Adhesion-regulated junction slippage controls cell intercalation dynamics in an Apposed-Cortex Adhesion Model

Cell intercalation is a key cell behaviour of morphogenesis and wound healing, where local cell neighbour exchanges can cause dramatic tissue deformations such as body axis extension. Substantial experimental work has identified the key molecular players facilitating intercalation, but there remains a lack of consensus and understanding of their physical roles. Existing biophysical models that represent cell-cell contacts with single edges cannot study cell neighbour exchange as a continuous process, where neighbouring cell cortices must uncouple. Here, we develop an Apposed-Cortex Adhesion Model (ACAM) to understand active cell intercalation behaviours in the context of a 2D epithelial tissue. The junctional actomyosin cortex of every cell is modelled as a continuous viscoelastic rope-loop, explicitly representing cortices facing each other at bicellular junctions and the adhesion molecules that couple them. The model parameters relate directly to the properties of the key subcellular players that drive dynamics, providing a multi-scale understanding of cell behaviours. We show that active cell neighbour exchanges can be driven by purely junctional mechanisms. Active contractility and cortical turnover in a single bicellular junction are sufficient to shrink and remove a junction. Next, a new, orthogonal junction extends passively. The ACAM reveals how the turnover of adhesion molecules regulates tension transmission and junction deformation rates by controlling slippage between apposed cell cortices. The model additionally predicts that rosettes, which form when a vertex becomes common to many cells, are more likely to occur in actively intercalating tissues with strong friction from adhesion molecules.

Mechanical Model for Catch-Bond-Mediated Cell Adhesion in Shear Flow

Catch bond, whose lifetime increases with applied tensile force, can often mediate rolling adhesion of cells in a hydrodynamic environment. However, the mechanical mechanism governing the kinetics of rolling adhesion of cells through catch-bond under shear flow is not yet clear. In this study, a mechanical model is proposed for catch-bond-mediated cell adhesion in shear flow. The stochastic reaction of bond formation and dissociation is described as a Markovian process, whereas the dynamic motion of cells follows classical analytical mechanics. The steady state of cells significantly depends on the shear rate of flow. The upper and lower critical shear rates required for cell detachment and attachment are extracted, respectively. When the shear rate increases from the lower threshold to the upper threshold, cell rolling became slower and more regular, implying the flow-enhanced adhesion phenomenon. Our results suggest that this flow-enhanced stability of rolling adhesion is attributed to the competition between stochastic reactions of bonds and dynamics of cell rolling, instead of force lengthening the lifetime of catch bonds, thereby challenging the current view in understanding the mechanism behind this flow-enhanced adhesion phenomenon. Moreover, the loading history of flow defining bistability of cell adhesion in shear flow is predicted. These theoretical predictions are verified by Monte Carlo simulations and are related to the experimental observations reported in literature.

Quantitative dynamics of reversible platelet aggregation: mathematical modelling and experiments

Although reversible platelet aggregation observed in response to ADP stimulation in the presence of calcium is a well-known phenomenon, its mechanisms are not entirely clear. To study them, we developed a simple kinetic mass-action-law-based mathematical model to use it in combination with experiments. Light transmission platelet aggregometry (LTA) induced by ADP was performed for platelet-rich plasma or washed platelets using both conventional light transmission and aggregate size monitoring method based on optical density fluctuations. Parameter values of the model were determined by means of parameter estimation techniques implemented in COPASI software. The mathematical model was able to describe reversible platelet aggregation LTA curves without assuming changes in platelet aggregation parameters over time, but with the assumption that platelet can enter the aggregate only once. In the model, the mean size of platelet aggregates correlated with the solution transparency. This corresponded with flow cytometry analysis and with optical density fluctuations data on aggregate size. The predicted values of model parameters correlated with ADP concentration used in experiments. These data suggest that, at the start of the aggregation, when platelet integrins switch “on”, large unstable platelet aggregates are rapidly formed, which leads to an increase in light transmission. However, upon fragmentation of these aggregates, the probability of the post-aggregate platelets’ attachment to each other decreases preventing new aggregation and resulting in the reversible aggregation phenomenon.

Long ligands reinforce biological adhesion under shear flow

In this work, computer modeling has been used to show that longer ligands allow biological cells (e.g., blood platelets) to withstand stronger flows after their adhesion to solid walls. A mechanistic model of polymer-mediated ligand-receptor adhesion between a microparticle (cell) and a flat wall has been developed. The theoretical threshold between adherent and non-adherent regimes has been derived analytically and confirmed by simulations. These results lead to a deeper understanding of numerous biophysical processes, e.g., arterial thrombosis, and to the design of new biomimetic colloid-polymer systems.

Modeling thrombosis in silico: Frontiers, challenges, unresolved problems and milestones

Hemostasis is a complex physiological mechanism that functions to maintain vascular integrity under any conditions. Its primary components are blood platelets and a coagulation network that interact to form the hemostatic plug, a combination of cell aggregate and gelatinous fibrin clot that stops bleeding upon vascular injury. Disorders of hemostasis result in bleeding or thrombosis, and are the major immediate cause of mortality and morbidity in the world. Regulation of hemostasis and thrombosis is immensely complex, as it depends on blood cell adhesion and mechanics, hydrodynamics and mass transport of various species, huge signal transduction networks in platelets, as well as spatiotemporal regulation of the blood coagulation network. Mathematical and computational modeling has been increasingly used to gain insight into this complexity over the last 30 years, but the limitations of the existing models remain profound. Here we review state-of-the-art-methods for computational modeling of thrombosis with the specific focus on the analysis of unresolved challenges. They include: a) fundamental issues related to physics of platelet aggregates and fibrin gels; b) computational challenges and limitations for solution of the models that combine cell adhesion, hydrodynamics and chemistry; c) biological mysteries and unknown parameters of processes; d) biophysical complexities of the spatiotemporal networks' regulation. Both relatively classical approaches and innovative computational techniques for their solution are considered; the subjects discussed with relation to thrombosis modeling include coarse-graining, continuum versus particle-based modeling, multiscale models, hybrid models, parameter estimation and others. Fundamental understanding gained from theoretical models are highlighted and a description of future prospects in the field and the nearest possible aims are given.

Influence of neighboring adherent cells on laminar flow induced shear stress in vitro-A systematic study

Cells experience forces if subjected to laminar flow. These forces, mostly of shear force character, are strongly dependent not only on the applied flow field itself but also on hydrodynamic effects originating from neighboring cells. This particularly becomes important for the interpretation of data from in vitro experiments in flow chambers without confluent cell layers. By employing numerical Finite Element Method simulations of such assemblies of deformable objects under shear flow, we investigate the occurring stress within elastic adherent cells and the influence of neighboring cells on these quantities. For this, we simulate single and multiple adherent cells of different shapes fixed on a solid substrate under laminar flow parallel to the substrate for different velocities. We determine the local stress within the cells close to the cell-substrate-interface and the overall stress of the cells by surface integration over the cell surface. Comparing each measurand in the case of a multiple cell situation with the corresponding one of single cells under identical conditions, we introduce a dimensionless influence factor. The systematic variation of the distance and angle between cells, where the latter is with respect to the flow direction, flow velocity, Young's modulus, cell shape, and cell number, enables us to describe the actual influence on a cell. Overall, we here demonstrate that the cell density is a crucial parameter for all studies on flow induced experiments on adherent cells in vitro.

Ligand-mediated adhesive mechanics of two static, deformed spheres

A self-consistent model is developed to investigate attachment/detachment kinetics of two static, deformable microspheres with irregular surface and coated with flexible binding ligands. The model highlights how the microscale binding kinetics of these ligands as well as the attractive/repulsive potential of the charged surface affects the macroscale static deformed configuration of the spheres. It is shown that in the limit of smooth, neutrally charged surface (i.e., the dimensionless inverse Debye length, [Formula: see text]), interacting via elastic binders (i.e., the dimensionless stiffness coefficient, [Formula: see text]) the adhesion mechanics approaches the regime of application of the JKR theory, and in this particular limit, the contact radius, R_c, scales with the particle radius, R, according to the scaling law, [Formula: see text]. We show that static, deformed, highly charged, ligand-coated surface of micro-spheres exhibit strong adhesion. Normal stress distribution within the contact area adjusts with the binder stiffness coefficient, from a maximum at the center to a maximum at the periphery of the region. Although reported in some in vitro experiments involving particle adhesion, until now a physical interpretation for this variation of the stress distribution for deformable, charged, ligand-coated microspheres is missing. Surface roughness results in a diminished adhesion with a distinct reduction in the pull-off force, larger separation gap, weaker normal stress and limited area of adhesion. These results are in agreement with the published experimental findings.

Surface deformation and shear flow in ligand mediated cell adhesion

We present a unified, multiscale model to study the attachment/detachment dynamics of two deforming, charged, near spherical cells, coated with binding ligands and subject to a slow, homogeneous shear flow in a viscous, ionic fluid medium. The binding ligands on the surface of the cells experience both attractive and repulsive forces in an ionic medium and exhibit finite resistance to rotation via bond tilting. The microscale drag forces and couples describing the fluid flow inside the small separation gap between the cells, are calculated using a combination of methods in lubrication theory and previously published numerical results. For a selected range of material and fluid parameters, a hysteretic transition of the sticking probability curves (i.e., the function [Formula: see text]) between the adhesion phase (when [Formula: see text]) and the fragmentation phase (when [Formula: see text]) is attributed to a nonlinear relation between the total nanoscale binding forces and the separation gap between the cells. We show that adhesion is favoured in highly ionic fluids, increased deformability of the cells, elastic binders and a higher fluid shear rate (until a critical threshold value of shear rate is reached). Within a selected range of critical shear rates, the continuation of the limit points (i.e., the turning points where the slope of [Formula: see text] changes sign) predict a bistable region, indicating an abrupt switching between the adhesion and the fragmentation regimes. Although, bistability in the adhesion-fragmentation phase diagram of two deformable, charged cells immersed in an ionic aqueous environment has been identified by some in vitro experiments, but until now, has not been quantified theoretically.

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.

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.

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.

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.

Cell crawling assisted by contractile stress induced retraction

Cell locomotion is a result of a series of synchronized chemo-mechanical processes. Crawling-type cell locomotion consists of three steps: protrusion, translocation, and retraction. Previous works have shown that both protrusion and retraction can produce cell movement. For the latter, a cell derives its propulsive force from retraction induced protrusion mechanism, which was experimentally verified by Chen (1979, "Induction of Spreading During Fibroblast Movement," J. Cell Biol., 81, pp. 684-691). In this paper, using finite element method, we take a computational biomimetic approach to study cell crawling assisted by contractile stress induced de-adhesion at the rear of the focal adhesion zone (FAZ). We assume the formation of the FAZ is driven by receptor-ligand bonds and nonspecific interactions. The contractile stress is generated due to the molecular activation of the intracellular actin-myosin machinery. The exerted contractile stress and its time dependency are modeled in a phenomenological manner as a two-spring mechanosensor proposed by Schwarz (2006, "Focal Adhesions as Mechanosensors: The Two-Spring Model," BioSystems, 83(2-3), pp. 225-232). Through coupling the kinetics of receptor-ligand bonds with contractile stress, de-adhesion can be achieved when the stall value of the contractile stress is larger than a critical one. De-adhesion at the rear end of the FAZ causes a redistribution of elastic energy and induces cell locomotion. Parametric studies were conducted to investigate the connection between the cell locomotion speed and stall stress, and receptor-ligand kinetics. Finally, we provide a scaling relationship that can be used to estimate the cell locomotion speed.

Adhesive dynamics of lubricated films

Membrane waves have been observed near the leading edge of a motile cell. Such phenomenon is the result of the interplay between hydrodynamics and adhesive dynamics. Here we consider membrane dynamics on a thin fluid gap supported by adhesive bonds. Using coupled lubrication theory and adhesive dynamics, we derive an evolution equation to account for membrane tension, bending, adhesion, and viscous lubrication. Four adhesion scenarios are examined: no adhesion, uniform adhesion, clustered adhesion, and focal adhesion. Two contrasting traveling wave types are found, namely, tension and adhesion waves. Tension waves disperse with time and space, whereas adhesion waves show increased amplitudes and are highly persistent. We show that the transition from tension to adhesion waves depends on a necessary, but insufficient, criterion that the wave amplitude must exceed a critical gap height, which is dependent on adhesion binding probability. We also show that strong adhesion results in sharp tension-to-adhesion wave transitions. The present work could explain the strong persistence of the waves observed in adhered cells using differential inference contrast (DIC) microscopy and the observation that the wavelengths decrease shortly after leading edge retraction.