs. AFM data also showed the ability for Aβ to increase cell stiffness and adhesion probability in bEND3 cells. On the contrary, Aβ lowered the overall force of membrane tether formation (Fmtf ), and produced a bimodal population of Fmtf , suggesting subcellular mechanical alterations in membrane tethering. The lower Fmtf population was similar to the results obtained from cells treated with an F-actin-disrupting drug, latrunculin A. Indeed, AFM results also showed that both Aβ and latrunculin A decreased membrane stiffness, suggesting a lower membrane-cytoskeleton adhesion, a factor resulting in lower Fmtf . In addition, these cerebral endothelial alterations induced by Aβ were abrogated by lovastatin, consistent with its anti-inflammatory effects. In sum, these results demonstrated the ability for Aβ to enhance p-selectin expression at the CEC surface and induce cytoskeleton reorganization, which in turn, resulted in changes in membrane-cytoskeleton adhesion and membrane tethering, mechanical factors important in transmigration of monocytes through the BBB.

Cyclic mechanical reinforcement of integrin-ligand interactions

Cells regulate adhesion in response to internally generated and externally applied forces. Integrins connect the extracellular matrix to the cytoskeleton and provide cells with mechanical anchorages and signaling platforms. Here we show that cyclic forces applied to a fibronectin-integrin α5β1 bond switch the bond from a short-lived state with 1 s lifetime to a long-lived state with 100 s lifetime. We term this phenomenon "cyclic mechanical reinforcement," as the bond strength remembers the history of force application and accumulates over repeated cycles, but does not require force to be sustained. Cyclic mechanical reinforcement strengthens the fibronectin-integrin α5β1 bond through the RGD binding site of the ligand with the synergy binding site greatly facilitating the process. A flexible integrin hybrid domain is also important for cyclic mechanical reinforcement. Our results reveal a mechanical regulation of receptor-ligand interactions and identify a molecular mechanism for cell adhesion strengthening by cyclic forces.

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.